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Title Continuous and Distributed Aystems : Theory and Applications / Mikhail Z. Zgurovsky, Victor A. Sadovnichiy, Editors
Published Cham ; New York : Springer, [2014]
©2014
Table of Contents
pt. I Abstract Algebra and Applications 
1.Algebra and Geometry Through Hamiltonian Systems / Andrei Konyaev3
1.1.Introduction3
1.2.Atoms and Their Symmetries4
1.3.Integer Lattices of Action Variables for "Spherical Pendulum" System7
1.4.Billiards in Confocal Quadrics10
1.5.Bertrand's Manifolds and Their Properties14
1.6.Lie Algebras with Generic Coadjoint Orbits of Dimension Two17
 References19
2.On Hyperbolic Zeta Function of Lattices / N. N. Dobrovolsky23
2.1.Introduction23
2.1.1.Lattices24
2.1.2.Exponential Sums of Lattices26
2.1.3.Multidimensional Quadrature Formulas and Hyperbolic Zeta Function of a Grid29
2.1.4.Hyperbolic Zeta Function of Lattices34
2.1.5.Generalised Hyperbolic Zeta Function of Lattices40
2.2.Functional Equation for Hyperbolic Zeta Function of Integer Lattices45
2.2.1.Periodized in the Parameter b Hurwitz Zeta Function46
2.2.2.Dirichlet Series with Periodical Coefficients47
2.2.3.Functional Equation for Hyperbolic Zeta Function of Integer Lattices50
2.3.Functional Equation for Hyperbolic Zeta Function of Cartesian Lattices52
2.4.On Some Unsolved Problems of the Theory of Hyperbolic Zeta Function of Lattices59
 References60
3.The Distribution of Values of Arithmetic Functions / G. V. Fedorov63
 References66
4.On the One Method of Constructing Digital Control System with Minimal Structure / V. V. Palin67
4.1.The Statement of Problem and Some Familiar Results67
4.2.Definitions and Some Preliminary Transformations68
4.3.The Method to Obtain the Characteristic of Completely Controllable69
4.4.Auxiliary Statements69
4.5.The Absence of Associated Vectors Case70
4.6.The Case of General Position71
 Reference71
5.On Norm Maps and "Universal Norms" of Formal Groups over Integer Rings of Local Fields / Nikolaj M. Glazunov73
5.1.Introduction73
5.2.Norm Maps75
5.3.Results78
 References80
6.Assignment of Factors Levels for Design of Experiments with Resource Constraints / N. A. Oriekhova81
6.1.Introduction81
6.2.Hansel Method82
6.3.Modification83
6.4.Example85
6.5.Conclusions86
 References86
pt. II Mechanics and Numerical Methods 
7.How to Formulate the Initial-Boundary-Value Problem of Elastodynamics in Terms of Stresses? / D. V. Georgievskii89
7.1.The Classic Formulation of the Dynamic Problem and Its Peculiarities89
7.2.Ignaczak--Nowacki' Formulation91
7.3.Konovalov' Formulation92
7.4.Pobedria' Formulation93
7.5.One More Possible Formulation93
 References95
8.Finite-Difference Method of Solution of the Shallow Water Equations on an Unstructured Mesh / A. V. Drutsa97
8.1.Introduction97
8.2.Formulation of the Problem97
8.3.Mesh and Mesh Operators98
8.4.Finite-Dimensional Problem100
8.5.Convergence101
8.6.Results of Numerical Experiments104
8.6.1.Estimation of Convergence Order104
8.6.2.Computation of the Real Geographic Domain105
 References113
9.Dynamics of Vortices in Near-wall Flows with Irregular Boundaries / O. V. Homenko115
9.1.Introduction115
9.2.Model of Standing Vortex117
9.3.Standing Vortex in Cross Groove119
9.4.Standing Vortex in an Angular Region121
9.5.Resonant Properties of Standing Vortices and Their Behavior in Perturbed Flow123
9.6.Summary128
 References128
10.Strongly Convergent Algorithms for Variational Inequality Problem Over the Set of Solutions the Equilibrium Problems / Vladimir V. Semenov131
10.1.Introduction131
10.2.Preliminaries134
10.3.Convergence Analysis135
10.4.Concluding Remarks145
 References145
pt. III Long-time Forecasting in Multidisciplinary Investigations 
11.Multivalued Dynamics of Solutions for Autonomous Operator Differential Equations in Strongest Topologies / Pavlo O. Kasyanov149
11.1.Introduction: Statement of the Problem149
11.2.Additional Properties of Solutions151
11.3.Attractors in Strongest Topologies158
11.4.Application160
11.5.Conclusions161
 References161
12.Structure of Uniform Global Attractor for General Non-Autonomous Reaction-Diffusion System / Mikhail Z. Zgurovsky163
