Труды сотрудников ИВМ СО РАН

[Электронный ресурс]. - Электрон. дан. (499 Кб) : диссертации на соискание ученой степени кандидата-физико математических наук (перевод на английский язык) / А.Н. Горбань. - Электрон. дан. (499 Кб). - [Б. м. : б. и.], 1997. - Б. ц.
Аннотация: The paper gives the systematic analysis of singularities of transition processes in general dynamical systems. Dynamical systems depending on parameter are studied. A system of relaxation times is constructed. Each relaxation time depends on three variables: initial conditions, parameters k of the system and accuracy ? of relaxation. This system of times contains: the time before the first entering of the motion into ?-neighbourhood of the limit set, the time of final entering in this neighbourhood and the time of stay of the motion outside the ?-neighbourhood of the limit set. The singularities of relaxation times as functions of (x0; k) under fixed ? are studied. A classification of different bifurcations (explosions) of limit sets is performed. The bifurcations fall into those with appearance of new limit points and bifurcations with appearance of new limit sets at finite distance from the existing ones. The relations between the singularities of relaxation times and bifurcations of limit sets are studied. The peculiarities of dynamics which entail singularities of transition processes without bifurcations are described as well. The peculiarities of transition processes under perturbations are studied. It is shown that the perturbations simplify the situation: the interrelations between the singularities of relaxation times and other peculiarities of dynamics for general dynamical system under small perturbations are the same as for smooth two-dimensional structural stable systems.

http://icm.krasn.ru/refextra.php?id=2806


Доп.точки доступа:
Gorban A.N.
Свободных экз. нет

[Text]. - Electronic data (249 Kb)
. - Режим доступа: http://icm.krasn.ru/refextra.php?id=788. - Электрон. версия печ. публикации . - Режим доступа: http://library.krasn.ru/trudy/1998/788gorban_AMLappr98.pdf (Полный текст) : статья / A.N. Gorban. - Electronic data (249 Kb) // Applied Mathematics Letters. - 1998. - Vol. 11, № 3. - p. 45-49
   Перевод заглавия: Аппроксимация непрерывных функций нескольких переменных с помощью произвольной нелинейной непрерывной функции одного переменного, линейных функций и их суперпозиций
Аннотация: Linear spaces of continuous functions of real variables closed under the superposition operation are considered. It has been proved that when such a space contains constants, linear functions, and at least one nonlinear function, it is dense in the space of all continuous functions in the topology of uniform convergence on compact sets. So, the approximation of continuous functions of several variables by an arbitrary nonlinear continuous function of one variable, linear functions, and their superpositions is possible.

http://icm.krasn.ru/refextra.php?id=788,
Полный текст

Держатели документа:
ИВМ СО РАН : 660036, Красноярск, Академгородок, 50, стр.44

Доп.точки доступа:
Горбань, Александр Николаевич

[Текст]. - Электрон. дан. (128 Кб)
. - Режим доступа: http://icm.krasn.ru/refextra.php?id=2083. - Электрон. версия печ. публикации . - Режим доступа: http://library.krasn.ru/trudy/1998/2083gorban_98SOROS.pdf (Полный текст) : статья / А.Н. Горбань. - Электрон. дан. (128 Кб) // Соросовский образовательный журнал. - 1998. - № 12. - С. 105-112
Аннотация: Обсуждается представление функций многих переменных с помощью функций одного переменного. Дано введение в теорию искусственных нейронных сетей. Показано, что с помощью нейросетей можно сколь угодно точно вычислить любую непрерывную функцию.
The following problems on the representation of function of multiple variables by means of simpler functions are discussed: are there functions of multiple variables which cannot be exactly represented by means of functions of one variable and when is an approximate representation of functions using simpler functions possible? An introduction to the theory of artificial neural networks is given. It is shown that with the aid of neural networks one can arbitrarily calculate precisely any continuous function.

http://icm.krasn.ru/refextra.php?id=2083,
Полный текст

Держатели документа:
ИВМ СО РАН : 660036, Красноярск, Академгородок, 50, стр.44

Доп.точки доступа:
Gorban A.N.

