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Gorban, Alexander N.

Co-Author Distance
Author ID: gorban.alexander-n Recent zbMATH articles by "Gorban, Alexander N."
Published as: Gorban, Alexander N.; Gorban’, A. N.; Gorban, A. N.; Gorban, Alexander
External Links: MGP · Wikidata · IdRef
Documents Indexed: 97 Publications since 1977, including 3 Books and 9 Additional arXiv Preprints
13 Contributions as Editor
Co-Authors: 74 Co-Authors with 77 Joint Publications
1,345 Co-Co-Authors
all top 5

Co-Authors

25 single-authored
20 Karlin, Iliya V.
17 Tyukin, Ivan Yu.
6 Verbitskij, V. I.
5 Mirkes, Evgeny M.
5 Tyukina, Tatiana A.
4 Cheresiz, Vladimir Mikhaĭlovich
4 Levesley, Jeremy
4 Öttinger, Hans Christian
4 Zinovyev, Andrey Yu.
3 Grechuk, Bogdan
3 Sadovskii, M. G.
3 Smirnova, Elena V.
3 Zinovyev, Andrei
2 Gorban, Pavel A.
2 Ilg, Patrick
2 Nijmeijer, Henk
2 Pokidysheva, Lyudmila I.
2 Popova, Tatyana G.
2 Prokhorov, Danil V.
2 Steur, Erik
2 Sutton, Oliver J.
1 Al-Ameri, J. M.
1 Allison, Penelope
1 Braverman, Maxim
1 Bugaenko, N. N.
1 Bykov, Valeriǐ I.
1 Calvo, Carlos Adolfo
1 Cangiani, Andrea
1 Davidchack, Ruslan L.
1 Elkington, Peter A. S.
1 Georgoulis, Emmanuil H.
1 Gerasimov, V. A.
1 Gilev, S. E.
1 Green, Stephen R.
1 Harel-Bellan, Annick
1 Jarman, N.
1 Judge, George G.
1 Kastalskiy, Innokentiy
1 Kazantsev, Victor B.
1 Kazantzis, Nikolaos K.
1 Kégl, Balázs
1 Kevrekidis, Ioannis George
1 Khlebopros, Rem G.
1 Kolokoltsov, Vassili N.
1 Korablev, Yuriy A.
1 Makarov, Valeri A.
1 Makarova, Yulia
1 McEwan, Alistair A.
1 Melamed, V. B.
1 Meshkinfamfard, Sepehr
1 Morozova, Nadya
1 Okhonin, Victor A.
1 Packwood, D. J.
1 Packwood, David
1 Petrovskii, Sergei V.
1 Romanenko, Ilya
1 Roose, Dirk
1 Rossiev, A. A.
1 Rossiev, D. A.
1 Sargsyan, H. P.
1 Shokin, Yuriĭ Ivanovich
1 Silantyev, Valentin
1 Sofeikov, Konstantin I.
1 Sumner, N. R.
1 Tatarinova, Larisa L.
1 Theodoropoulos, Constantinos
1 Tretyakov, Michael V.
1 Tsibul’skij, G. M.
1 Utyubaev, G. Sh.
1 van Helden, Daniël P.
1 van Leeuwen, Cees
1 Verbitskij, B. I.
1 Whetton, James A.
1 Wunsch, Donald C. II
1 Zheng, Zedong
1 Zhou, Qinghua
1 Zmievskij, Vladimir B.
all top 5

Serials

8 Mathematical Modelling of Natural Phenomena
6 Information Sciences
5 Transport Theory and Statistical Physics
3 Bulletin of Mathematical Biology
3 Siberian Mathematical Journal
3 Neural Networks
3 Open Systems & Information Dynamics
3 Sibirskiĭ Zhurnal Industrial’noĭ Matematiki
2 Computers & Mathematics with Applications
2 Physica A
2 Sibirskiĭ Matematicheskiĭ Zhurnal
2 Soviet Mathematics. Doklady
2 Applied Mathematics Letters
2 Mathematical and Computer Modelling
2 Journal of Non-Newtonian Fluid Mechanics
2 Doklady Mathematics
2 Communications in Nonlinear Science and Numerical Simulation
2 Entropy
2 Lecture Notes in Computational Science and Engineering
2 Philosophical Transactions of the Royal Society of London. A. Mathematical, Physical and Engineering Sciences
1 Computing
1 Differentsial’nye Uravneniya
1 SIAM Journal on Control and Optimization
1 Soviet Mathematics
1 Advances in Modeling & Simulation
1 Numerical Algorithms
1 Bulletin of the American Mathematical Society. New Series
1 Notices of the American Mathematical Society
1 Continuum Mechanics and Thermodynamics
1 Russian Mathematics
1 Journal of Computer and Systems Sciences International
1 Vychislitel’nye Tekhnologii
1 Sorosovskiĭ Obrazovatel’nyĭ Zhurnal
1 Sibirskiĭ Zhurnal Vychislitel’noĭ Matematiki
1 Annalen der Physik. 8th Series
1 SIAM Journal on Applied Dynamical Systems
1 Mathematical Medicine and Biology
1 Mathematical Biosciences and Engineering
1 Electronic Journal of Differential Equations. Monograph
1 Lecture Notes in Physics
1 Mathematical Geosciences
1 Journal of Theoretical Biology
1 London Mathematical Society. Newsletter
all top 5

