Zgurovsky, Mikhail Z., Sadovnichiy, Victor A. (Eds.)
2014, XIX, 333 p. 33 illus., 14 illus. in color.
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Closes the gap between mathematical approaches and practical applications
International team of experienced authors
Concise presentation of the subject
In this volume, the authors close 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.
Readers will also benefit from the presentation of modern mathematical modeling methods for the numerical solution of complicated engineering problems in hydromechanics, geophysics and mechanics of continua. This compilation will be of interest to mathematicians and engineers working at the interface of these field. It presents selected works of the open seminar series of Lomonosov Moscow State University and the National Technical University of Ukraine “Kyiv Polytechnic Institute”. The authors come from Germany, Italy, Spain, Russia, Ukraine, and the USA.
Content Level »Research
Keywords »Control Theory and Decision Making - Global Attractors - Long-time Forecasting - Optimal Control Problems - Variational Inequality Problems
Part I Abstract Algebra and Applications.- Algebra And Geometry Through Hamiltonian Systems.- On Hyperbolic Zeta Function of Lattices.- The Distribution Of Values Of Arithmetic Functions.- On the One Method of Constructing Digital Control System with Minimal Structure.- On Norm Maps and “Universal Norms” of Formal Groups over Integer Rings of Local Fields.- Assignment of Factors Levels for Design of Experiments with Resource Constraints.- Part II Mechanics and Numerical Methods.- How to Formulate the Initial-Boundary-Value Problem of Elastodynamics in Terms of Stresses?.- Finite-difference Method of Solution of the Shallow Water Equations on an Unstructured Mesh.- Dynamics of Vortices in Near-wall Flows with Irregular Boundaries.- Strongly Convergent Algorithms for Variational Inequality Problems over the Set of Solutions the Equilibrium Problems.- Part III Long-time Forecasting in Multidisciplinary Investigations.- Multivalued Dynamics Of Solutions for Autonomous Operator Differential Equations in Strongest Topologies.- Structure of Uniform Global Attractor for General Non-Autonomous Reaction-Diffusion System.- Topological Properties of Strong Solutions for the 3D Navier-Stokes Equations.- Inertial Manifolds and Spectral Gap Properties for Wave Equations with Weak and Strong Dissipation.- On Regularity of All Weak Solutions and Their Attractors for Reaction-Diffusion Inclusion in Unbounded Domain.- On Global Attractors for Autonomous Damped Wave Equation with Discontinuous Nonlinearity.- Part IV Control Theory and Decision Making.- On the Regularities of Mass Random Phenomena.- Optimality Conditions for Total-Cost Partially Observable Markov Decision Processes.- On Existence of Optimal Solutions to Boundary Control Problem for an Elastic Body with Quasistatic Evolution of Damage.- On Existence and Attainability of Solutions to Optimal Control Problems in Coefficients for Degenerate Variational Inequalities of Monotone Type.- Distributive Optimal Control in One Non-Self-Adjoint Boundary Value Problem.- Guaranteed Safety Operation of Complex Engineering Systems.- Part V Short Communications.- To The Arithmetics Of The Bose – Maslov Condensate Statistics.- Numerical Algorithms for Multiphase Flows and Applications.- Singular Trajectories of the First Order in Problems with Multidimensional Control Lying in a Polyhedron.- The Guaranteed Result Principle in Decision Problems.