About the Book
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.
Table of Contents:
Part I: Differential Equations, Optimal Control and Stabilization.- Burlakov, E. O. and Zhukovskiy, E. S: On Abstract Volterra Equations in Partially Ordered Spaces and Their Applications.- Burlakov, E. O. and Pluzhnikova, E. A: On Implicit Abstract Volterra Equations in Metric Spaces.- Vdovin, A. Yu. and Rubleva, S. S: On the Choice of Parameters of the Method of Dynamic Regularization for the Problem of Differentiation.- Gorbova, T. V., Pimenov, V. G., and Solodushkin, S. I: Numerical Algorithm for Nonlinear Partial Differential Equation with Heredity and its Program Implementation.- Zhukovskiy, S. E.: On Coincidence Points of Mappings between Partially Ordered Sets.- Zykov, I. V.: An Algorithm for Constructing Reachable Sets for Systems with Multiple Integral Constraints.- Kim, A. V., Andryushechkina, N. A., and Kim, V. V: Similarity and Structural Stability with respect to Delay of FDE Phase Portraits.- Kim, A. V. and Andryushechkina, N. A: Real-Time Modeling of System State During the Process of More Precise Estimation of the Initial Position.-Kim, A. V. and Andryushechkina, N. A: Finite Difference Scheme for Special System of Partial Differential Equations.- Layton, W. and McLaughlin, M: On URANS Congruity with Time Averaging: Analytical Laws Suggest Improved Models.- Lebedev, P. D. and Uspenskii, A. A: Geometric Singularities of the Solution of the Dirichlet Boundary Problem for Hamilton–Jacobi Equation with a Low Order of Smoothness of the Border Curve.- Pavlova, N. G.: Applications of the Theory of Covering Maps to the Study of Dynamic Models of Economic Processes with Continuous Time.- Cherepennikov, V. B. and Kim, A. V: Smooth Solutions of Linear Functional Differential Equations of Neutral Type.- Chernikova, N. Yu., Laneev, E. B., Muratov, M. N., and Ponomarenko, E. Yu: On an Inverse Problem to a Mixed Problem for the Poisson Equation.- Shevchenko, R. I.: Stabilization of the Two Degree of Freedom Linear Milling Model.- Part II: Stochastic Methods.- Bashkirtseva, I. A. and Belyaeva, T. D: Stochastic Sensitivity Analysis and Control in the Bistable Electronic Generator.- Bashkirtseva, I. A. and Zaitseva, S. S: Noise-induced Effects in Goldbeter Model.- Belyaev, A. V. and Ryazanova, T. V: Piecewise Smooth Map of Neuronal Activity: Deterministic and Stochastic Cases.- Kolinichenko, A. P. and Ryashko, L. B: Analysis of Spatial Patterns in the Distributed Stochastic Brusselator.- Nasyrova, V. M. and Ryashko, L. B: Stochastic Splitting of Oscillations in a Discrete Model of Neural Activity.- Ryashko, L. B. and Slepukhina, E. S: Stochastic Deformation of Invariant Tori in Neuron Model.- Part III: Topology and Function Approximation.- Lipin, A. E.: Resolvability of Pseudocompact Spaces at a Point.- Pleshcheva, E. A: Fast Algorithms for Function Decomposition Based on n-Separate Periodic Wavelets.- Part IV: Mathematical Biology and Bioinformatics.- Averbukh, V. L., Mikhailov, I. O., Forghani, M. A., and Vasev, P. A: 3D Visualization to Analyze Multidimensional QBiological and Medical Data.- Markov, N. S. and Ryvkin, A. M: The Peculiarities of Calcium Sparks Formation in Cardiac Cells in silico.- Myachina, T. A. and Lookin, O. N: A Configurable Algorithm for Determining the Mean Sarcomere Length of a Cardiomyocyte by Discrete Fourier Transform.- Pravdin, S. F., Nezlobinsky, T. V., Epanchintsev, T. I., Dierckx, H. and Panfilov, A. V: Simulation of Low-voltage Cardioversion in a Two-Dimensional Isotropic Excitable Medium Using Ionic Cell Models.- Razumov, A. A. and Ushenin, K. S: The Influence of Left Ventricle Wall Thickness and Scar Fibrosis on Pseudo-ECG.- Ryvkin, A. M. and Budeeva, E. A: Modeling the Effect of Ion Channel Inhibitors on the Functioning of the Cardiac Sinoatrial Node Cells.- Khamzin, S. Yu. and Iaparov, B. I: The Influence of Ryanodine Receptors’ Non-uniform Arrangement on the Probability of Ca2+ Sparks.- Stroshkov, V. P., Zotova, N. V., Novikov, N. V., Nosyrev, M. B., Semin,A. N., Kitonsa, H: Methods of Evaluating the Adaptation of the Body of Agricultural Workers to Changing Conditions of Social and Industrial Environment.- Part V: Mathematical Modelling in Mining.- Makarov, N. V., V.N. Makarov., V. N., Lifanov, A. V., Materov, A. Y., and Kitonsa, H:Development of Mathematical Model of Circular Grill of Piece-Smooth Profiles and Creation on its Basis of Gas-Sucking Fans.- Makarov, V. N., Makarov, N. V., Lifanov, A. V., Materov, A. Y., and Kitonsa, H: Mathematical Model of Conformal Mappings in the Theory of Radial Grids of Mine Turbomachines.- Nosyrev, M. B., Makarov, N. V., Makarov, V. N., Ugolnikov, A. V., and Kitonsa, H: Mathematical Model of Hydrovortex Hetero-Coagulation.- Part VI: Mathematical Modelling in Economics.- Kolesnikov, S. I. and Dolzhenko, L. M: Methodology for Assessing the Level of the Territory’s Economic Security.- Novikov, N. V., Nosyrev, M. B., Plotnikov, N. S., Semin, A. N., Stroshkov, V. P., and Kitonsa H: TheThird Dimension of the Supply-Demand Diagram.- Part VII: Computer Science and Image Processing.- Veretennikov, A. B.: Proximity Full-text Searches of Frequently Occurring Words with a Response Time Guarantee.- Kostousov, V. B. and Dunaevskaya, K. V: Development and Research of Algorithm for Coordinates Correction on the Basis of Microrelief.- Kornilov, F. A. and Dunaeva, A. V: Method for Constructing Orthorectified Satellite Image using Stereo Imagery and Digital Surface Model.- Serezhnikova, T. I: An Effective Subgradient Method for Simultaneous Restoration and Segmentation of Blurred Images.