Fields

28 Biology and other natural sciences (92-XX)
26 Computer science (68-XX)
19 Statistical mechanics, structure of matter (82-XX)
18 Fluid mechanics (76-XX)
14 General and overarching topics; collections (00-XX)
10 Dynamical systems and ergodic theory (37-XX)
10 Statistics (62-XX)
8 Ordinary differential equations (34-XX)
8 Probability theory and stochastic processes (60-XX)
8 Classical thermodynamics, heat transfer (80-XX)
6 Approximations and expansions (41-XX)
6 Functional analysis (46-XX)
6 Systems theory; control (93-XX)
5 Real functions (26-XX)
5 Partial differential equations (35-XX)
5 General topology (54-XX)
5 Numerical analysis (65-XX)
4 Operator theory (47-XX)
4 Game theory, economics, finance, and other social and behavioral sciences (91-XX)
3 History and biography (01-XX)
3 Measure and integration (28-XX)
3 Operations research, mathematical programming (90-XX)
3 Information and communication theory, circuits (94-XX)
2 Convex and discrete geometry (52-XX)
2 Global analysis, analysis on manifolds (58-XX)
1 Integral equations (45-XX)
1 Quantum theory (81-XX)
1 Geophysics (86-XX)

Publications by Year

all cited Publications top 5 cited Publications

Citations contained in zbMATH Open

62 Publications have been cited 443 times in 317 Documents Cited by ▼ Year ▼
Invariant manifolds for physical and chemical kinetics. Zbl 1086.82009
Gorban, Alexander N.; Karlin, Iliya V.
70
2005
Hilbert’s 6th problem: exact and approximate hydrodynamic manifolds for kinetic equations. Zbl 1294.35052
Gorban, Alexander N.; Karlin, Ilya
26
2014
Selection theorem for systems with inheritance. Zbl 1337.92150
Gorban, A. N.
25
2007
Approximation with random bases: pro et contra. Zbl 1427.68361
Gorban, Alexander N.; Tyukin, Ivan Yu.; Prokhorov, Danil V.; Sofeikov, Konstantin I.
25
2016
Hydrodynamics from Grad’s equations: What can we learn from exact solutions? Zbl 1068.76074
Karlin, Iliya V.; Gorban, Alexander N.
25
2002
Entropy: the Markov ordering approach. Zbl 1229.60085
Gorban, Alexander N.; Gorban, Pavel A.; Judge, George
18
2010
Blessing of dimensionality: mathematical foundations of the statistical physics of data. Zbl 1470.82004
Gorban, A. N.; Tyukin, I. Y.
17
2018
Quasichemical models of multicomponent nonlinear diffusion. Zbl 1234.35131
Gorban, A. N.; Sargsyan, H. P.; Wahab, H. A.
17
2011
Model reduction and coarse-graining approaches for multiscale phenomena. Selected papers from the workshop held at the University of Leicester, Leicester, UK, August 24–26, 2005. Zbl 1129.82005
16
2006
Principal manifolds for data visualization and dimension reduction. Reviews and original papers presented partially at the workshop ‘Principal manifolds for data cartography and dimension reduction’, Leicester, UK, August 24–26, 2006. Zbl 1125.68003
15
2008
Method of invariant manifolds and regularization of acoustic spectra. Zbl 0812.76077
Gorban, Alexander N.; Karlin, Iliya V.
15
1994
Structure and approximations of the Chapman-Enskog expansion for the linearized Grad equations. Zbl 0756.76066
Gorban, Alexander N.; Karlin, Iliya V.
13
1992
Corrections and enhancements of quasi-equilibrium states. Zbl 1060.82520
Gorban, Alexander N.; Karlin, Iliya V.; Ilg, Patrick; Öttinger, Hans Christian
10
2001
Enhancement of the stability of lattice Boltzmann methods by dissipation control. Zbl 1395.76068
Gorban, A. N.; Packwood, D. J.
10
2014
Stochastic separation theorems. Zbl 1429.68217
Gorban, A. N.; Tyukin, I. Y.
9
2017
The Michaelis-Menten-Stueckelberg theorem. Zbl 1303.92152
Gorban, Alexander N.; Shahzad, Muhammad
9
2011
Elastic principal graphs and manifolds and their practical applications. Zbl 1274.62408
Gorban, A.; Zinovyev, A.
8
2005
Stable simulation of fluid flow with high-Reynolds number using Ehrenfest’s steps. Zbl 1121.76049
Brownlee, R.; Gorban, A. N.; Levesley, J.
