[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,
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Держатели документа:
ИВМ СО РАН : 660036, Красноярск, Академгородок, 50, стр.44
Доп.точки доступа:
Горбань, Александр Николаевич
Труды сотрудников ИВМ СО РАН
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Найдено документов в текущей БД: 7
В16
G65
G65
Approximation of continuous functions of several variables by an arbitrary nonlinear continuous function of one variable, linear functions, and their superpositions .
Engineering, Multidisciplinary
H99
H99
Information technology of mathematical modelling of a three-dimensional supersonic flow on the basis of particular solutions of hydrodynamic problems
/ V. A. Shchepanovskii // Russ. J. Numer. Anal. Math. Model. - 1997. - Vol. 12, Is. 4. - P373-397, DOI 10.1515/rnam.1997.12.4.373. - Cited References: 47
. - ISSN 0927-6467
РУБ Engineering, Multidisciplinary + Mathematics, Applied
Аннотация: We propose the formalized methods of mathematical modelling of a three-dimensional supersonic flow on the basis of solutions of smaller dimensionality. We separate a base algorithm for constructing the solution and derive an equation for the streamlined space surface. We introduce concrete techniques, viz. the procedures of superposition, completion, and convergence. We construct test forms for debugging the multidimensional computational algorithms and study various parts of hypersonic aircraft.
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Держатели документа:
Computer Center, Siberian Br. Russ. Acad. of Sci., Krasnoyarsk 660036, Russian Federation
ИВМ СО РАН
Доп.точки доступа:
Shchepanovskii, V.A.; Щепановский, Владимир Александрович
Аннотация: We propose the formalized methods of mathematical modelling of a three-dimensional supersonic flow on the basis of solutions of smaller dimensionality. We separate a base algorithm for constructing the solution and derive an equation for the streamlined space surface. We introduce concrete techniques, viz. the procedures of superposition, completion, and convergence. We construct test forms for debugging the multidimensional computational algorithms and study various parts of hypersonic aircraft.
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Scopus
Держатели документа:
Computer Center, Siberian Br. Russ. Acad. of Sci., Krasnoyarsk 660036, Russian Federation
ИВМ СО РАН
Доп.точки доступа:
Shchepanovskii, V.A.; Щепановский, Владимир Александрович
The general approximation theorem
[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 0-7803-4860-5
РУБ Computer Science, Artificial Intelligence + Computer Science, Interdisciplinary Applications + Engineering, Biomedical + Engineering, Electrical & Electronic + Medical Informatics + Neurosciences
Кл.слова (ненормированные):
approximation -- superposition -- neural networks -- Stone-Weierstrass theorem
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.
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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.
Кл.слова (ненормированные):
approximation -- superposition -- neural networks -- Stone-Weierstrass theorem
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.
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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.
Method of superposition of dislocations for finding stress-strain state around fan-shaped structure in a brittle rock
/ V. M. Sadovskii, O. V. Sadovskaya // AIP Conference Proceedings. - 2016. - Vol. 1773: 8th International Conference for Promoting the Application of Mathematics in Technical and Natural Sciences, AMiTaNS 2016 (22 June 2016 through 27 June 2016, ) Conference code: 124420, DOI 10.1063/1.4964988
. -
Аннотация: The Tarasov fan-shaped mechanism, simulating the formation of shear ruptures in a brittle rock at stress conditions corresponding to seismogenic depths, is analyzed. For computation of the stress-strain state of a rock near the equilibrium fan-structure the original method is constructed. The fault is modeled as a narrow elongated layer, filled with the domino-blocks, between two elastic half-spaces. Displacements and stresses around the fan are represented in the integral form as a superposition of edge dislocations with an unknown function of distribution of the Burgers vector. To take into account the stresses of lateral thrust, the solution of plane problem of the elasticity is used for a tensile crack, on the surfaces of which the previously unknown normal stresses are distributed. The exact formulation of the problem leads to a system of two nonlinear singular integral equations, which is solved numerically by the method of successive approximations. The obtained solution is used, when setting the initial data in computations of the dynamics of the Tarasov fan-shaped mechanism. With the help of this solution the discontinuous nature of shear ruptures, observed in natural and laboratory experiments, is explained. © 2016 Author(s).
