Computational Methods and Mathematical Modeling in Cyberphysics and Engineering Applications 3

Dmitri Koroliouk, National Technical University of Ukraine (Igor Sikorsky Kyiv Polytechnic Institute).Sergiy Lyashko, Taras Shevchenko National University of Kyiv.Nikolaos Limnios, University of Technology of Compiegne, France.

• Chapter 1. Prediction of Pixel Component Brightness in the Process of Progressive Hierarchical Lossless Image Compression 1A. SHPORTKO and A. BOMBA1.1. Introduction 11.2. Problem statement 31.3. Pixel bypass sequence for implementing progressive hierarchical lossless image compression 61.4. Basic and additional symmetric hierarchical predictors 91.5. Asymmetric hierarchical predictors 141.6. Integrated application of hierarchical predictors 211.7. Conclusions and further prospects 261.8. References 27Chapter 2. Spatial Analogues of Numerical Quasiconformal Mapping Methods for Identifying the Parameters of Quasiideal Fields 29A. BOMBA and M. BOICHURA2.1. Introduction 292.2. Problem statement 302.3. Problem statement in the complex quasipotential domain 372.4. An approximate representation of the problem 422.5. Conclusions and further prospects 582.6. References 59Chapter 3. Complexity of Extragradient-type Methods for Variational Inequalities in Banach Space 61V. SEMENOV, O. KOVALENKO and S. DENYSOV3.1. Introduction 613.2. Preliminaries 653.3. Variational inequalities 693.4. Algorithms 713.5. Analysis 733.6. Conclusions 813.7. Acknowledgments 823.8. References 82Chapter 4. Effect of Heat Generation Resulting from Biodegradation on the Surface Subsidence of a Solid Waste Storage Facility 87L. SHOSTAK and P. MARTYNIUK4.1. Introduction 874.2. Heat generation during the biodegradation of organic residues 894.3. Generation of greenhouse gases during the biodegradation of organic residues 954.4. Kinetics of biodegradation processes 974.5. Surface settlement of a solid waste landfill 994.6. The kinematic boundary condition at the upper moving boundary in the case of biodegradation 1014.7. Modified consolidation equation considering biodegradation 1044.8. Mathematical model of MSW landfill compaction considering the effect of biodegradation and heat release 1074.9. Finite element method in the problem of non-isothermal waste consolidation 1094.10. Approximation of the kinematic boundary condition 1134.11. Results of numerical experiments 1144.12. Conclusion 1224.13. References 122Chapter 5. Grid Computing in the Study of Magnetic Levitation Systems 127S. LYASHKO, S.S. ZUB, I.G. YALOVEGA and V.S. LYASHKO5.1. Overview of the computational approach 1275.2. Introduction 1285.3. Poisson brackets and motion equations 1295.4. Mathematical model 1315.5. Numerical experiment method 1345.6. Geometric integrator 1355.7. Estimation of the model's physical quantities 1365.8. Methods and programming tools 1375.9. Parallel computing using grid and cloud resources for Monte Carlo trajectory generation 1385.10. Conclusions 1405.11. References 140Chapter 6. Simulation and Optimization of Water Transfer in a Porous Pipe System and Polygon Porous Medium 143D.A. KLYUSHIN, V.A. KOLESNYKOV and A.A. TYMOSHENKO6.1. Introduction 1436.2. Physical model 1446.3. Richards–Klute equation on a graph 1466.4. Weak form of the Richards–Klute equation on a graph 1486.5. Existence theorem 1516.6. Stability results 1526.7. Numerical approximation 1546.8. Numerical experiments 1556.9. Optimal control of source intensity in Richards' equation for polygon-type areas in a porous medium 1586.10. Variational method 1606.11. Numerical approach 1616.12. Area examples 1646.13. Alternating direction method 1656.14. Conclusion 1676.15. References 168Chapter 7. Some Basic Properties of Gamma Processes 171F. FOURATI and N. LIMNIOS7.1. Introduction 1717.3. Gamma processes 1817.4. Gamma process as a Markov process 1887.5. Gamma processes in random environment 1907.6. Extended gamma processes and their connection with Cox processes 1927.7. References 196Chapter 8. A Hidden Markov Model Framework for Reliability Evaluation and Maintenance Planning 199M.L. GAMIZ, N. LIMNIOS and M.C. SEGOVIA-GARCIA8.1. Introduction 1998.2. Hidden Markov models 2028.3. Reliability estimation and maintenance policies 2208.4. Conclusion 2348.5. Acknowledgments 2358.6. References 235Chapter 9. Matrix Polynomials on a Set of Noncommutative Matrices: Basic Properties 237V.L. MAKAROV, O.F. KASHPUR and B.O. BOICHENKO9.1. Introduction 2379.2. Laguerre and Laguerre–Cayley matrix polynomials: basic properties 2389.3. Hermite matrix polynomials: basic properties 2449.4. Fundamental Lagrange matrix polynomials 2459.5. Conclusion 2469.6. References 246Chapter 10. Quantum Hypothesis of Olfactory Perception. 249D. KOROLIOUK, V. COLIZZI, M. ZOZIUK, M. MATTEI, and S. MARINI10.1. Introduction 24910.2. Functional-analytic framework 25110.3. Molecular vibrational spectra and spectral theory 25410.4. Spectroscopic observables and selection rules 25710.5. Inelastic electron tunneling model: Hamiltonian formulation 26010.6. Transition rates and resonance conditions 26210.7. Thermal and open-system effects 26510.8. Relation to Marcus theory and semiclassical limits 26710.9. Engineering implications and design principles 27010.10. Critical assessment and limitations 27210.11. Conclusions and outlook 27310.12. Appendix. Implications for medical sciences and biomedical ligand design 27410.13. References 281List of Authors 285Index 289