[Text] : alternative Grad equations / A.N. Gorban, I.V. Karlin // Physical Review E. - 1996. - Vol. 54, № 4. - p. R3109-R3112
   Перевод заглавия: Скорости рассеяния вместо моментов. Альтернативные уравнения Грэда
Аннотация: Scattering rates moments of collision integral! are treated as independent variables, and as an alternative to moments of the distribution function, to describe the rarefied gas near local equilibrium. A version of the entropy maximum principle is used to derive the Grad-like description in terms of a finite number of scattering rates. The equations are compared to the Grad moment system in the heat nonconductive case. Estimations for hard spheres demonstrate, in particular, some 10% excess of the viscosity coefficient resulting from the scattering rate description, as compared to the Grad moment estimation.

http://icm.krasn.ru/refextra.php?id=69,
Полный текст

Держатели документа:
ИВМ СО РАН : 660036, Красноярск, Академгородок, 50, стр.44

Доп.точки доступа:
Karlin, I.V.; Карлин, Илья Вениаминович; Горбань, Александр Николаевич

[Electronic resource]. - Electronic text data : статья / A. N. Gorban. - Electronic text data // Electronic Journal of Differential Equations. - 1997. - Translation of Candidat (Ph.D) Thesis
Аннотация: The paper gives a systematic analysis of singularities of transition processes in dynamical systems. General dynamical systems with dependence on parameter are studied. A system of relaxation times is constructed. Each relaxation time depends on three variables: initial conditions, parameters k of the system and accuracy ε of the relaxation. The singularities of relaxation times as functions of (x0,k) under fixed ε are studied. The classification of different bifurcations (explosions) of limit sets is performed. The relations between the singularities of relaxation times and bifurcations of limit sets are studied. The peculiarities of dynamics which entail singularities of transition processes without bifurcations are described as well. The analogue of the Smale order for general dynamical systems under perturbations is constructed. It is shown that the perturbations simplify the situation: the interrelations between the singularities of relaxation times and other peculiarities of dynamics for general dynamical system under small perturbations are the same as for the Morse-Smale systems.

Полный текст

Держатели документа:
ИВМ СО РАН : 660036, Красноярск, Академгородок, 50, стр.44

Доп.точки доступа:
Горбань, Александр Николаевич

/ V.V. Kuznetsov, V.K. Andreev // Thermophys. Aeromechanics. - 2013. - Vol. 20, Is. 1. - P17-28. - Cited References: 7. - The work was financially supported by the Russian Foundation for Basic Research (Grant No. 10-01-00007), Federal Target Program "Scientific and Scientific-Pedagogical Personnel of Innovative Russia" (State Contract 14.740.11.0355) and Program of Fundamental Research of OEM RAS No. 2.13.2. . - 12. - ISSN 0869-8643РУБ Thermodynamics + Mechanics

Аннотация: The problem of stabilized combined motion of the gas flow and liquid film in a microchannel under the action of local heating with consideration of evaporation processes was set in selected variables. The exact solutions to the linearized problem were derived. The analytical formulas for calculation of the film thickness stabilized below the heater and the total rate of liquid evaporation were obtained. The technique of approximate calculation of total heat transfer is shown. Exemplary calculations are presented.

Полный текст


Доп.точки доступа:
Kuznetsov, V.V.; Andreev, V.K.; Андреев, Виктор Константинович

/ A.V. Lapko, V.A. Lapko // Optoelectronics, Instrumentation and Data Processing. - 2012. - Vol. 48, Is. 4. - pp. 416-422, DOI 10.3103/S8756699012040139 . - ISSN 8756-6990
Аннотация: Asymptotic properties of a nonparametric estimate of the separating surface equation defined in the space of independent attributes of classified objects are studied. Based on this analysis, the importance of the influence of a priori information about independence of random variables on the approximation properties of the nonparametric decision function in a two-alternative problem of pattern recognition is established. В© 2012 Allerton Press, Inc.

Scopus


Доп.точки доступа:
Lapko, V.A.; Лапко, Василий Александрович; Лапко, Александр Васильевич

/ O. V. Sadovskaya // Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). - 2013. - Vol. 8236 LNCS: 5th International Conference on Numerical Analysis and Applications, NAA 2012 (15 June 2013 through 20 June 2013, Lozenetz. - P471-478, DOI 10.1007/978-3-642-41515-9_53 . -
Аннотация: Parallel program systems for numerical solution of 2D and 3D problems of the dynamics of deformable media with constitutive relationships of rather general form on the basis of universal mathematical model describing small strains of elastic, elastic-plastic and granular materials are worked out. Computational algorithm is based on the splitting methods with respect to physical processes and spatial variables. Some computations of dynamic problems with and without taking into account the moment properties of a material were performed on clusters. В© 2013 Springer-Verlag.

