A Mathematical Approach to Research Problems of Science and Technology

Part I Algebra.- Mathematics - As An Infrastructure of Technology and Science.- Remarks on Quantum Interaction Models by Lie Theory and Modular Forms via Non-Commutative Harmonic Oscillators.- Introduction to Public-Key Cryptography.- Code-Based Public-Key Encryption.- Gröbner bases and its applications.- Part II Geometry.- Stability Analysis for Variational Problems for Surfaces with Constraint.- Discrete Models of Isoperimetric Deformation of Plane Curves.- Computing Optimal Cycles of Homology Groups.- Singularity Theory of Differentiable Maps and Data Visualization.- Part III Analysis.- Mathematical Analysis for Pattern Formation Problems.- Models and Applications of Organism Transportation.- The Renormalization Group Method for Ordinary Differential Equations.- A Phase Field Approach to Mathematical Modeling of Crack Propagation.- Variational Methods in Differential Equations.- Part IV Probability and Statistics.- Finite Markov Chains and Markov Decision Processes.- Introduction to The Premium Principle Based on The Wang Transform.- Stochastic Process Models.- Signal Detection and Model Selection.- Regression Analysis and Its Development.- Stochastic Analytical Models in Mathematical Finance.- An Introduction to the Minimum Description Length Principle.- An Introduction to Ergodic Theory.- Part V Applied Mathematics.- Discrete Optimization: Network Flows and Matchings.- Strict Feasibility of Conic Optimization Problems.- Theory of Automata, Abstraction and Applications.- Markov Chain Monte Carlo Algorithms.- Modeling of Fluid Flows by Nonlinear Schrödinger Equation.- Financial Applications of Quasi-Monte Carlo Methods.- Pure Mathematics and Applied Mathematics are Inseparably intertwined - Observation of the Early Analysis of the Infinity.- High Performance Computing for Mathematical Optimization Problem.- Part VI Application of Mathematics.- Modeling of Head-Disk Interface for Magnetic Recording.- Non-Stationary Analysis of Blast Furnace ThroughSolution of