8
2007
Hilbert’s sixth problem: the endless road to rigour. Zbl 1470.81010
Gorban, A. N.
7
2018
Correction of AI systems by linear discriminants: probabilistic foundations. Zbl 1441.68201
Gorban, A. N.; Golubkov, A.; Grechuk, B.; Mirkes, E. M.; Tyukin, I. Y.
7
2018
Approximation of continuous functions of several variables by an arbitrary nonlinear continuous function of one variable, linear functions, and their superpositions. Zbl 0940.41017
Gorban, A. N.
5
1998
Irreversibility in the short memory approximation. Zbl 1031.82020
Karlin, Iliya V.; Tatarinova, Larisa L.; Gorban, Alexander N.; Öttinger, Hans Christian
5
2003
A generalized approximation theorem and computational capabilities of neural networks. Zbl 0903.68152
Gorban’, A. N.
5
1998
Three waves of chemical dynamics. Zbl 1330.92007
Gorban, A. N.; Yablonsky, G. S.
5
2015
Neural networks on a personal computer. (Nejronnye seti na personal’nom komp’yutere.) Zbl 0931.68114
Gorban’, A. N.; Rossiev, D. A.
5
1996
High-dimensional brain: a tool for encoding and rapid learning of memories by single neurons. Zbl 1432.92025
Tyukin, Ivan; Gorban, Alexander N.; Calvo, Carlos; Makarova, Julia; Makarov, Valeri A.
5
2019
Maxallent: maximizers of all entropies and uncertainty of uncertainty. Zbl 1384.62018
Gorban, A. N.
4
2013
Singularities of transition processes in dynamical systems: Qualitative theory of critical delays. Zbl 1057.54028
Gorban, Alexander N.
4
2004
One-trial correction of legacy AI systems and stochastic separation theorems. Zbl 1448.68369
Gorban, Alexander N.; Burton, Richard; Romanenko, Ilya; Tyukin, Ivan Yu.
4
2019
Basic types of coarse-graining. Zbl 1141.82012
Gorban, A. N.
4
2006
Neural network iterative method of principal curves for data with gaps. Zbl 1077.68763
Gorban’, A. N.; Rossiev, A. A.
4
1999
Leaders do not look back, or do they? Zbl 1332.34074
Gorban, A. N.; Jarman, N.; Steur, E.; van Leeuwen, C.; Tyukin, I. Yu.
4
2015
Lyapunov-like conditions of forward invariance and boundedness for a class of unstable systems. Zbl 1283.34050
Gorban, A. N.; Tyukin, I.; Steur, E.; Nijmeijer, H.
4
2013
Evolution of adaptation mechanisms: adaptation energy, stress, and oscillating death. Zbl 1343.92344
Gorban, Alexander N.; Tyukina, Tatiana A.; Smirnova, Elena V.; Pokidysheva, Lyudmila I.
3
2016
Topological grammars for data approximation. Zbl 1167.68378
Gorban, A. N.; Sumner, N. R.; Zinovyev, A. Y.
3
2007
Legendre integrators, post-processing and quasi-equilibrium. Zbl 1143.76533
Gorban, Alexander N.; Gorban, Pavel A.; Karlin, Iliya V.
3
2004
Thermodynamic tree: the space of admissible paths. Zbl 1283.37009
Gorban, Alexander N.
3
2013
Systems with heredity and effects of selection. Zbl 0801.92014
Gorban’, A. N.
3
1992
Fast construction of correcting ensembles for legacy artificial intelligence systems: algorithms and a case study. Zbl 1448.68370
Tyukin, Ivan Yu.; Gorban, Alexander N.; Green, Stephen; Prokhorov, Danil
2
2019
Self-organizing approach for automated gene identification. Zbl 1034.92012
Zinovyev, Andrey Yu.; Gorban, Alexander N.; Popova, Tatyana G.
2
2003
Modified Kirchhoff flow with a partially penetrable obstacle and its application to the efficiency of free flow turbines. Zbl 1076.76516
Gorban, A.; Braverman, M.; Silantyev, V.
2
2002
Maximum entropy method in analysis of genetic text and measurement of its information content. Zbl 0986.92022
Bugaenko, N. N.; Gorban, A. N.; Sadovsky, M. G.
2
1998
Two-step approximation of space-independent relaxation. Zbl 0946.76085
Gorban, Alexander N.; Karlin, Iliya V.; Zmievskij, Vladimir B.
2
1999
Coping with complexity: Model reduction and data analysis. Selected papers based on the presentations at the international research workshop, Ambleside, UK, August 31–September 4, 2009. Zbl 1202.00097
2
2011