Scopus,
Полный текст

Держатели документа:
Institute of Computational Modeling SB RAS, Akademgorodok 50/44, 660036 Krasnoyarsk, Russian Federation

Доп.точки доступа:
Sadovskaya, O.V.; Садовская, Оксана Викторовна

[Text] / O. V. Kaptsov // Program. Comput. Softw. - 2014. - Vol. 40, Is. 2. - P63-70, DOI 10.1134/S0361768814020054. - Cited References: 23. - This study was supported by the Russian Foundation for Basic Research (project nos. 12-01-00648-a and 10-01-00435-a) and by the Grant for Support of Leading Scientific Schools (NSh 544.2012.1). . - ISSN 0361-7688. - ISSN 1608-3261РУБ Computer Science, Software Engineering

Аннотация: Differential algebra of convergent power series that depend on an arbitrary finite number of variables is considered. The concept of a passive family of generators is defined for a differential ideal of this algebra. It is a further extension of the concept of the Groebner basis. The theorem that allows checking whether a family of generators is passive and ensures that the point solution of an infinite system of equations exists and is unique in this algebra is proved.

Полный текст

Держатели документа:
Russian Acad Sci, Siberian Branch, Inst Comp Modeling, Krasnoyarsk 660036, Russia
ИВМ СО РАН

Доп.точки доступа:
Kaptsov, O.V.; Капцов, Олег Викторович; Russian Foundation for Basic Research [12-01-00648-a, 10-01-00435-a]; Grant for Support of Leading Scientific Schools [NSh 544.2012.1]

[] / A. V. Lapko, V. A. Lapko // Optoelectron. Instrum. Data Proces. - 2014. - Vol. 50, Is. 1. - P68-74, DOI 10.3103/S8756699014010099 . - ISSN 1934-7944
Аннотация: Asymptotic properties of a nonparametric estimate of the two-dimensional probability density of independent random variables are studied. Based on these results, the dependence of its efficiency on data incompleteness in the initial statistical information is determined. © 2014 Allerton Press, Inc.

Scopus

Держатели документа:
Institute of Computational Modeling, Siberian Branch, Russian Academy of Sciences, Akademgorodok 50, building 44, Krasnoyarsk, 660036, Russian Federation
Reshetnev Siberian State Aerospace University, pr. im. Gazety Krasnoyarskii rabochii 31, Krasnoyarsk, 660014, Russian Federation

Доп.точки доступа:
Lapko, V.A.; Лапко, Василий Александрович; Лапко, Александр Васильевич

[] / D. A. Krasnova // J. Sib. Fed. Univ. Math. Phys. - 2014. - Vol. 7, Is. 1. - P58-67 . - ISSN 1997-1397
Аннотация: Lie group analysis of equations of an ideal fluid written in variables of trajectories and Weber's potential was conducted. It was shown that the use of volume conserving arbitrary Lagrangian coordinates is in fact an equivalent transformation for the equations. The defining Lie algebra equations for the initial velocity distribution were obtained. The basic Lie group and its extensions were found. © Siberian Federal University. All rights reserved.

Scopus,
РИНЦ

Держатели документа:
Institute of Computational Modelling, Siberian Branch of the Russian Academy of Sciences, Akademgorodok, 50/44, Krasnoyarsk, 660036, Russian Federation

Доп.точки доступа:
Krasnova, D.A.; Краснова Д.А.

/ A. V. Lapko, V. A. Lapko // Optoelectron. Instrum. Data Proces. - 2014. - Vol. 50, Is. 4. - P383-388, DOI 10.3103/S8756699014040098 . - ISSN 8756-6990
Аннотация: A new method of decomposition of the interval of the values of random variables based on results of optimization of the nonparametric estimate of the probability density of the Rosenblatt-Parzen type is proposed. Its application in the problem of testing the hypothesis of identity of the distribution laws of two sequences of one-dimensional random variables is considered.