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Держатели документа:
Institute of Computational Modeling, SB RAS, Akademgorodok 50/44, Krasnoyarsk, Russian Federation
Доп.точки доступа:
Sadovskii, V. M.; Sadovskaya, O. V.
Аннотация: The Tarasov fan-shaped mechanism, simulating the formation of shear ruptures in a brittle rock at stress conditions corresponding to seismogenic depths, is analyzed. For computation of the stress-strain state of a rock near the equilibrium fan-structure the original method is constructed. The fault is modeled as a narrow elongated layer, filled with the domino-blocks, between two elastic half-spaces. Displacements and stresses around the fan are represented in the integral form as a superposition of edge dislocations with an unknown function of distribution of the Burgers vector. To take into account the stresses of lateral thrust, the solution of plane problem of the elasticity is used for a tensile crack, on the surfaces of which the previously unknown normal stresses are distributed. The exact formulation of the problem leads to a system of two nonlinear singular integral equations, which is solved numerically by the method of successive approximations. The obtained solution is used, when setting the initial data in computations of the dynamics of the Tarasov fan-shaped mechanism. With the help of this solution the discontinuous nature of shear ruptures, observed in natural and laboratory experiments, is explained. © 2016 Author(s).
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Держатели документа:
Institute of Computational Modeling, SB RAS, Akademgorodok 50/44, Krasnoyarsk, Russian Federation
Доп.точки доступа:
Sadovskii, V. M.; Sadovskaya, O. V.
539.374
М744
М744
Моделирование веерообразования в вершине глубинной трещины сдвига на основе уравнений плоской теории упругости
[Текст] : статья / Борис Григорьевич Тарасов, Владимир Михайлович Садовский, Оксана Викторовна Садовская // Физическая мезомеханика. - 2016. - Т. 19, № 4. - С. 28-37
. - ISSN 1683-805X
Перевод заглавия: Modeling of fan formation in the shear rupture head on the basis of equations of plane elasticity
Кл.слова (ненормированные):
Трещина сдвига -- веерный механизм -- упругость -- краевая дислокация -- вектор Бюргерса -- сингулярное интегральное уравнение -- shear rupture -- fan-shaped mechanism -- elasticity -- edge dislocation -- Burgers vector -- singular integral equation
Аннотация: В приближении плоской деформации строится математическая модель равновесного веера в прослойке между двумя упругими полуплоскостями, имитирующей головную зону растущей трещины сдвига в прочной горной породе в условиях сильного гидростатического сжатия. Напряженно-деформированное состояние вдали от веера анализируется с помощью решения задачи о краевой дислокации. В полной постановке задача решается на основе оригинального метода суперпозиции дислокаций, приводящего к двум нелинейным интегральным уравнениям в зоне веера, для численного исследования которых применяется метод последовательных приближений.
The mathematical model of an equilibrium fan formation in the interlayer between two elastic half-planes which simulates the shear rupture head in a hard rock under high hydrostatic pressure has been constructed in the plane strain approximation. The stress-strain state far from the fan is analyzed by solving the problem of edge dislocation. This problem in a complete formulation is solved on the basis of an original method of superposition of dislocations that yields two nonlinear integral equations in the fan zone. The integral equations are solved numerically using the method of successive approximations.
РИНЦ
Держатели документа:
Centre for Offshore Foundation Systems, University of Western Australia
Институт вычислительного моделирования СО РАН
Доп.точки доступа:
Садовский, Владимир Михайлович; Sadovskii V.M.; Садовская, Оксана Викторовна; Sadovskaya O.V.; Tarasov B.G.
Перевод заглавия: Modeling of fan formation in the shear rupture head on the basis of equations of plane elasticity
| УДК |
Кл.слова (ненормированные):
Трещина сдвига -- веерный механизм -- упругость -- краевая дислокация -- вектор Бюргерса -- сингулярное интегральное уравнение -- shear rupture -- fan-shaped mechanism -- elasticity -- edge dislocation -- Burgers vector -- singular integral equation
Аннотация: В приближении плоской деформации строится математическая модель равновесного веера в прослойке между двумя упругими полуплоскостями, имитирующей головную зону растущей трещины сдвига в прочной горной породе в условиях сильного гидростатического сжатия. Напряженно-деформированное состояние вдали от веера анализируется с помощью решения задачи о краевой дислокации. В полной постановке задача решается на основе оригинального метода суперпозиции дислокаций, приводящего к двум нелинейным интегральным уравнениям в зоне веера, для численного исследования которых применяется метод последовательных приближений.
