IKBFU's Vestnik

Physics, mathematics, and technology

Theoretical Computer Science

Formal languages and automata VII: Formal tree series (Part I)

Abstract

This is the seventh 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 seventh paper of this series deals with tree (series) automata and systems of equations over tree. The main topics of the paper are the following. 1. Tree automata (resp. nite, polynomial tree automata), whose behaviors are tree series over a semiring, and systems of equations (resp. nite, polynomial systems of equations), whose least solutions are tuples of tree series over a semiring, are equivalent. 2. A Kleene result: the class of recognizable tree series is characterized by rational tree series expressions.

Download an article

Mathematical Modeling

Computer simulation of synthesis processes in NiO—Al system

Abstract

Features of physical and chemical conversions in the reacting powder system NiO-Al were investigated by computer simulation methods.. Multivariability of the synthesis of nickel aluminides in powder systems with varying degrees of concentration inhomogeneity is taken into account. The estimates of the state parameters of reacting system at all stages of physical and chemical transformations was obtained.

Download an article

Mathematical modeling of a injury of a backbone

Abstract

A plenty of proceedings of various disciplines fundamental and applied science is devoted to studying of vertebral damage. The special role in studying this pathology is played with methods of mathematical modelling since allow to predict development of adverse deformations of a backbone and to optimize methods of elimination of these damages. Using mathematical model three-vertebra a complex the algorithm of surgical treatment of typical spinal damages is developed.

Download an article

Results of simulating of instabilities of the equatorial F-layer of the ionosphere

Abstract

The results of numerical experiments of the dynamic ionospheric bubbles in the equatorial F-region are described. Generation bubbles by gravitational waves is investigated. A trigger mechanism of generation bubbles in F-layer by clouds in E-layer is studied. Influences of a conductivity of the E-layer on dynamics of bubbles are considered. It is shown that in the bubbles the molecular ions NO+ effectively transported to the higher altitude. The possibility of the formation of isolated bubbles at the altitude above the maximum of F-layer is founded. Parameters of thermal mode of three-dimensional bubbles are presented. The morphology of a multi-bubble system are researched.

Download an article

Multiple-factor mathematical models of heterogeneous metasystems

Abstract

Nonlinear mathematical modeling of physical processes in heterogeneous metasystems with bubble or a solid-state filler allows to receive the parities convenient for numerical calculations and comparison of theoretical results with the data of experiments. For creation of almost effective models certain offers concerning the top and bottom borders of the sizes of a filler, their distribution and concentration, the dipolar moments, character and results of interpartial interaction are formulated.

Download an article

Algorithms and Computing Methods

Numerical solution of the Schrödinger equations with polynomial potentials (Part II)

Abstract

The algorithm of the numerical realization of a fundamental solution of a Cauchy problem for the one-dimensional Schrodinger equation with polynomial potentials is described. The stationary Schrodinger equation for a proton in the double potential well is solved by using Ritz variation method. The Green’s function is formed on a discrete spectrum of these solutions and after that the fundamental solution of the non-stationary Schrodinger equation is numerically calculated and applied to compounds with intramolecular hydrogen bonds.

Download an article

Set of algorithms for constructing university timetable — part 2: Data presentation structure and algorithm for building a base solution

Abstract

An algorithm for building a base multitude of solutions for the university timetabling problem is proposed. An algorithm allowed to get at least one correct timetable if such exists. Computational complexity is reduced with using a special set of heuristics and timetable data presentation model.

Download an article

Physics

The reconstruction of the measured qubit under the unsharp measure-ments

Abstract

Evolution operator of a combined system consisting of the measured qubit and the auxiliary system is derived. Conditions on the choice of parameters in the formula for the reconstruction of the measured qubit states are obtained. The evolution operator of the combined system leads to the probability operator (or effect) with a structure that corresponds to unsharp measurements.

Download an article

Other papers

Subsets of prime numbers in the generalized arithmetical progressions

Abstract

The concept of the generalized arithmetical progression of the power k  and difference d is given. For k  1,7 formulas of nth member of such progressions and for k  1, 2, 3 formulas for the sum of the first n its members are obtained. Progressions ( ) , k p d M with the first member prime number p and difference being a positive even number d  2m (m  ) are considered. Such progressions define subsets ( )
, , k h p d M of h prime numbers (h  ). For k  20, p  95467, d  108 all subsets (1) h,p,d M with h  15 prime numbers are obtained. Some properties that connect the power k of generalized arithmetical progression and its difference d for 2  k  60, p  1014, h  5 are established.

Download an article

Study of the configuration of the core of the magnetization source of magnetic systems of electric propulsion

Abstract

Results of researches of influence of various forms of cores of external sources of magnetising force of magnetic systems of electric propulsion on azimuthal evenness of magnetic field distribution in an operating interpolar interval are presented.

Download an article