Scopus

Держатели документа:
Institute of Computational Modeling, Siberian Branch, Russian Academy of Sciences, Akademgorodok 50, building 44Krasnoyarsk, Russian Federation
Reshetnev Siberian State Aerospace University, pr. im. Gazety “Krasnoyarskii rabochii” 31Krasnoyarsk, Russian Federation

Доп.точки доступа:
Lapko, V.A.; Лапко, Василий Александрович; Лапко, Александр Васильевич

/ L. I. Shkutin, N. A. Feodorova // Modelling, simulation & control. B. - 1995. - Vol. 58, Is. 3-4. - P11-20 . - ISSN 0761-2516
Аннотация: The double approximation of a displacement field in relation to the transversal coordinate is applied in constructing the two-dimensional model of a shell finite deformation. One of them, linear, is used in calculating the tangential derivatives of displacement field, the other, quadratic, is for the transversal derivative. In result, the displacement field gradient is approximated by the linear function of the transversal coordinate and the Green-Lagrange strain tensor is done by the quadratic one. The two-dimensional model of a shell finite deformation, accordant with the double approximation, contains three unknown vectors as internal kinematical variables of a shell base surface. Only two of them, coefficients of the linear approximation, are factors of the kinematical boundary conditions. They are primary vectorial parameters of the model and give six scalar degrees of shell freedom. The double approximation model of a shell finite deformation can be interpreted as the six-parametrical one with complete strain tensor. The model can be recommended for numerical analysis of shells, heterogeneous through thickness and laminated specifically.

Scopus

Держатели документа:
Computing Cent of the Siberian, Branch of the Russian Acad of, Sciences, Krasnoyarsk, Russian Federation
ИВМ СО РАН

Доп.точки доступа:
Shkutin, L.I.; Шкутин, Леонид Иванович; Feodorova, N.A.

[Text] / I. V. Karlin, G. . Dukek, T. F. Nonnenmacher // Phys. Rev. E. - 1997. - Vol. 55, Is. 2. - P1573-1576, DOI 10.1103/PhysRevE.55.1573. - Cited References: 6 . - ISSN 1063-651XРУБ Physics, Fluids & Plasmas + Physics, Mathematical

Аннотация: Invariance of nonhydrodynamic variables is put forward as a working principle of extending hydrodynamics into a highly nonequilibrium domain. Following this principle, the leading modification of the viscosity due to the gradient of the average velocity is derived explicitly from nonlinear moment Grad equations [Commun. Pure Appl. Math. 2, 331 (1949)].

WOS

Держатели документа:
RUSSIAN ACAD SCI,CTR COMP,KRASNOYARSK 660036,RUSSIA
ИВМ СО РАН

Доп.точки доступа:
Karlin, I.V.; Карлин, Илья Вениаминович; Dukek, G.; Nonnenmacher, T.F.

/ I. V. Karlin, G. Dukek, T. F. Nonnenmacher // Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics. - 1997. - Vol. 55, Is. 2. - P1573-1576 . - ISSN 1063-651X
Аннотация: Invariance of nonhydrodynamic variables is put forward as a working principle of extending hydrodynamics into a highly nonequilibrium domain. Following this principle, the leading modification of the viscosity due to the gradient of the average velocity is derived explicitly from nonlinear moment Grad equations [Commun. Pure Appl. Math. 2, 331 (1949)].

Scopus

Держатели документа:
Department of Mathematical Physics, University of Ulm, Ulm, D-89069, Germany
Computing Center, Russian Academy of Sciences, Krasnoyarsk 660036, Russian Federation
ИВМ СО РАН

Доп.точки доступа:
Karlin, I.V.; Карлин, Илья Вениаминович; Dukek, G.; Nonnenmacher, T.F.

[Text] / A. N. Gorban, D. C. Wunsch // IEEE WORLD CONGRESS ON COMPUTATIONAL INTELLIGENCE : IEEE, 1998. - 2nd IEEE World Congress on Computational Intelligence (WCCI 98) (MAY 04-09, 1998, ANCHORAGE, AK). - P1271-1274. - Cited References: 0 . - ISBN 0-7803-4860-5РУБ Computer Science, Artificial Intelligence + Computer Science, Interdisciplinary Applications + Engineering, Biomedical + Engineering, Electrical & Electronic + Medical Informatics + Neurosciences

Аннотация: A general approximation theorem is proved. It uniformly envelopes both the classical Stone theorem and approximation of functions of several variables by means of superpositions and linear combinations of functions of one variable. This theorem is interpreted asa statement on universal approximating possibilities ("approximating omnipotence") of arbitrary nonlinearity. For the neural networks, our result states that the function of neuron activation must be nonlinear - and nothing else.