The mathematical model of an equilibrium fan formation in the interlayer between two elastic half-planes which simulates the shear rupture head in a hard rock under high hydrostatic pressure has been constructed in the plane strain approximation. The stress-strain state far from the fan is analyzed by solving the problem of edge dislocation. This problem in a complete formulation is solved on the basis of an original method of superposition of dislocations that yields two nonlinear integral equations in the fan zone. The integral equations are solved numerically using the method of successive approximations.
РИНЦ
Держатели документа:
Centre for Offshore Foundation Systems, University of Western Australia
Институт вычислительного моделирования СО РАН
Доп.точки доступа:
Садовский, Владимир Михайлович; Sadovskii V.M.; Садовская, Оксана Викторовна; Sadovskaya O.V.; Tarasov B.G.
Modelling the static stress–strain state around the fan-structure in the shear rupture head
/ B. G. Tarasov [et al.] // Appl. Math. Model. - 2018. - Vol. 57. - P268-279, DOI 10.1016/j.apm.2018.01.020
. - ISSN 0307-904X
Кл.слова (ненормированные):
Edge dislocation -- Fan-shaped mechanism -- Shear rupture -- Singular integral equation -- Successive approximations -- Approximation theory -- Edge dislocations -- Nonlinear equations -- Structural geology -- Tectonics -- High confining pressure -- Method of successive approximations -- Nonlinear integral equations -- Seismogenic zones -- Shear ruptures -- Singular integral equations -- Successive approximations -- Tangential stress -- Integral equations
Аннотация: The mathematical model of an equilibrium fan-structure in the interface between two elastic blocks, simulating the shear rupture head in a hard rock under high confining pressure, is constructed. The stress–strain state far from the fan-structure is analyzed with the help of a solution of the problem on edge dislocation. The fan length is estimated using this solution. The model of formation of two oppositely directed fans due to the localized action of tangential stress, which pushes two edge dislocations with antiparallel Burgers vectors, is proposed. In complete formulation, the problem on an equilibrium fan-structure in the interface between infinite elastic half-planes is analyzed by means of original method of superposition of dislocations, leading to two nonlinear integral equations in the fan zone. To solve them numerically, the method of successive approximations is applied. Based on this method, fields of stresses and displacements around the equilibrium fan modelling of a deep-seated shear rupture in the seismogenic zone of the Earth's crust are computed. Such fields can be used, when setting the initial data in the analysis of dynamics of the fan-shaped mechanism. © 2018 Elsevier Inc.
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Держатели документа:
Centre for Offshore Foundation Systems, University of Western Australia, Perth, WA, Australia
Institute of Computational Modelling SB RAS, Krasnoyarsk, Russian Federation
Доп.точки доступа:
Tarasov, B. G.; Sadovskii, V. M.; Sadovskaya, O. V.; Cassidy, M. J.; Randolph, M. F.
Кл.слова (ненормированные):
Edge dislocation -- Fan-shaped mechanism -- Shear rupture -- Singular integral equation -- Successive approximations -- Approximation theory -- Edge dislocations -- Nonlinear equations -- Structural geology -- Tectonics -- High confining pressure -- Method of successive approximations -- Nonlinear integral equations -- Seismogenic zones -- Shear ruptures -- Singular integral equations -- Successive approximations -- Tangential stress -- Integral equations
Аннотация: The mathematical model of an equilibrium fan-structure in the interface between two elastic blocks, simulating the shear rupture head in a hard rock under high confining pressure, is constructed. The stress–strain state far from the fan-structure is analyzed with the help of a solution of the problem on edge dislocation. The fan length is estimated using this solution. The model of formation of two oppositely directed fans due to the localized action of tangential stress, which pushes two edge dislocations with antiparallel Burgers vectors, is proposed. In complete formulation, the problem on an equilibrium fan-structure in the interface between infinite elastic half-planes is analyzed by means of original method of superposition of dislocations, leading to two nonlinear integral equations in the fan zone. To solve them numerically, the method of successive approximations is applied. Based on this method, fields of stresses and displacements around the equilibrium fan modelling of a deep-seated shear rupture in the seismogenic zone of the Earth's crust are computed. Such fields can be used, when setting the initial data in the analysis of dynamics of the fan-shaped mechanism. © 2018 Elsevier Inc.
