Результаты поиска по 'commutators':
Найдено статей: 3
  1. Yakovenko G.N.
    Reasons for nonlinearity: globality and noncommutativity
    Computer Research and Modeling, 2009, v. 1, no. 4, pp. 355-358

    A dynamic process modeled by ordinary differential equations is considered. If a nonautonomous system of ordinary differential equations has a general solution in a certain area, than the system can be simplified by nonautonomous substitution of variables: right parts turn to zeroes. Right parts of an autonomous system of ordinary differential equations in the neighborhood of nonsingular points can be linearized. A separable system where the right part contains linear combination of autonomous vector fields and factors are functions of independent variable is considered. If the fields commute than they can be linearized by general substitution of variables.

    Keywords: nonlinearity, nonautonomous systems, dynamic processes.
    Views (last year): 3.
  2. Breev A.I., Shapovalov A.V., Kozlov A.V.
    Integration the relativistic wave equations in Bianchi IX cosmology model
    Computer Research and Modeling, 2016, v. 8, no. 3, pp. 433-443

    We consider integration Clein–Gordon and Dirac equations in Bianchi IX cosmology model. Using the noncommutative integration method we found the new exact solutions for Taub universe.

    Noncommutative integration method for Bianchi IX model is based on the use of the special infinite-dimensional holomorphic representation of the rotation group, which is based on the nondegenerate orbit adjoint representation, and complex polarization of degenerate covector. The matrix elements of the representation of form a complete and orthogonal set and allow you to use the generalized Fourier transform. Casimir operator for rotation group under this transformation becomes constant. And the symmetry operators generated by the Killing vector fields in the linear differential operators of the first order from one dependent variable. Thus, the relativistic wave equation on the rotation group allow non-commutative reduction to ordinary differential equations. In contrast to the well-known method of separation of variables, noncommutative integration method takes into account the non-Abelian algebra of symmetry operators and provides solutions that carry information about the non-commutative symmetry of the task. Such solutions can be useful for measuring the vacuum quantum effects and the calculation of the Green’s functions by the splitting-point method.

    The work for the Taub model compared the solutions obtained with the known, which are obtained by separation of variables. It is shown that the non-commutative solutions are expressed in terms of elementary functions, while the known solutions are defined by the Wigner function. And commutative reduced by the Klein–Gordon equation for Taub model coincides with the equation, reduced by separation of variables. A commutative reduced by the Dirac equation is equivalent to the reduced equation obtained by separation of variables.

    Keywords: noncommutative integration, Bianchi IX.
    Views (last year): 5.
  3. Kalinin I.N., Glukharev K.K.
    Interchange integral characteristics study via microscopic traffic flow models
    Computer Research and Modeling, 2014, v. 6, no. 4, pp. 523-534

    The problem of application of miscroscopic traffic models for the analysis of large network segments is discussed with an example of discrete flow with safe distance. A concept of integral charasteristics of network segments is introduced, a method for obtaining such characteristics via microscopic traffic flow models is presented. Said method is applied to a circular unidirectional interchange, obtained characteristics analysed.

    Keywords: traffic flow, commutators, microscopic traffic models, interchange and crossroad simulation.
    Views (last year): 4. Citations: 7 (RSCI).

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