A Mathematical Approach to Research Problems of Science and Technology: Theoretical Basis and Developments in Mathematical Modeling

Front Matter....Pages i-xii
Front Matter....Pages 1-1
Mathematics: As an Infrastructure of Technology and Science....Pages 3-15
Remarks on Quantum Interaction Models by Lie Theory and Modular Forms via Non-commutative Harmonic Oscillators....Pages 17-34
Introduction to Public-Key Cryptography....Pages 35-45
Code-Based Public-Key Encryption....Pages 47-55
Gröbner Basis and Its Applications....Pages 57-67
Front Matter....Pages 69-69
Stability Analysis for Variational Problems for Surfaces with Constraint....Pages 71-87
Discrete Models of Isoperimetric Deformation of Plane Curves....Pages 89-99
Computing Optimal Cycles of Homology Groups....Pages 101-118
Singularity Theory of Differentiable Maps and Data Visualization....Pages 119-130
Front Matter....Pages 131-131
Mathematical Analysis for Pattern Formation Problems....Pages 133-139
Models and Applications of Organism Transportation....Pages 141-150
The Renormalization Group Method for Ordinary Differential Equations....Pages 151-159
A Phase Field Approach to Mathematical Modeling of Crack Propagation....Pages 161-170
Variational Methods in Differential Equations....Pages 171-186
Front Matter....Pages 187-187
Finite Markov Chains and Markov Decision Processes....Pages 189-206
Introduction to the Premium Principle Based on the Wang Transform....Pages 207-217
Stochastic Process Models....Pages 219-238
Signal Detection and Model Selection....Pages 239-248
Regression Analysis and Its Development....Pages 249-262
Stochastic Analytical Models in Mathematical Finance....Pages 263-277
Front Matter....Pages 187-187
An Introduction to the Minimum Description Length Principle....Pages 279-296
An Introduction to Ergodic Theory....Pages 297-309
Front Matter....Pages 311-311
Discrete Optimization: Network Flows and Matchings....Pages 313-323
Strict Feasibility of Conic Optimization Problems....Pages 325-335
Theory of Automata, Abstraction and Applications....Pages 337-348
Markov Chain Monte Carlo Algorithms....Pages 349-363
Modeling of Fluid Flows by Nonlinear Schrödinger Equation....Pages 365-378
Financial Applications of Quasi-Monte Carlo Methods....Pages 379-392
Pure Mathematics and Applied Mathematics are Inseparably Intertwined: Observation of the Early Analysis of the Infinity....Pages 393-399
High Performance Computing for Mathematical Optimization Problem....Pages 401-421
Front Matter....Pages 423-423
Modeling of Head-Disk Interface for Magnetic Recording....Pages 425-438
Nonstationary Analysis of Blast Furnace Through Solution of Inverse Problem and Recurrence Plot....Pages 439-452
Time-Periodic Nonlinear Steady Field Analysis....Pages 453-466
Mathematical Models in First-Principles Calculations for Materials Science....Pages 467-480
Mathematics and Manufacturing: The Symbolic Approach....Pages 481-494
Error Correcting Codes Based on Probabilistic Decoding and Sparse Matrices....Pages 495-504
Back Matter....Pages 505-507