Physics, mathematics, and technology

This is the fth paper of a series of papers that will give a survey on several topics on formal languages and automata by using semirings, formal power series, matrices and xed point theory. The fth paper of this series deals with the basic results in the theory of nite automata over quemirings generalizing the classical nite automata accepting nite and innite words. The presentation of these results is based on semiring-semimodule pairs, especially on Conway semiring-semimodule pairs. A Conway semiring-semimodule pair is a pair consisting of a
Conway semiring and a semimodule that satises the sum-omega equation and the product-omega equation. We dene these Conway
semiring-semimodule pairs and state some of their important properties. Then we introduce nite automata over quemirings and prove a Kleene Theorem. Furthermore, we introduce linear systems over quemirings as a generalization of regular grammars with nite and innite derivations, and connect certain solutions of these linear systems with the behavior of nite automata over quemirings.

For backbone complex of the human’s spine with alternative of a cuneiform strain mean backbone the stabilizing rigid lamina (for front and
back abutment complexes) holds optimization of stiffness of stabilizing of a lamina Ссt1 on an objective function of offset 2 backbone, at its sufficient mobility.

Concerned issues are related to the modeling of high speed impact with different variants of the smoothed particle hydrodynamics method and applying this method to the solution of problems of mechanics of the deformed solid body.Results of solution of the problem of disintegration of discontinuity were obtained and comparative analysis was performed.

The mass-spectrometer model of thermal ionospheric ions measurements was considered in case of charged satellite. Hyperboloid device characteristics onboard Interball-2 satellite was used for mathematical model of measurements. It was shown that angular ion distribution function changed due to temperature anisotropy and it can be interprets by different ways. Positive satellite potential increases these effects.

Some multiprocessors realizations of the α–β-iteration algorithm for solution of five-dots difference equations systems are considered.

A variant of multigrid method for solving large systems of linear equations with block tridiagonal matrices that have higher robustness properties is presented.In this method the construction of coarse grid correction operators is based on approximation of the Schur complement. Numerical experiments show high efficiency of presented methods.

A problem of operational industrial planning at а machine-building enterprise with custom-made, small-scale character of manufacture is considered, and an approach to decision of similar problems on the basis of methodology of functional hybrid intellectual systems with coordination is described.

A model of a knowledge base based on Petri net is considered.

A system predator-prey is explored and the parameters, by which its operating is stable. Biological balance of the system species is defined by mathematic methods.

A quantum statistical model of intramolecular tautomeric transformation is offered, accounts for the vibration of a proton as a result of its interaction with the surrounding medium simulated by the quantized field of radiation. Effective adiabatic potentials of the proton are approximated by the parabolas of various curvatures. The estimation for the vibrational relaxation time and the formula for the constant of tautomeric equilibrium.

Family of centered planes in projective space is investigated. It is shown that composite clothing of this family induces 6 bunches of group connections. In each of this bunches one connection is allocated. Their conditions of coinciding are found. Geometric interpretation each of them is done.