Результаты поиска по 'generalized Green’s operator':
Найдено статей: 5
  1. Chujko S.M.
    Linear Noether boundary value problem for linear differential-algebraic system
    Computer Research and Modeling, 2013, v. 5, no. 5, pp. 769-783

    We find sufficient conditions for the solvability and construction of the generalized Green’s operator for linear Noether boundary value problem for linear differential-algebraic system.

    Views (last year): 1. Citations: 7 (RSCI).
  2. Chujko S.M.
    Boundary value problems for differential-algebraic systems with interface conditions
    Computer Research and Modeling, 2014, v. 6, no. 4, pp. 465-477

    We find sufficient conditions for the solvability and construction of the generalized Green’s operator for linear Noether boundary value problem for degenerate linear differential-algebraic system with interface conditions.

    Views (last year): 5.
  3. 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.

    Views (last year): 5.
  4. Chujko S.M., Nesmelova (Starkova) O.V., Sysoev D.V.
    Nonlinear boudary value problem in the case of parametric resonance
    Computer Research and Modeling, 2015, v. 7, no. 4, pp. 821-833

    We construct necessary and sufficient conditions for the existence of solution of seminonlinear matrix boundary value problem for a parametric excitation system of ordinary differential equations. The convergent iteration algorithms for the construction of the solutions of the semi-nonlinear matrix boundary value problem for a parametric excitation system differential equations in the critical case have been found. Using the convergent iteration algorithms we expand solution of seminonlinear periodical boundary value problem for a parametric excitation Riccati type equation in the neighborhood of the generating solution. Estimates for the value of residual of the solutions of the seminonlinear periodical boundary value problem for a parametric excitation Riccati type equation are found.

    Views (last year): 2.
  5. Vrazhnov D.A., Shapovalov A.V., Nikolaev V.V.
    Symmetries of differential equations in computer vision applications
    Computer Research and Modeling, 2010, v. 2, no. 4, pp. 369-376

    In our work we present generalization of well-known approach for construction of invariant feature vectors of images in computer vision applications. Basic feature of the suggested algorithm is replacement of commonly used Gaussian filter by convolution of image function with Green’s function of evolution operator, which inherits symmetries of this operator. The use of general filtration allows to obtain additional characteristics of invariant feature vectors.

    Views (last year): 8. Citations: 4 (RSCI).

Indexed in Scopus

Full-text version of the journal is also available on the web site of the scientific electronic library eLIBRARY.RU

The journal is included in the Russian Science Citation Index

The journal is included in the RSCI

International Interdisciplinary Conference "Mathematics. Computing. Education"