Modern Mathematics and Mechanics

1. Front Matter

   Pages i-xxii

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2. Differential Geometry

   1. Front Matter

      Pages 1-1

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   2. Convergence Almost Everywhere of Orthorecursive Expansions in Systems of Translates and Dilates

      • Vladimir V. Galatenko, Taras P. Lukashenko, Victor A. Sadovnichiy

      Pages 3-11

   3. Three-Dimensional Manifolds of Constant Energy and Invariants of Integrable Hamiltonian Systems

      • Anatoly T. Fomenko, Kirill I. Solodskih

      Pages 13-30

   4. Applying Circulant Matrices Properties to Synchronization Problems

      • Jose S. Cánovas

      Pages 31-56

   5. Existence and Invariance of Global Attractors for Impulsive Parabolic System Without Uniqueness

      • Sergey Dashkovskiy, Petro Feketa, Oleksiy V. Kapustyan, Iryna V. Romaniuk

      Pages 57-78

   6. Fraktal and Differential Properties of the Inversor of Digits of Q _s-Representation of Real Number

      • Oleg Barabash, Oleg Kopiika, Iryna Zamrii, Valentyn Sobchuk, Andrey Musienko

      Pages 79-95

   7. Almost Sure Asymptotic Properties of Solutions of a Class of Non-homogeneous Stochastic Differential Equations

      • Oleg I. Klesov, Olena A. Tymoshenko

      Pages 97-114

3. Solid Mechanics

   1. Front Matter

      Pages 115-115

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   2. Procedure of the Galerkin Representation in Transversely Isotropic Elasticity

      • Dimitri V. Georgievskii

      Pages 117-124

   3. Symmetries and Fundamental Solutions of Displacement Equations for a Transversely Isotropic Elastic Medium

      • Alexander V. Aksenov

      Pages 125-135

   4. Modification of Hydrodynamic and Acoustic Fields Generated by a Cavity with Fluid Suction

      • Volodymyr G. Basovsky, Iryna M. Gorban, Olha V. Khomenko

      Pages 137-158

   5. Numerical Modeling of the Wing Aerodynamics at Angle-of-Attack at Low Reynolds Numbers

      • Iryna M. Gorban, Oleksiy G. Lebid

      Pages 159-179

   6. Strong Solutions of the Thin Film Equation in Spherical Geometry

      • Roman M. Taranets

      Pages 181-192

4. Dynamics of Differential and Difference Equations and Applications

   1. Front Matter

      Pages 193-193

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   2. Sequence Spaces with Variable Exponents for Lattice Systems with Nonlinear Diffusion

      • Xiaoying Han, Peter E. Kloeden, Jacson Simsen

      Pages 195-214

   3. Attractors for a Random Evolution Equation with Infinite Memory: An Application

      • María J. Garrido-Atienza, Björn Schmalfuß, José Valero

      Pages 215-236

   4. Non-Lipschitz Homogeneous Volterra Integral Equations

      • M. R. Arias, R. Benítez, V. J. Bolós

      Pages 237-259

   5. Solving Random Ordinary and Partial Differential Equations Through the Probability Density Function: Theory and Computing with Applications

      • J. Calatayud, J.-C. Cortés, M. Jornet, A. Navarro-Quiles

      Pages 261-282

   6. A Strong Averaging Principle for Lévy Diffusions in Foliated Spaces with Unbounded Leaves

      • Paulo Henrique da Costa, Michael A. Högele, Paulo Regis Ruffino

      Pages 283-311

In this book international expert authors provide solutions for modern fundamental problems including the complexity of computing of critical points for set-valued mappings, the behaviour of solutions of ordinary differential equations, partial differential equations and difference equations, or the development of an abstract theory of global attractors for multi-valued impulsive dynamical systems. These abstract mathematical approaches are applied to problem-solving in solid mechanics, hydro- and aerodynamics, optimization, decision making theory and control theory. This volume is therefore relevant to mathematicians as well as engineers working at the interface of these fields.

• differential geometry
• solid mechanics
• modern methods of optimization and control
• difference equations and applications
• decision-making theory
• Integrable Hamiltonian Systems
• Topological entropy

• Lomonosov Moscow State University, Moscow, Russia

  Victor A. Sadovnichiy

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

  Michael Z. Zgurovsky

Victor Antonovich Sadovnichiy is a Russian mathematician, winner of the 1989 USSR State Prize. Since 1992 he has been the rector of Moscow State University. Sadovnichiy was born in the village Krasnopavlovka in Kharkiv Oblast, now in Ukraine. He graduated from the Department of Mechanics and Mathematics of Moscow State University and defended his doctoral thesis in 1974. In 1975 he became Professor, since 1982 until the present day he is the head of the Mathematical Analysis chair of the department. He held different offices in the administration of the University until he was elected the rector in 1992. In 1996, 2001 and 2005 Sadovnichiy was reelected without any other candidates. On numerous occasions Viktor Sadovnichiy was accused of being one of the organizers of the infamous antisemitic admission policies of the Department of Mechanics and Mathematics during the 1970s and the 1980s. 
Sadovnichiy has been a member of the Russian Academy of Sciences since 1994, Doctor Emeritus of many universities throughout the world, as well as the author of some 150 works. In 1989 he was awarded with the USSR State Prize. He is also currently a Vice-President of the Russian Academy of Sciences. In 2008, Sadovnichiy received an honorary doctorate from the University of Belgrade. In his article “On the Possibilities to Forecast the Current Crisis and its Second Wave” (with Askar Akaev and Andrey Korotayev) in the Russian academic journal “Ekonomicheskaya politika” (December 2010. Issue 6. Pages 39-46[1]) he published «a forecast of the second wave of the crisis, which suggests that it may start in July — August, 2011».

Michael Zgurovsky is the Rector of National Technical University of Ukraine Kiev Polytechnic Institute since 1992. He was born on January 30, 1950 in Scala-Podilska. He studied at the College of Control Systems of Kiev Polytechnic Institute, and graduated from Kiev Polytechnic Institute in 1975. Michael Zgurovsky is the Doctor of Technical Sciences, Academician of the National Academy of Sciences of Ukraine and Academician of the Academy of Sciences of Russian Federation. During 1994-1999 he was the Minister of Education of Ukraine. He is the Director of the Institute for Applied System Analysis of the National Academy of Sciences of Ukraine and Ministry of Education and Science of Ukraine. Among his scientific interests are sustainable development, system analysis, decision making under uncertainty conditions, and analysis and modeling of complex systems of various nature.
Michael Zgurovsky is an author of more that 300 scientific publications, including 30 books published in different countries and he has made 25 inventions. He is the President of the Association of Rectors of Technical Universities of Ukraine. He is a Member of the Academies of Science of many countries, and many international educational institutions, Senior Member of IEEE, Member of the Governing Board of UNESCO Institute for Information Technologiesin Education (Moscow, Russia), the National Representative of Ukraine in CODATA, Member of EDNES, National Representative of Ukraine in ICSU.

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