General stochastic separation theorems with optimal bounds. Zbl 1521.68120
Grechuk, Bogdan; Gorban, Alexander N.; Tyukin, Ivan Y.
2
2021
Editorial: Grasping complexity. Zbl 1339.00026
1
2013
Nonarbitrary regularization of acoustic spectra. Zbl 0772.76064
Gorban, Alexander N.; Karlin, Iliya V.
1
1993
Piece-wise quadratic approximations of arbitrary error functions for fast and robust machine learning. Zbl 1428.68239
Gorban, A. N.; Mirkes, E. M.; Zinovyev, A.
1
2016
The mystery of two straight lines in bacterial genome statistics. Zbl 1298.92065
Gorban, A. N.; Zinovyev, A. Y.
1
2007
Riabouchinsky flow with partially penetrable obstacle. Zbl 1027.76006
Gorban’, A.; Silantyev, V.
1
2002
Classification of symbol sequences over their frequency dictionaries: Towards the connection between structure and natural taxonomy. Zbl 0956.92003
Gorban, A. N.; Popova, T. G.; Sadovsky, M. G.
1
2000
Thermodynamic constraints and conditions for being quasithermodynamic in chemical kinetics. Zbl 0967.80503
Verbitskij, V. I.; Gorban’, A. N.
1
1989
Generalized mass action law and thermodynamics of nonlinear Markov processes. Zbl 1327.80015
Gorban, A. N.; Kolokoltsov, V. N.
1
2015
Forward-invariant peeling in chemical dynamics: a simple case study. Zbl 1382.80005
Gorban, A. N.
1
2015
Fast sampling of evolving systems with periodic trajectories. Zbl 1390.93238
Tyukin, I. Yu.; Gorban, A. N.; Tyukina, T. A.; Al-Ameri, J. M.; Korablev, Yu. A.
1
2016
A generalized approximation theorem and an exact representation of polynomials of several variables by superpositions of polynomials of one variable. Zbl 1497.41003
Gorban’, A. N.
1
1998
Quasi-equilibrium approximations and nonstandard expansions in the theory of the Boltzmann kinetic equation. Zbl 0820.76074
Gorban’, A. N.; Karlin, I. V.
1
1992
On “solid liquid” limit of hydrodynamic equations. Zbl 0891.76004
Gorban, A. N.; Karlin, I. V.
1
1995
A numerical analyst’s view of the lattice Boltzmann method. Zbl 1426.76604
Levesley, Jeremy; Gorban, Alexander N.; Packwood, David
1
2011
Numerical mathematics and advanced applications 2011. Proceedings of ENUMATH 2011, the 9th European conference on numerical mathematics and advanced applications, Leicester, UK, September 5–9, 2011. Zbl 1257.65002
1
2013
Law of the minimum paradoxes. Zbl 1225.92042
Gorban, Alexander N.; Pokidysheva, Lyudmila I.; Smirnova, Elena V.; Tyukina, Tatiana A.
1
2011
Stochastic separation theorems: how geometry may help to correct AI errors. Zbl 07750555
Gorban, Alexander; Grechuk, Bogdan; Tyukin, Ivan
1
2023
Stochastic separation theorems: how geometry may help to correct AI errors. Zbl 07750555
Gorban, Alexander; Grechuk, Bogdan; Tyukin, Ivan
1
2023
General stochastic separation theorems with optimal bounds. Zbl 1521.68120
Grechuk, Bogdan; Gorban, Alexander N.; Tyukin, Ivan Y.
2
2021
High-dimensional brain: a tool for encoding and rapid learning of memories by single neurons. Zbl 1432.92025
Tyukin, Ivan; Gorban, Alexander N.; Calvo, Carlos; Makarova, Julia; Makarov, Valeri A.
5
2019
One-trial correction of legacy AI systems and stochastic separation theorems. Zbl 1448.68369
Gorban, Alexander N.; Burton, Richard; Romanenko, Ilya; Tyukin, Ivan Yu.
4
2019
Fast construction of correcting ensembles for legacy artificial intelligence systems: algorithms and a case study. Zbl 1448.68370
Tyukin, Ivan Yu.; Gorban, Alexander N.; Green, Stephen; Prokhorov, Danil
2
2019
Blessing of dimensionality: mathematical foundations of the statistical physics of data. Zbl 1470.82004
Gorban, A. N.; Tyukin, I. Y.
17
2018
Hilbert’s sixth problem: the endless road to rigour. Zbl 1470.81010
Gorban, A. N.
7
2018
Correction of AI systems by linear discriminants: probabilistic foundations. Zbl 1441.68201
Gorban, A. N.; Golubkov, A.; Grechuk, B.; Mirkes, E. M.; Tyukin, I. Y.
7
2018
