[en] Consideration is given to iterative methods of solving boundary-value problems of neutron transport theory on the basis of cross-section averaging. Positive operator theory in Banach space with light cone is used to determine integrability conditions and properties of the appropriate solutions of linear and nonlinear critical problems arizing in the framework of the mentioned averaging

No abstract available

[en] The properties of the roots of a functional that appears in an analytical solution of a coupled one-speed (group) neutron transport equation are investigated. The problems of the number of roots, their parity, possible place in the complex plane, and some others are considered. Some final results and different criteria are presented that may be found useful in numerical calculation of roots

[en] Conditions of solvability of boundary problems for multigroup transport equations with anisotropic scattering in media with piecewise-constant coefficients in a class of absolutely integrable functions are shown to be equivalent to conditions of solvability of the system of singular integral equations with additional conditions presented in the paper. The system relates values of a flux on interfaces and on an external surface

[en] New methods of numerical solution of stationary and non-stationary problems of neutron transport theory and the theory of nuclear reactors by reduction to systems of nonlinear algebraic equations in the most important reactor functionals of integral type to the spatial cells of the reactor, the energetic groups and time intervals, neutron flux, integral unilateral flux through the faces of cells, reaction rates are viewed. Circuits of methods for solving inhomogeneous boundary problems such as protection of nuclear reactor, calculation of accelerator driven reactors are presented. Schemes of method for solving homogeneous conditionally critical tasks are given. Schemes of method for unsteady flows are described

No abstract available

[en] Theoretical aspects of quality improvement in assessment of reactivity effects in deformable nuclear reactor cores which are actual from the nuclear safety point of view, are discussed. An approach based on transition from the traditional diffusion approximation to the point kinetic theory of neutron transport is realized. The problems with the piece-constant cross sections by the space coordinate in three-dimensional Cartesian and cylindrical (r-z) configurations are used as examples. It is shown that the technique applied permits generalization for the general case

No abstract available

[en] A problem is considered on development of algorithms for selection principles for homogenizing group constants providing for the given group division, the conservation of the definite set of functionals of Ksub(eff) type, process numbers, fluxes and currents on the transition from the initial problem to the multigroup one with any preassigned accuracy limited certainly by indeterminancies of nuclear data. These algorithms can find the application for instance as algorithms of convolution of groups

[en] Some mathematical modeling problem of delayed neutron reactor kinetics simulation and reactivity determination are considered and investigated. The new criterion of the delayed neutrons data optimal choice is presented and established