N. N. Voitovich, A. B. Dogadkin, B. Z. Katsenelenbaum. Lens-waveguide line. Radiotekhnika i Elektronika, v. 9, No. 9, 1964, p.1707-1708 (In Russian).

Abstract. Metallic waveguide with lenses periodically placed inside it is investigated. Lenses are considered as phase correctors. Shape of lenses is determined by minimization of the basic mode ohmic losses.

N. N. Voitovich, V. V. Semenov. Forming a field of prescribed structure. Radio Engineering and Electronic Physics, v.13, No.7, 1968 (Transl. from Radiotekhnika i Elektronika, v.13, No.7, 1968, p. 1213-1221).

Abstract. An iterative method for calculating the shape of lenses considered as phase correctors for transformation a field with given amplitude distribution on the exciting aperture into a field with given amplitude distribution on the receiving aperture, is proposed and numerically realized. A two-dimensional scalar problem is considered. Optimization criterion is chosen in the form of the normalized inner product of given and obtained fields on the second aperture. The method provides increasing the optimization criterion on every step. Numerical results are given.

N. N. Voitovich, V. V. Semenov. Quasioptical lines as feeders. Radio Engineering and Electronic Physics. v.15, No.4, 1970 (Transl. from Radiotekhnika i Elektronika, v.15, No.4, 1970, p. 697-704).

Abstract. An iterative method for calculating the lens shapes in multilens quasioptical line transforming one given field (on the exciting aperture) into other given field (on the receiving aperture), is proposed and numerically realized. The method consists in successive improving the shapes of single lenses by usage a specially transformed expression of the functional to be maximize (normalized inner product of given and obtained field distributions on the receiving aperture). Numerical results concerning transformations of different field distributions are shown.

N. N. Voitovich, P. A. Savenko. Generalized criterion of patterns proximity in the problem of antenna synthesis by V.V.Semenov's method. Radio Engineering and Electronic Physics, v. 18, No.9, 1973 (Transl. from Radiotekhnika i Elektronika, v. 18, No.9. 1973, p. 1794-1798).

N. N. Voitovich, Yu. N. Kazantsev, V. P. Tkachuk. Forming given directivity pattern by quasioptical line. Radiotekhnika i Elektronika, v. 29, No.6, 1984, p. 1023-1028. (In Russian).

Abstract. A segment of the quasioptical line consisting of the series of sloped semitransparent mirrors is considered as a radiation system. The problem consists in determining the variable parameters of the mirrors (reflection and transmission factors) which provide obtaining a given directivity pattern by reflection beams. Modulus of normalized inner product of given and obtained patterns is used as an optimization criterion. An iterative algorithm for solving this problem is proposed. The algorithm improve the parameters of single mirrors by turn. A special transformations of the criterion expression permit to minimize the calculation expenses for this procedure. Numerical results concerning the lines of 4 and 10 mirrors are presented.

N. N. Voitovich, V. P. Tkachuk, Yu. N. Kazantsev. Synthesis of quasi-optical radiating system. Proc. of 1989 Int. Sympos. on Antennas and Propagation. Tokyo, 1989, v.4, p. 893-896.

Abstract. In the review form, a method and results of the quasi-optical radiating system synthesis is described. The system consists of a set of inclined semitransparent mirrors having the reflection and transmission factors variable along their surfaces. The problem consists in defining these factor distributions in order to obtain the given directivity pattern. The scheme of algorithm as well as some numerical results are shown.

O. V. Kusyi, S. S. Shaposhnikov, R. B. Vaganov, N. N. Voitovich. Bicriterion optimization problems for power transmitting line. Direct and Inverse Problems of Electromagnetic and Acoustic Wave Theory (DIPED-2002), Lviv-Tbilisi, 2002, p. 127-130.

Abstract. Two bicriterial optimization problems consisting in minimization of functionals, describing the energy and ecology requirements (transmission efficiency, surface usage, side radiation) are considered. The numerical method is proposed and results are presented.

B. Z. Katsenelenbaum, O. V. Kusyi, N. N. Voitovich. Comparision of two optimization criteria for power transmission lines. Direct and Inverse Problems of Electromagnetic and Acoustic Wave Theory (DIPED-2003), Lviv, 2003, 131-134.

Abstract. The problem of comparison of two optimization criteria for antenna-rectenna power transmission lines is considered. The behavior of each criteria on functions optimal for another is studied. Numerical results for rectangular and circular apertures are shown and analyzed.

Abstract. Two criteria of antenna synthesis by the amplitude radiation pattern are compared. They use the reactive power and weighted current norm, respectively, both supplying the mean square difference between the desired and obtained amplitude patterns. The technique based on the generating polynomial concept is applied to nonlinear integral equations in both cases. Numerical results are presented.

B. Z. Katsenelenbaum, O. V. Kusyi, N. N. Voitovich. Comparision of two optimization criteria for quasy-optical power transmission lines. Quasi-Optical Control of Intense Microwave Transmission. NATO Science Series II: Mathematics, Physics and Chemistry.Vol. 203, Springer, 2005, p. 65-72.

Abstract. Two optimization criteria for antenna-rectenna power transmission lines are compared. The criteria describe the energy transmission coefficient and the mean-square residual of obtained and desired fields in the rectenna plane. The behavior of each criterion on functions optimal for another is studied. Numerical results for rectangular and circular apertures are shown and analyzed.

N. N. Voitovich, M. I. Andriychuk. Transformation of field in regular waveguide via phase correctors. Proc. of XIIth International Seminar/Workshop on Direct and Inverse Problems of Electromagnetic and Acoustic Wave Theory. Lviv, Ukraine. Lviv, 2007, p. 63-66.

Abstract. The problem of the electromagnetic field transformation in regular waveguides is solved with use of phase correctors placed at its input and output. The variational statement of the problem consists in maximization of inner product of the prescribed and received fields. The solution is carried out by an iterative procedure improves the functional value in each step. The approach permits generalization to the case of more than two correctors. Results of numerical calculations are presented.

Abstract. A new book prepared to publication in the WILEY-VCH Verlag (Germany) is announced. Variational problems with independently involved moduli and arguments of the complex functions in optimization criteria or restrictions, arisen in various physical applications, are considered. The problems are reduced to nonlinear integral equations of the Hammerstain type. A class of such type equations, which have analytical solutions, is found and analyzed. Numerical methods for solving obtained nonlinear equations are developed and applied to various concrete problems. Nonstandard inverse problems of the diffraction theory, such as minimization of the backscattering are considered