Stochastic separation theorems. Zbl 1429.68217
Gorban, A. N.; Tyukin, I. Y.
9
2017
Approximation with random bases: pro et contra. Zbl 1427.68361
Gorban, Alexander N.; Tyukin, Ivan Yu.; Prokhorov, Danil V.; Sofeikov, Konstantin I.
25
2016
Evolution of adaptation mechanisms: adaptation energy, stress, and oscillating death. Zbl 1343.92344
Gorban, Alexander N.; Tyukina, Tatiana A.; Smirnova, Elena V.; Pokidysheva, Lyudmila I.
3
2016
Piece-wise quadratic approximations of arbitrary error functions for fast and robust machine learning. Zbl 1428.68239
Gorban, A. N.; Mirkes, E. M.; Zinovyev, A.
1
2016
Fast sampling of evolving systems with periodic trajectories. Zbl 1390.93238
Tyukin, I. Yu.; Gorban, A. N.; Tyukina, T. A.; Al-Ameri, J. M.; Korablev, Yu. A.
1
2016
Three waves of chemical dynamics. Zbl 1330.92007
Gorban, A. N.; Yablonsky, G. S.
5
2015
Leaders do not look back, or do they? Zbl 1332.34074
Gorban, A. N.; Jarman, N.; Steur, E.; van Leeuwen, C.; Tyukin, I. Yu.
4
2015
Generalized mass action law and thermodynamics of nonlinear Markov processes. Zbl 1327.80015
Gorban, A. N.; Kolokoltsov, V. N.
1
2015
Forward-invariant peeling in chemical dynamics: a simple case study. Zbl 1382.80005
Gorban, A. N.
1
2015
Hilbert’s 6th problem: exact and approximate hydrodynamic manifolds for kinetic equations. Zbl 1294.35052
Gorban, Alexander N.; Karlin, Ilya
26
2014
Enhancement of the stability of lattice Boltzmann methods by dissipation control. Zbl 1395.76068
Gorban, A. N.; Packwood, D. J.
10
2014
Maxallent: maximizers of all entropies and uncertainty of uncertainty. Zbl 1384.62018
Gorban, A. N.
4
2013
Lyapunov-like conditions of forward invariance and boundedness for a class of unstable systems. Zbl 1283.34050
Gorban, A. N.; Tyukin, I.; Steur, E.; Nijmeijer, H.
4
2013
Thermodynamic tree: the space of admissible paths. Zbl 1283.37009
Gorban, Alexander N.
3
2013
Editorial: Grasping complexity. Zbl 1339.00026
1
2013
Numerical mathematics and advanced applications 2011. Proceedings of ENUMATH 2011, the 9th European conference on numerical mathematics and advanced applications, Leicester, UK, September 5–9, 2011. Zbl 1257.65002
1
2013
Quasichemical models of multicomponent nonlinear diffusion. Zbl 1234.35131
Gorban, A. N.; Sargsyan, H. P.; Wahab, H. A.
17
2011
The Michaelis-Menten-Stueckelberg theorem. Zbl 1303.92152
Gorban, Alexander N.; Shahzad, Muhammad
9
2011
Coping with complexity: Model reduction and data analysis. Selected papers based on the presentations at the international research workshop, Ambleside, UK, August 31–September 4, 2009. Zbl 1202.00097
2
2011
A numerical analyst’s view of the lattice Boltzmann method. Zbl 1426.76604
Levesley, Jeremy; Gorban, Alexander N.; Packwood, David
1
2011
Law of the minimum paradoxes. Zbl 1225.92042
Gorban, Alexander N.; Pokidysheva, Lyudmila I.; Smirnova, Elena V.; Tyukina, Tatiana A.
1
2011
Entropy: the Markov ordering approach. Zbl 1229.60085
Gorban, Alexander N.; Gorban, Pavel A.; Judge, George
18
2010
Principal manifolds for data visualization and dimension reduction. Reviews and original papers presented partially at the workshop ‘Principal manifolds for data cartography and dimension reduction’, Leicester, UK, August 24–26, 2006. Zbl 1125.68003
15
2008
Selection theorem for systems with inheritance. Zbl 1337.92150
Gorban, A. N.
25
2007
Stable simulation of fluid flow with high-Reynolds number using Ehrenfest’s steps. Zbl 1121.76049
Brownlee, R.; Gorban, A. N.; Levesley, J.
8
2007
Topological grammars for data approximation. Zbl 1167.68378
Gorban, A. N.; Sumner, N. R.; Zinovyev, A. Y.
3
2007
The mystery of two straight lines in bacterial genome statistics. Zbl 1298.92065
Gorban, A. N.; Zinovyev, A. Y.
1
2007
Model reduction and coarse-graining approaches for multiscale phenomena. Selected papers from the workshop held at the University of Leicester, Leicester, UK, August 24–26, 2005. Zbl 1129.82005