12.1.Introduction163
12.2.Setting of the Problem164
12.3.Multivalued Processes and Uniform Attractors165
12.4.Uniform Global Attractor for RD-System174
 References180
13.Topological Properties of Strong Solutions for the 3D Navier-Stokes Equations / Nina V. Zadoianchuk181
13.1.Introduction181
13.2.Topological Properties of Strong Solutions183
13.3.Proof of Theorem 13.2184
13.4.Proof of Theorem 13.1185
 References187
14.Inertial Manifolds and Spectral Gap Properties for Wave Equations with Weak and Strong Dissipation / Natalia Chalkina189
14.1.Introduction189
14.2.Statement of the Problem and Spectrum of the Linear Operator191
14.3.Sufficient Conditions for the Existence of Inertial Manifolds193
14.4.Proof of Theorem 14.3197
14.4.1.New Norm in the Spaces Hk, k = 1, ... k1197
14.4.2.New Norm in the Spaces Hk, k = k1 + 1, ..., k2198
14.4.3.New Norm in the Space H[∞]200
14.4.4.End of the Proof of Theorem 14.3202
 References203
15.On Regularity of All Weak Solutions and Their Attractors for Reaction-Diffusion Inclusion in Unbounded Domain / Pavlo O. Kasyanov205
15.1.Introduction205
15.2.On Compact Global Attractor for Reaction-Diffusion Inclusion in Unbounded Domain208
15.3.Regularity of All Weak Solutions and Their Attractors217
 References219
16.On Global Attractors for Autonomous Damped Wave Equation with Discontinuous Nonlinearity / Liliia S. Paliichuk221
16.1.Introduction221
16.2.Setting of the Problem222
16.3.Preliminaries223
16.4.Properties of Solutions225
16.5.The Existence of a Global Attractor231
16.6.Global Attractors for Typically Discontinuous Interaction Functions232
 References237
pt. IV Control Theory and Decision Making 
17.On the Regularities ofMass Random Phenomena / Valery A. Labkovsky241
17.1.Introduction241
17.2.Theorem of Existence of Statistical Regularities243
17.3.The Proof246
17.4.Applications in Decision Theory247
17.5.Concluding Remarks249
 References249
18.Optimality Conditions for Partially Observable Markov Decision Processes / Mikhail Z. Zgurovsky251
18.1.Introduction251
18.2.Model Description252
18.3.Reduction of POMDPs to COMDPs and Optimality Results256
18.4.Example262
18.5.Conclusions263
 References264
19.On Existence of Optimal Solutions to Boundary Control Problem for an Elastic Body with Quasistatic Evolution of Damage / Gunter Leugering265
19.1.Introduction265
19.2.Notation and Preliminaries266
19.3.Radon Measures and Convergence in Variable Spaces270
19.4.The Model of Quasistatic Evolution of Damage in an Elastic Material273
19.5.Setting of the Optimal Control Problems and Existence Theorem for Optimal Traction278
 References286
20.On Existence and Attainability of Solutions to Optimal Control Problems in Coefficients for Degenerate Variational Inequalities of Monotone Type / Olga P. Kupenko287
20.1.Introduction287
20.2.Notation and Preliminaries289
20.3.Setting of the Optimal Control Problem294
20.4.Compensated Compactness Lemma in Variable Lebesgue and Sobolev Spaces295
20.5.Existence of H-Optimal Solutions296
20.6.Attainability of H-Optimal Solutions297
 References300
21.Distributed Optimal Control in One Non-Self-Adjoint Boundary Value Problem / O. K. Mazur303
21.1.Introduction303
21.2.Setting of the Problem304
21.3.Main Results305
21.4.Conclusions311
 References312
22.Guaranteed Safety Operation of Complex Engineering Systems / Andrii M. Raduk313
22.1.Introduction314
22.2.Information Platform of Engineering Diagnostics of the Complex Object Operation315
22.3.Diagnostic of Reanimobile's Functioning321
22.4.Conclusion325
 References326
Appendix A To the Arithmetics of the Bose--Maslov Condensate Statistics327
Appendix B Numerical Algorithms for Multiphase Flows and Applications329
Appendix C Singular Trajectories of the First Order in Problems with Multidimensional Control Lying in a Polyhedron331
Appendix D The Guaranteed Result Principle in Decision Problems333

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Description 1 online resource (334 pages)
Series Solid mechanics and its applications, 2214-7764 ; v. 211
Solid mechanics and its applications ; v. 211. 2214-7764
