A Mathematical Approach to Research Problems of Science and Technology: Theoretical Basis and Developments in Mathematical Modeling (Mathematics for Industry Book 5)

This book deals with one of the most novel advances in mathematical modeling for applied scientific technology, including computer graphics, public-key encryption, data visualization, statistical data analysis, symbolic calculation, encryption, error correcting codes, and risk management. It also shows that mathematics can be used to solve problems from nature, e.g., slime mold algorithms. One of the unique features of this book is that it shows readers how to use pure and applied mathematics, especially those mathematical theory/techniques developed in the twentieth century, and developing now, to solve applied problems in several fields of industry. Each chapter includes clues on how to use "mathematics" to solve concrete problems faced in industry as well as practical applications. The target audience is not limited to researchers working in applied mathematics and includes those in engineering, material sciences, economics, and life sciences. 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