16
2006
Basic types of coarse-graining. Zbl 1141.82012
Gorban, A. N.
4
2006
Invariant manifolds for physical and chemical kinetics. Zbl 1086.82009
Gorban, Alexander N.; Karlin, Iliya V.
70
2005
Elastic principal graphs and manifolds and their practical applications. Zbl 1274.62408
Gorban, A.; Zinovyev, A.
8
2005
Singularities of transition processes in dynamical systems: Qualitative theory of critical delays. Zbl 1057.54028
Gorban, Alexander N.
4
2004
Legendre integrators, post-processing and quasi-equilibrium. Zbl 1143.76533
Gorban, Alexander N.; Gorban, Pavel A.; Karlin, Iliya V.
3
2004
Irreversibility in the short memory approximation. Zbl 1031.82020
Karlin, Iliya V.; Tatarinova, Larisa L.; Gorban, Alexander N.; Öttinger, Hans Christian
5
2003
Self-organizing approach for automated gene identification. Zbl 1034.92012
Zinovyev, Andrey Yu.; Gorban, Alexander N.; Popova, Tatyana G.
2
2003
Hydrodynamics from Grad’s equations: What can we learn from exact solutions? Zbl 1068.76074
Karlin, Iliya V.; Gorban, Alexander N.
25
2002
Modified Kirchhoff flow with a partially penetrable obstacle and its application to the efficiency of free flow turbines. Zbl 1076.76516
Gorban, A.; Braverman, M.; Silantyev, V.
2
2002
Riabouchinsky flow with partially penetrable obstacle. Zbl 1027.76006
Gorban’, A.; Silantyev, V.
1
2002
Corrections and enhancements of quasi-equilibrium states. Zbl 1060.82520
Gorban, Alexander N.; Karlin, Iliya V.; Ilg, Patrick; Öttinger, Hans Christian
10
2001
Classification of symbol sequences over their frequency dictionaries: Towards the connection between structure and natural taxonomy. Zbl 0956.92003
Gorban, A. N.; Popova, T. G.; Sadovsky, M. G.
1
2000
Neural network iterative method of principal curves for data with gaps. Zbl 1077.68763
Gorban’, A. N.; Rossiev, A. A.
4
1999
Two-step approximation of space-independent relaxation. Zbl 0946.76085
Gorban, Alexander N.; Karlin, Iliya V.; Zmievskij, Vladimir B.
2
1999
Approximation of continuous functions of several variables by an arbitrary nonlinear continuous function of one variable, linear functions, and their superpositions. Zbl 0940.41017
Gorban, A. N.
5
1998
A generalized approximation theorem and computational capabilities of neural networks. Zbl 0903.68152
Gorban’, A. N.
5
1998
Maximum entropy method in analysis of genetic text and measurement of its information content. Zbl 0986.92022
Bugaenko, N. N.; Gorban, A. N.; Sadovsky, M. G.
2
1998
A generalized approximation theorem and an exact representation of polynomials of several variables by superpositions of polynomials of one variable. Zbl 1497.41003
Gorban’, A. N.
1
1998
Neural networks on a personal computer. (Nejronnye seti na personal’nom komp’yutere.) Zbl 0931.68114
Gorban’, A. N.; Rossiev, D. A.
5
1996
On “solid liquid” limit of hydrodynamic equations. Zbl 0891.76004
Gorban, A. N.; Karlin, I. V.
1
1995
Method of invariant manifolds and regularization of acoustic spectra. Zbl 0812.76077
Gorban, Alexander N.; Karlin, Iliya V.
15
1994
Nonarbitrary regularization of acoustic spectra. Zbl 0772.76064
Gorban, Alexander N.; Karlin, Iliya V.
1
1993
Structure and approximations of the Chapman-Enskog expansion for the linearized Grad equations. Zbl 0756.76066
Gorban, Alexander N.; Karlin, Iliya V.
13
1992
Systems with heredity and effects of selection. Zbl 0801.92014
Gorban’, A. N.
3
1992
Quasi-equilibrium approximations and nonstandard expansions in the theory of the Boltzmann kinetic equation. Zbl 0820.76074
Gorban’, A. N.; Karlin, I. V.
1
1992
Thermodynamic constraints and conditions for being quasithermodynamic in chemical kinetics. Zbl 0967.80503
Verbitskij, V. I.; Gorban’, A. N.
1
1989
all cited Publications top 5 cited Publications
all top 5

