Mathematical Analysis With Applications

1. Front Matter

   Pages i-xlii

   PDF

2. Differential Equations, Optimal Control and Stabilization

   1. Front Matter

      Pages 1-1

      PDF

   2. On Abstract Volterra Equations in Partially Ordered Spaces and Their Applications

      • E. O. Burlakov, E. S. Zhukovskiy

      Pages 3-11

   3. On Implicit Abstract Volterra Equations in Metric Spaces

      • E. O. Burlakov, E. A. Pluzhnikova

      Pages 13-23

   4. On the Choice of Parameters of the Method of Dynamic Regularization for the Problem of Differentiation

      • A. Yu. Vdovin, S. S. Rubleva

      Pages 25-32

   5. Crank–Nicolson Numerical Algorithm for Nonlinear Partial Differential Equation with Heredity and Its Program Implementation

      • T. V. Gorbova, V. G. Pimenov, S. I. Solodushkin

      Pages 33-43

   6. On Coincidence Points of Mappings Between Partially Ordered Sets

      • S. E. Zhukovskiy

      Pages 45-50

   7. An Algorithm for Constructing Reachable Sets for Systems with Multiple Integral Constraints

      • I. V. Zykov

      Pages 51-60

   8. Similarity and Structural Stability with Respect to Delay of FDE Phase Portraits

      • A. V. Kim, N. A. Andryushechkina, V. V. Kim

      Pages 61-67

   9. Real-Time Modeling of System State During the Process of More Precise Estimation of the Initial Position

      • A. V. Kim, N. A. Andryushechkina

      Pages 69-77

   10. Finite Difference Scheme for Special System of Partial Differential Equations

       • A. V. Kim, N. A. Andryushechkina

       Pages 79-83

   11. On URANS Congruity with Time Averaging: Analytical Laws Suggest Improved Models

       • W. Layton, M. McLaughlin

       Pages 85-108

   12. Geometric Singularities of the Solution of the Dirichlet Boundary Problem for Hamilton–Jacobi Equation with a Low Order of Smoothness of the Border Curve

       • P. D. Lebedev, A. A. Uspenskii

       Pages 109-122

   13. Applications of the Theory of Covering Maps to the Study of Dynamic Models of Economic Processes with Continuous Time

       • N. G. Pavlova

       Pages 123-129

   14. Smooth Solutions of Linear Functional Differential Equations of Neutral Type

       • V. B. Cherepennikov, A. V. Kim

       Pages 131-139

   15. On an Inverse Problem to a Mixed Problem for the Poisson Equation

       • N. Yu. Chernikova, E. B. Laneev, M. N. Muratov, E. Yu. Ponomarenko

       Pages 141-149

   16. Stabilization of the Two Degree of Freedom Linear Milling Model

       • R. I. Shevchenko

       Pages 151-159

3. Stochastic Methods

   1. Front Matter

      Pages 161-161

      PDF

   2. Stochastic Sensitivity Analysis and Control in the Bistable Electronic Generator

      • I. A. Bashkirtseva, T. D. Belyaeva

      Pages 163-172

   3. Noise-Induced Effects in Goldbeter Model

      • I. A. Bashkirtseva, S. S. Zaitseva

      Pages 173-182

This proceedings volume covers research in key areas of applied mathematical analysis, and gathers works presented at the international conference “Concord-90,” in honor of the 90th birthday of Professor Constantin Corduneanu (1928-2018). The event – which Professor Corduneanu was able to attend – was held at Ural Federal University in Ekaterinburg, Russia, on July 26-28, 2018.


Professor Corduneanu’s research in mathematical analysis spanned nearly seven decades and explored a range of important issues in the field, including studies of global existence, stability problems, and oscillation theory, with special emphasis on various classes of nonlinear equations. He published over two hundred articles and several books, including “Almost Periodic Oscillations and Waves” (Springer, 2009).


In this volume the reader will find selected, peer-reviewed articles from seven fields of research – Differential Equations, Optimal Control and Stabilization; Stochastic Methods; Topology and Functions Approximation; Mathematical Biology and Bioinformatics; Mathematical Modeling in Mining; Mathematical Modeling in Economics; and Computer Science and Image Processing – which honor and reflect Professor Corduneanu’s legacy in the fields of oscillation, stability and control theory.

• Nonlinear Analysis
• Partial Differential Equations
• Difference Equations
• Ordinary Differential Equations
• Numerical Analysis
• Fourier Analysis
• Harmonic Analysis
• Stability Theory

• Department of Exact Sciences and Engineering, Portuguese Military Academy, Amadora, Portugal

  Sandra Pinelas

• Ural Branch, Russian Academy of Sciences, Yekaterinburg, Russia

  Arkadii Kim

• Faculty of Mechanics and Mathematics, Moscow State University, Moscow, Russia

  Victor Vlasov

Sandra Pinelas is a Professor at the Department of Exact Sciences and Engineering, which is part of the Military Academy in Amadora, Portugal. She currently serves on the editorial boards of several journals, including the International Journal of Mathematics and Computation, and Contemporary Analysis and Applied Mathematics.

Arkadii Kim is a Senior Researcher at the Institute of Mathematics and Mechanics, Ural Federal University, Russia. He currently serves on the editorial board of the International Journal of Control, Automation and Systems, published by Springer.


Victor Vlasov is a Professor at the Faculty of Mechanics and Mathematics, Moscow Lomonosov State University, Russia. He currently serves on the editorial board of the Differential Equations journal, published by Springer.

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