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Contemporary Approaches and Methods in Fundamental Mathematics and Mechanics

  • Book
  • © 2021

Overview

Editors:
  1. Victor A. Sadovnichiy

    1. Lomonosov Moscow State University, Moscow, Russia

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  2. Michael Z. Zgurovsky

    1. National Technical University of Ukraine “Igor Sikorsky Kyiv Polytechnic Institute”, Kyiv, Ukraine

    View editor publications

    You can also search for this editor in PubMed   Google Scholar

  • Focuses on the contemporary approaches and methods in fundamental mathematics and mechanics
  • Presents research and review papers on recent advances in deterministic and stochastic modeling in real-world problems
  • Bridges the gap between mathematical approaches and practical applications

Part of the book series: Understanding Complex Systems (UCS)

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About this book

This book focuses on the latest approaches and methods in fundamental mathematics and mechanics, and discusses the practical application of abstract mathematical approaches, such as differential geometry, and differential and difference equations in solid mechanics, hydrodynamics, aerodynamics, optimization, decision-making theory and control theory. Featuring selected contributions to the open seminar series of Lomonosov Moscow State University and Igor Sikorsky Kyiv Polytechnic Institute by mathematicians from China, Germany, France, Italy, Spain, Russia, Ukraine and the USA, the book will appeal to mathematicians and engineers working at the interface of these fields

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Table of contents (24 chapters)

  1. Front Matter

    Pages i-xviii
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  2. Modern Mechanics and Its Applications

    1. Front Matter

      Pages 1-1
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    2. Saddle Singularities in Integrable Hamiltonian Systems: Examples and Algorithms

      • Anatoly T. Fomenko, Vladislav A. Kibkalo
      Pages 3-26

    3. Reduction of the Lamé Tensor Equations to the System of Non-Coupled Tetraharmonic Equations

      • D. V. Georgievskii
      Pages 27-33

    4. Junction Flow Around Cylinder Group on Flat Platee

      • V. A. Voskoboinick, I. M. Gorban, A. A. Voskoboinick, L. N. Tereshchenko, A. V. Voskoboinick
      Pages 35-50

    5. Accounting for Shear Deformation in the Problem of Vibrations and Dissipative Heating of Flexible Viscoelastic Structural Element with Piezoelectric Sensor and Actuator

      • I. F. Kirichok, Y. A. Zhuk, S. Yu. Kruts
      Pages 51-69

    6. A Stochastic Theory of Scale-Structural Fatigue and Structure Durability at Operational Loading

      • E. B. Zavoychinskaya
      Pages 71-89

    7. On Tikhonov Regularization of Optimal Distributed Control Problem for an Ill-Posed Elliptic Equation with p-Laplace Operator and \(L^1\)-type of Non-linearity

      • Peter I. Kogut, Olha P. Kupenko
      Pages 91-111

    8. Symmetries and Conservation Laws of the Equations of Two-Dimensional Shallow Water Over Uneven Bottom

      • A. V. Aksenov, K. P. Druzhkov
      Pages 113-163

    9. Existence and Stability Analysis of Solutions for an Ultradian Glucocorticoid Rhythmicity and Acute Stress Model

      • Casey Johnson, Roman M. Taranets, Nataliya Vasylyeva, Marina Chugunova
      Pages 165-194

    10. Mixed Dirichlet-Transmission Problems in Non-smooth Domains

      • Nataliya Vasylyeva
      Pages 195-229

  4. Advances in Control and Optimization

    1. Front Matter

      Pages 345-345
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    2. Uniform Global Attractor for a Class of Nonautonomous Evolution Hemivariational Inequalities with Multidimensional “Reaction-Velocity” Law

      • Michael Z. Zgurovsky, Ciro D’Apice, Umberto De Maio, Nataliia V. Gorban, Pavlo O. Kasyanov, Oleksiy V. Kapustyan et al.
      Pages 347-368

    3. On a Lyapunov Characterization of Input-To-State Stability for Impulsive Systems with Unstable Continuous Dynamics

      • Petro Feketa, Alexander Schaum, Thomas Meurer
      Pages 369-380
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Editors and Affiliations

  • Lomonosov Moscow State University, Moscow, Russia

    Victor A. Sadovnichiy

  • National Technical University of Ukraine “Igor Sikorsky Kyiv Polytechnic Institute”, Kyiv, Ukraine

    Michael Z. Zgurovsky

Bibliographic Information

  • Book Title: Contemporary Approaches and Methods in Fundamental Mathematics and Mechanics

  • Editors: Victor A. Sadovnichiy, Michael Z. Zgurovsky

  • Series Title: Understanding Complex Systems

  • DOI: https://doi.org/10.1007/978-3-030-50302-4

  • Publisher: Springer Cham

  • eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)

  • Copyright Information: Springer Nature Switzerland AG 2021

  • Softcover ISBN: 978-3-030-50301-7Published: 25 November 2020

  • eBook ISBN: 978-3-030-50302-4Published: 24 November 2020

  • Series ISSN: 1860-0832

  • Series E-ISSN: 1860-0840

  • Edition Number: 1

  • Number of Pages: XVIII, 522

  • Number of Illustrations: 21 b/w illustrations, 28 illustrations in colour

  • Topics: Applications of Mathematics, Complexity, Civil Engineering

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