Responding to the growing demand for rigorous modeling frameworks capable of addressing complex technological challenges across disciplines, this book offers a coherent panorama of contemporary methodologies. These span lossless image compression algorithms, electrical impedance tomography and extragradient methods for variational inequalities in Banach spaces. It further examines multiphysics modeling in environmental engineering, grid-supported magnetic levitation systems and the optimization of water transport in porous media for sustainable irrigation. Foundational stochastic tools – such as gamma processes and hidden Markov models for reliability and maintenance planning – are integrated with theoretical advances, including matrix polynomials on noncommutative sets.
Table of Contents:
Chapter 1. Prediction of Pixel Component Brightness in the Process of Progressive Hierarchical Lossless Image Compression 1
A. SHPORTKO and A. BOMBA
1.1. Introduction 1
1.2. Problem statement 3
1.3. Pixel bypass sequence for implementing progressive hierarchical lossless image compression 6
1.4. Basic and additional symmetric hierarchical predictors 9
1.5. Asymmetric hierarchical predictors 14
1.6. Integrated application of hierarchical predictors 21
1.7. Conclusions and further prospects 26
1.8. References 27
Chapter 2. Spatial Analogues of Numerical Quasiconformal Mapping Methods for Identifying the Parameters of Quasiideal Fields 29
A. BOMBA and M. BOICHURA
2.1. Introduction 29
2.2. Problem statement 30
2.3. Problem statement in the complex quasipotential domain 37
2.4. An approximate representation of the problem 42
2.5. Conclusions and further prospects 58
2.6. References 59
Chapter 3. Complexity of Extragradient-type Methods for Variational Inequalities in Banach Space 61
V. SEMENOV, O. KOVALENKO and S. DENYSOV
3.1. Introduction 61
3.2. Preliminaries 65
3.3. Variational inequalities 69
3.4. Algorithms 71
3.5. Analysis 73
3.6. Conclusions 81
3.7. Acknowledgments 82
3.8. References 82
Chapter 4. Effect of Heat Generation Resulting from Biodegradation on the Surface Subsidence of a Solid Waste Storage Facility 87
L. SHOSTAK and P. MARTYNIUK
4.1. Introduction 87
4.2. Heat generation during the biodegradation of organic residues 89
4.3. Generation of greenhouse gases during the biodegradation of organic residues 95
4.4. Kinetics of biodegradation processes 97
4.5. Surface settlement of a solid waste landfill 99
4.6. The kinematic boundary condition at the upper moving boundary in the case of biodegradation 101
4.7. Modified consolidation equation considering biodegradation 104
4.8. Mathematical model of MSW landfill compaction considering the effect of biodegradation and heat release 107
4.9. Finite element method in the problem of non-isothermal waste consolidation 109
4.10. Approximation of the kinematic boundary condition 113
4.11. Results of numerical experiments 114
4.12. Conclusion 122
4.13. References 122
Chapter 5. Grid Computing in the Study of Magnetic Levitation Systems 127
S. LYASHKO, S.S. ZUB, I.G. YALOVEGA and V.S. LYASHKO
5.1. Overview of the computational approach 127
5.2. Introduction 128
5.3. Poisson brackets and motion equations 129
5.4. Mathematical model 131
5.5. Numerical experiment method 134
5.6. Geometric integrator 135
5.7. Estimation of the model's physical quantities 136
5.8. Methods and programming tools 137
5.9. Parallel computing using grid and cloud resources for Monte Carlo trajectory generation 138
5.10. Conclusions 140
5.11. References 140
Chapter 6. Simulation and Optimization of Water Transfer in a Porous Pipe System and Polygon Porous Medium 143
D.A. KLYUSHIN, V.A. KOLESNYKOV and A.A. TYMOSHENKO
6.1. Introduction 143
6.2. Physical model 144
6.3. Richards–Klute equation on a graph 146
6.4. Weak form of the Richards–Klute equation on a graph 148
6.5. Existence theorem 151
6.6. Stability results 152
6.7. Numerical approximation 154
6.8. Numerical experiments 155
6.9. Optimal control of source intensity in Richards' equation for polygon-type areas in a porous medium 158
6.10. Variational method 160
6.11. Numerical approach 161
6.12. Area examples 164
6.13. Alternating direction method 165
6.14. Conclusion 167
6.15. References 168
Chapter 7. Some Basic Properties of Gamma Processes 171
F. FOURATI and N. LIMNIOS
7.1. Introduction 171
7.3. Gamma processes 181
7.4. Gamma process as a Markov process 188
7.5. Gamma processes in random environment 190
7.6. Extended gamma processes and their connection with Cox processes 192
7.7. References 196
Chapter 8. A Hidden Markov Model Framework for Reliability Evaluation and Maintenance Planning 199
M.L. GAMIZ, N. LIMNIOS and M.C. SEGOVIA-GARCIA
8.1. Introduction 199
8.2. Hidden Markov models 202
8.3. Reliability estimation and maintenance policies 220
8.4. Conclusion 234
8.5. Acknowledgments 235
8.6. References 235
Chapter 9. Matrix Polynomials on a Set of Noncommutative Matrices: Basic Properties 237
V.L. MAKAROV, O.F. KASHPUR and B.O. BOICHENKO
9.1. Introduction 237
9.2. Laguerre and Laguerre–Cayley matrix polynomials: basic properties 238
9.3. Hermite matrix polynomials: basic properties 244
9.4. Fundamental Lagrange matrix polynomials 245
9.5. Conclusion 246
9.6. References 246
Chapter 10. Quantum Hypothesis of Olfactory Perception. 249
D. KOROLIOUK, V. COLIZZI, M. ZOZIUK, M. MATTEI, and S. MARINI
10.1. Introduction 249
10.2. Functional-analytic framework 251
10.3. Molecular vibrational spectra and spectral theory 254
10.4. Spectroscopic observables and selection rules 257
10.5. Inelastic electron tunneling model: Hamiltonian formulation 260
10.6. Transition rates and resonance conditions 262
10.7. Thermal and open-system effects 265
10.8. Relation to Marcus theory and semiclassical limits 267
10.9. Engineering implications and design principles 270
10.10. Critical assessment and limitations 272
10.11. Conclusions and outlook 273
10.12. Appendix. Implications for medical sciences and biomedical ligand design 274
10.13. References 281
List of Authors 285
Index 289
About the Author :
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.