Contents Part I. Abstract Algebra and Applications -- Algebra and Geometry Through Hamiltonian Systems / Anatoly T. Fomenko and Andrei Konyaev -- On Hyperbolic Zeta Function of Lattices / L.P. Dobrovolskaya, M.N. Dobrovolsky, N.M. Dobrovol'skii and N.N. Dobrovolsky -- The Distribution of Values of Arithmetic Functions / G.V. Fedorov -- On the One Method of Constructing Digital Control System with Minimal Structure / V.V. Palin -- On Norm Maps and "Universal Norms" of Formal Groups Over Integer Rings of Local Fields / Nikolaj M. Glazunov -- Assignment of Factors Levels for Design of Experiments with Resource Constraints / S.A. Smirnov, O.O. Glushchenko, K.A. Ilchuk, I.L. Makeenko and N.A. Oriekhova -- Part II. Mechanics and Numerical Methods -- How to Formulate the Initial-Boundary-Value Problem of Elastodynamics in Terms of Stresses? / D.V. Georgievskii -- Finite-Difference Method of Solution of the Shallow Water Equations on an Unstructured Mesh / G.M. Kobelkov and A.V. Drutsa -- Dynamics of Vortices in Near-Wall Flows with Irregular Boundaries / I.M. Gorban and O.V. Khomenko -- Strongly Convergent Algorithms for Variational Inequality Problem Over the Set of Solutions the Equilibrium Problems / Vladimir V. Semenov -- Part III. Long-time Forecasting in Multidisciplinary Investigations -- Multivalued Dynamics of Solutions for Autonomous Operator Differential Equations in Strongest Topologies / Mikhail Z. Zgurovsky and Pavlo O. Kasyanov -- Structure of Uniform Global Attractor for General Non-Autonomous Reaction-Diffusion System / Oleksiy V. Kapustyan, Pavlo O. Kasyanov, José Valero and Mikhail Z. Zgurovsky -- Topological Properties of Strong Solutions for the 3D Navier-Stokes Equations / Pavlo O. Kasyanov, Luisa Toscano and Nina V. Zadoianchuk -- Inertial Manifolds and Spectral Gap Properties for Wave Equations with Weak and Strong Dissipation / Natalia Chalkina -- On Regularity of All Weak Solutions and Their Attractors for Reaction-Diffusion Inclusion in Unbounded Domain / Nataliia V. Gorban and Pavlo O. Kasyanov -- On Global Attractors for Autonomous Damped Wave Equation with Discontinuous Nonlinearity / Nataliia V. Gorban, Oleksiy V. Kapustyan, Pavlo O. Kasyanov and Liliia S. Paliichuk -- Part IV. Control Theory and Decision Making -- On the Regularities of Mass Random Phenomena / Victor I. Ivanenko and Valery A. Labkovsky -- Optimality Conditions for Partially Observable Markov Decision Processes / Eugene A. Feinberg, Pavlo O. Kasyanov and Mikhail Z. Zgurovsky -- On Existence of Optimal Solutions to Boundary Control Problem for an Elastic Body with Quasistatic Evolution of Damage / Peter I. Kogut and Günter Leugering -- On Existence and Attainability of Solutions to Optimal Control Problems in Coefficients for Degenerate Variational Inequalities of Monotone Type / Olga P. Kupenko -- Distributed Optimal Control in One Non-Self-Adjoint Boundary Value Problem / V.O. Kapustyan, O.A. Kapustian and O.K. Mazur -- Guaranteed Safety Operation of Complex Engineering Systems / Nataliya D. Pankratova and Andrii M. Raduk
Summary This volume closes the gap between abstract mathematical approaches, such as abstract algebra, number theory, nonlinear functional analysis, partial differential equations, methods of nonlinear and multi-valued analysis, on the one hand, and practical applications in nonlinear mechanics, decision making theory and control theory on the other
Bibliography Includes bibliographical references and index
Notes Online resource; title from PDF title page (ebrary, viewed December 30, 2013)
Subject Distributed parameter systems.
Electronic data processing -- Distributed processing.
Mathematical optimization.
Structural control (Engineering)
SCIENCE -- System Theory.
TECHNOLOGY & ENGINEERING -- Operations Research.
Ingénierie.
Distributed parameter systems
Electronic data processing -- Distributed processing
Mathematical optimization
Structural control (Engineering)
Form Electronic book
Author Sadovnichiĭ, V. A. (Viktor Antonovich)
Zhurovsʹkyĭ, M. Z. (Mykhaĭlo Zakharovych)
ISBN 9783319031460
3319031465
3319031457
9783319031453