Cited by 497 Authors

30 Gorban, Alexander N.
15 Tyukin, Ivan Yu.
13 Karlin, Iliya V.
12 Grmela, Miroslav
8 Kuzenkov, Oleg A.
8 Morozov, Andrew Yu.
8 Skakauskas, Vladas
6 Pavelka, Michal
6 Radkevich, Evgeniĭ Vladimirovich
6 Sadovsky, Michael G.
6 Slemrod, Marshall
5 Karev, Georgiĭ Petrovich
5 Kazantzis, Nikolaos K.
5 Mirkes, Evgeny M.
5 Noack, Bernd R.
5 Tyukina, Tatiana A.
5 Wang, Dianhui
4 Klika, Václav
4 Kogelbauer, Florian
4 Palin, Vladimir Vladimirovich
3 Bellomo, Nicola
3 Burini, Diletta
3 Chiavazzo, Eliodoro
3 Chikatamarla, Shyam Sunder
3 Chouhad, Nadia
3 Colangeli, Matteo
3 Dorschner, Benedikt
3 Hoessly, Linard
3 Katauskis, Pranas
3 Kevrekidis, Ioannis George
3 Kůrková, Věra
3 Muntean, Adrian
3 Öttinger, Hans Christian
3 Radulescu, Ovidiu
3 Sanguineti, Marcello
3 Steur, Erik
3 Struchtrup, Henning
2 Acharya, Amit
2 Adrover, Alessandra
2 Alekseev, Aleksey K.
2 Ansumali, Santosh
2 Bekezhanova, Victoria B.
2 Bobylev, Alexandre Vasiljévitch
2 Bondarev, A. E.
2 Bykov, Viatcheslav
2 Čiegis, Raimondas
2 Deng, Nan
2 Dudek, Grzegorz
2 Duong, Manh Hong
2 Esen, Oğul
2 Garikipati, Krishna
2 Giona, Massimiliano
2 Goncharova, Olga N.
2 Goussis, Dimitris A.
2 Grechuk, Bogdan
2 Grigor’ev, Dmitriĭ Yur’evich
2 Guo, Hongwei
2 Hangos, Katalin Mária
2 Hosseini, Seyed Ali
2 Ilg, Patrick
2 Judge, George G.
2 Kalogeropoulos, Nikolaos
2 Kareva, Irina Georgievna
2 Kazantzi, Vasiliki
2 Korobeinikov, Andrei
2 Kovalev, Vladimir F.
2 Lebiedz, Dirk
2 Levesley, Jeremy
2 Li, Ming
2 Morzyński, Marek
2 Nijmeijer, Henk
2 Niven, Robert K.
2 Obregón, Octavio
2 Outada, Nisrine
2 Petrovskii, Sergei V.
2 Pokidysheva, Lyudmila I.
2 Prokhorov, Danil V.
2 Rahkooy, Hamid
2 Ramm, Alexander G.
2 Romano, Vittorio
2 Ryabova, E. A.
2 Saint-Raymond, Laure
2 Sandhu, Simran Kaur
2 Sandler, Uziel
2 Sazhin, Sergei S.
2 Shang, Pengjian
2 Siettos, Constantinos I.
2 Smirnova, Elena V.
2 Srivastava, Siddhartha
2 Sturm, Thomas
2 Sutton, Oliver J.
2 Tao, Youshan
2 van Leeuwen, Cees
2 Venditti, Claudia
2 Volpert, Vitaly A.
2 Winkler, Michael
2 Zinovyev, Andrey Yu.
1 Abaev, Lev Ch.
1 Abdollahi, Vahid
1 Agrawal, Samarth
...and 397 more Authors
all top 5

