Book Volume 5 2014

A Mathematical Approach to Research Problems of Science and Technology

Theoretical Basis and Developments in Mathematical Modeling

ISBN: 978-4-431-55059-4 (Print) 978-4-431-55060-0 (Online)

Table of contents (36 chapters)

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  1. Front Matter

    Pages i-xii

  2. Algebra

    1. Front Matter

      Pages 1-1

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      Chapter

      Pages 3-15

      Mathematics: As an Infrastructure of Technology and Science

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      Chapter

      Pages 17-34

      Remarks on Quantum Interaction Models by Lie Theory and Modular Forms via Non-commutative Harmonic Oscillators

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      Chapter

      Pages 35-45

      Introduction to Public-Key Cryptography

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      Chapter

      Pages 47-55

      Code-Based Public-Key Encryption

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      Chapter

      Pages 57-67

      Gröbner Basis and Its Applications

  3. Geometry

    1. Front Matter

      Pages 69-69

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      Chapter

      Pages 71-87

      Stability Analysis for Variational Problems for Surfaces with Constraint

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      Chapter

      Pages 89-99

      Discrete Models of Isoperimetric Deformation of Plane Curves

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      Chapter

      Pages 101-118

      Computing Optimal Cycles of Homology Groups

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      Chapter

      Pages 119-130

      Singularity Theory of Differentiable Maps and Data Visualization

  4. Analysis

    1. Front Matter

      Pages 131-131

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      Chapter

      Pages 133-139

      Mathematical Analysis for Pattern Formation Problems

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      Chapter

      Pages 141-150

      Models and Applications of Organism Transportation

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      Chapter

      Pages 151-159

      The Renormalization Group Method for Ordinary Differential Equations

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      Chapter

      Pages 161-170

      A Phase Field Approach to Mathematical Modeling of Crack Propagation

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      Chapter

      Pages 171-186

      Variational Methods in Differential Equations

  5. Probability and Statistics

    1. Front Matter

      Pages 187-187

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      Chapter

      Pages 189-206

      Finite Markov Chains and Markov Decision Processes

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      Chapter

      Pages 207-217

      Introduction to the Premium Principle Based on the Wang Transform

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      Chapter

      Pages 219-238

      Stochastic Process Models

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      Chapter

      Pages 239-248

      Signal Detection and Model Selection

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      Chapter

      Pages 249-262

      Regression Analysis and Its Development

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      Chapter

      Pages 263-277

      Stochastic Analytical Models in Mathematical Finance

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