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Держатели документа:
Centre for Offshore Foundation Systems, University of Western Australia, Perth, WA, Australia
Institute of Computational Modelling SB RAS, Krasnoyarsk, Russian Federation
Доп.точки доступа:
Tarasov, B. G.; Sadovskii, V. M.; Sadovskaya, O. V.; Cassidy, M. J.; Randolph, M. F.
Is There Any Hidden Symmetry in the Stripe Structure of Perovskite High-Temperature Superconductors?
/ V. A. Gavrichkov [et al.] // J. Phys. Chem. Lett. - 2019. - Vol. 10, Is. 8. - P1840-1844, DOI 10.1021/acs.jpclett.9b00513. - Cited References:68. - One of the authors (V.A.G.) is grateful to RFBR, the Government of the Krasnoyarsk Region and Krasnoyarsk Regional Fund of Science for the research Grant No. 18-42-240017
. - ISSN 1948-7185
РУБ Chemistry, Physical + Nanoscience & Nanotechnology + Materials Science,
Аннотация: Local and fast structural probes using synchrotron radiation have shown nanoscale striped puddles and nanoscale phase separation in doped perovskites. It is known that the striped phases in doped perovskites are due to competing interactions involving charge, spin, and lattice degrees of freedom. In this work, we show that two different stripes can be represented as a superposition of a pair of stripes, U(theta(n)) or D(theta(n)), characterized by perovskite tilts where one of the pair is rotated in relation to the other partner by an angle Delta theta(n) = pi/2. The spatial distribution of the U and D stripes is reduced to all possible maps in the well-known mathematical four-color theorem. Both the periodic striped puddles and random structures can be represented by using planar graphs with a chromatic numbers chi
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Держатели документа:
Russian Acad Sci, Kirensky Inst Phys, KSC Siberian Branch, Fed Res Ctr, Krasnoyarsk 660036, Russia.
Russian Acad Sci, Siberian Branch, Inst Computat Modeling, Krasnoyarsk 660036, Russia.
Rome Int Ctr Mat Sci Superstripes RICMASS, Via Sabelli 119A, I-00185 Rome, Italy.
CNR, Inst Cristallog, I-00015 Monterotondo, Italy.
Natl Res Nucl Univ MEPhI, Moscow Engn Phys Inst, Moscow 115409, Russia.
Доп.точки доступа:
Gavrichkov, Vladimir A.; Shan'ko, Yury; Zamkova, Natalia G.; Bianconi, Antonio; RFBR [18-42-240017]; Government of the Krasnoyarsk Region [18-42-240017]; Krasnoyarsk Regional Fund of Science [18-42-240017]
Аннотация: Local and fast structural probes using synchrotron radiation have shown nanoscale striped puddles and nanoscale phase separation in doped perovskites. It is known that the striped phases in doped perovskites are due to competing interactions involving charge, spin, and lattice degrees of freedom. In this work, we show that two different stripes can be represented as a superposition of a pair of stripes, U(theta(n)) or D(theta(n)), characterized by perovskite tilts where one of the pair is rotated in relation to the other partner by an angle Delta theta(n) = pi/2. The spatial distribution of the U and D stripes is reduced to all possible maps in the well-known mathematical four-color theorem. Both the periodic striped puddles and random structures can be represented by using planar graphs with a chromatic numbers chi
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РИНЦ
Держатели документа:
Russian Acad Sci, Kirensky Inst Phys, KSC Siberian Branch, Fed Res Ctr, Krasnoyarsk 660036, Russia.
Russian Acad Sci, Siberian Branch, Inst Computat Modeling, Krasnoyarsk 660036, Russia.
Rome Int Ctr Mat Sci Superstripes RICMASS, Via Sabelli 119A, I-00185 Rome, Italy.
CNR, Inst Cristallog, I-00015 Monterotondo, Italy.
Natl Res Nucl Univ MEPhI, Moscow Engn Phys Inst, Moscow 115409, Russia.
Доп.точки доступа:
Gavrichkov, Vladimir A.; Shan'ko, Yury; Zamkova, Natalia G.; Bianconi, Antonio; RFBR [18-42-240017]; Government of the Krasnoyarsk Region [18-42-240017]; Krasnoyarsk Regional Fund of Science [18-42-240017]