Cited in 112 Serials

16 Information Sciences
15 Bulletin of Mathematical Biology
14 Physica A
12 Journal of Mathematical Chemistry
11 Communications in Nonlinear Science and Numerical Simulation
11 Mathematical Modelling of Natural Phenomena
10 Computers & Mathematics with Applications
9 Journal of Fluid Mechanics
9 Journal of Statistical Physics
8 Philosophical Transactions of the Royal Society of London. A. Mathematical, Physical and Engineering Sciences
7 Entropy
6 Physica D
6 Neural Networks
6 M\(^3\)AS. Mathematical Models & Methods in Applied Sciences
6 Journal of Mathematical Sciences (New York)
6 Journal of Siberian Federal University. Mathematics & Physics
5 Computer Methods in Applied Mechanics and Engineering
5 Journal of Computational Physics
4 Computers and Fluids
4 Journal of Mathematical Biology
4 Continuum Mechanics and Thermodynamics
4 Chaos
4 SIAM Journal on Applied Dynamical Systems
4 Journal of Theoretical Biology
3 Fluid Dynamics
3 Automatica
3 Mathematics and Computers in Simulation
3 Systems & Control Letters
3 Journal of Scientific Computing
3 Bulletin of the American Mathematical Society. New Series
3 Combustion Theory and Modelling
3 Journal of Physics A: Mathematical and Theoretical
2 Journal of Mathematical Physics
2 Applied Mathematics and Computation
2 Journal of the American Statistical Association
2 Quarterly of Applied Mathematics
2 SIAM Journal on Applied Mathematics
2 International Journal of Bifurcation and Chaos in Applied Sciences and Engineering
2 Physics of Fluids
2 Mathematical Problems in Engineering
2 European Journal of Control
2 Nonlinear Dynamics
2 Open Systems & Information Dynamics
2 Nonlinear Analysis. Modelling and Control
2 Communications in Computational Physics
1 International Journal of Modern Physics A
1 Archive for Rational Mechanics and Analysis
1 Communications in Mathematical Physics
1 International Journal of Control
1 International Journal of General Systems
1 International Journal of Theoretical Physics
1 Journal of Mathematical Analysis and Applications
1 Journal of the Mechanics and Physics of Solids
1 Mathematical Biosciences
1 Nonlinearity
1 Physics Letters. B
1 Physics Reports
1 Transport Theory and Statistical Physics
1 Chaos, Solitons and Fractals
1 Journal of Geometry and Physics
1 Biometrics
1 Computing
1 International Journal for Numerical Methods in Engineering
1 Journal of Approximation Theory
1 Meccanica
1 Programming and Computer Software
1 Siberian Mathematical Journal
1 Probability Theory and Related Fields
1 Computers & Operations Research
1 Applied Mathematics Letters
1 Mathematical and Computer Modelling
1 Numerical Algorithms
1 Computational Statistics
1 Computational Mathematics and Mathematical Physics
1 Applied Mathematical Modelling
1 Communications in Statistics. Theory and Methods
1 SIAM Review
1 Journal of Mathematical Imaging and Vision
1 Journal of Nonlinear Science
1 Russian Mathematics
1 Computational Optimization and Applications
1 Russian Journal of Mathematical Physics
1 Statistical Papers
1 ETNA. Electronic Transactions on Numerical Analysis
1 Computer Science Journal of Moldova
1 Discrete and Continuous Dynamical Systems
1 Multibody System Dynamics
1 Soft Computing
1 Sibirskiĭ Zhurnal Vychislitel’noĭ Matematiki
1 Sibirskiĭ Zhurnal Industrial’noĭ Matematiki
1 Philosophical Transactions of the Royal Society of London. Series A. Mathematical, Physical and Engineering Sciences
1 Acta Mathematica Sinica. English Series
1 Doklady Physics
1 International Journal of Modern Physics C
1 Journal of Nonlinear Mathematical Physics
1 Differential Equations
1 Journal of Machine Learning Research (JMLR)
1 Advances in Complex Systems
1 International Journal of Wavelets, Multiresolution and Information Processing
1 International Journal of Geometric Methods in Modern Physics
...and 12 more Serials
all top 5

Cited in 37 Fields

84 Biology and other natural sciences (92-XX)
75 Fluid mechanics (76-XX)
55 Statistical mechanics, structure of matter (82-XX)
52 Partial differential equations (35-XX)
46 Computer science (68-XX)
38 Statistics (62-XX)
33 Classical thermodynamics, heat transfer (80-XX)
32 Numerical analysis (65-XX)
25 Ordinary differential equations (34-XX)
25 Systems theory; control (93-XX)
23 Probability theory and stochastic processes (60-XX)
20 Dynamical systems and ergodic theory (37-XX)
12 Information and communication theory, circuits (94-XX)
11 Game theory, economics, finance, and other social and behavioral sciences (91-XX)
9 Mechanics of particles and systems (70-XX)
9 Quantum theory (81-XX)
8 Operations research, mathematical programming (90-XX)
6 Mechanics of deformable solids (74-XX)
4 General and overarching topics; collections (00-XX)
4 Approximations and expansions (41-XX)
3 Functional analysis (46-XX)
3 Calculus of variations and optimal control; optimization (49-XX)
3 Differential geometry (53-XX)
2 Combinatorics (05-XX)
2 Harmonic analysis on Euclidean spaces (42-XX)
2 Optics, electromagnetic theory (78-XX)
1 History and biography (01-XX)
1 Commutative algebra (13-XX)
1 Algebraic geometry (14-XX)
1 Nonassociative rings and algebras (17-XX)
1 Group theory and generalizations (20-XX)
1 Real functions (26-XX)
1 Operator theory (47-XX)
1 Convex and discrete geometry (52-XX)
1 General topology (54-XX)
1 Manifolds and cell complexes (57-XX)
1 Relativity and gravitational theory (83-XX)

Citations by Year

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