WOS

Держатели документа:
Russian Acad Sci, Krasnoyarsk Comp Ctr, Siberian Branch, Krasnoyarsk 660036 36, Russia
ИВМ СО РАН

Доп.точки доступа:
Gorban, A.N.; Горбань, Александр Николаевич; Wunsch, D.C.

/ O. V. Sadovskaya // AIP Conference Proceedings. - 2014. - Vol. 1629: 6th International Conference for Promoting the Application of Mathematics in Technical and Natural Sciences, AMiTaNS 2014 (26 June 2014 through 1 July 2014, ) Conference code: 109043. - P303-310, DOI 10.1063/1.4902286 . -
Аннотация: Parallel computational algorithm is worked out for numerical implementation of two-dimensional dynamic model of a liquid crystal, which takes into account the mutual influence of three physical effects - transfer of acoustic energy due to translational motion, viscoelastic rotation of the particles under the action of tangential stresses, anisotropic thermal expansion and compression. The algorithm is based on the Godunov gap decay method, the Ivanov scheme with controlled dissipation of energy and the splitting method with respect to spatial variables. The CUDA technology for computer systems with graphic accelerators is used. Results of computations demonstrating the efficiency of proposed method and algorithm are represented.

Scopus,
Полный текст (доступен только в локальной сети),
WOS

Держатели документа:
Institute of Computational Modeling, SB RAS, Akademgorodok 50/44Krasnoyarsk, Russian Federation

Доп.точки доступа:
Sadovskaya, O.V.; Садовская, Оксана Викторовна

/ A. V. Lapko, V. A. Lapko // Optoelectronics, Instrumentation and Data Processing. - 2012. - Vol. 48, Is. 1. - P. 37-41DOI 10.3103/S8756699012010050 . -
Аннотация: A possibility of using nonparametric algorithms of pattern recognition in the problem of comparing empirical and theoretical distribution functions of random variables is considered. Results of computational experiments are analyzed.

Полный текст на сайте правообладателя


Доп.точки доступа:
Lapko, V.A.; Лапко, Василий Александрович; Лапко, Александр Васильевич

[Text] / V. Shaydurov, A. Vyatkin // AIP Conference Proceedings. - 2015. - Vol. 1648: International Conference on Numerical Analysis and Applied Mathematics (SEP 22-28, 2014, Rhodes, GREECE). - Ст. UNSP 85004, DOI 10.1063/1.4913096. - Cited References:11 . - ISSN 0094-243XРУБ Mathematics, Applied + Physics, Applied

Аннотация: We consider a semi-Lagrangian algorithm and formulate the basic equality for a local temporal-spatial domain. This equality involves integrals over domains at neighboring temporal levels. To get the numerical scheme, we approximate each component of the equality within second-order accuracy. To compute an integral at the previous time level, we make the change of variables. After that the quadrature formulas are implemented with nodes and weights defined with the help of the Cauchy problem for a system of ordinary differential equations.

WOS,
Полный текст на сайте правообладателя,
Scopus

Держатели документа:
Siberian Fed Univ, Krasnoyarsk 660041, Svobodny Prospe, Russia
Inst Computat Modeling SB RAS, Akademgorodok 660036, Russia

Доп.точки доступа:
Vyatkin, Alexander; Вяткин, Александр Владимирович; Шайдуров, Владимир Викторович

/ A. V. Lapko, V. A. Lapko // Optoelectron. Instrum. Data Proces. - 2015. - Vol. 51, Is. 4. - P372-377, DOI 10.3103/S875669901504007X . - ISSN 8756-6990
Аннотация: A nonparametric estimate of the decision function in a two-alternative problem of pattern recognition is considered. The principle of expansion of the learning sample and the analysis of the probabilistic characteristics of the obtained sets of random variables are used to synthesize this estimate. On this basis, a technique of construction of confidence boundaries for the Bayesian equation of the separating surface is derived. The efficiency of this technique is proved by results of computational experiments. © 2015, Allerton Press, Inc.

Scopus

Держатели документа:
Institute of Computational Modeling, Siberian Branch, Russian Academy of Sciences, Akademgorodok 50, building 44, Krasnoyarsk, Russian Federation
Reshetnev Siberian State Aerospace University, pr. im. Gazety “Krasnoyarskii rabochii” 31, Krasnoyarsk, Russian Federation

Доп.точки доступа:
Lapko, V. A.; Лапко, Василий Александрович; Лапко, Александр Васильевич