Operations Research Engineering and Cyber Security Trends in Applied Mathematics and Technology 1st Edition by Nicholas Daras, Themistocles Rassias ISBN 3319846671 9783319846675

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ISBN 10:       3319846671
ISBN 13: 978-3319846675
Author:         Nicholas J. Daras, Themistocles M. Rassias

Mathematical methods and theories with interdisciplinary applications are presented in this book. The eighteen contributions presented in this Work have been written by eminent scientists; a few papers are based on talks which took place at the International Conference at the Hellenic Artillery School in May 2015. Each paper evaluates possible solutions to long-standing problems such as the solvability of the direct electromagnetic scattering problem, geometric approaches to cyber security, ellipsoid targeting with overlap, non-equilibrium solutions of dynamic networks, measuring ballistic dispersion, elliptic regularity theory for the numerical solution of variational problems, approximation theory for polynomials on the real line and the unit circle, complementarity and variational inequalities in electronics, new two-slope parameterized achievement scalarizing functions for nonlinear multiobjective optimization, and strong and weak convexity of closed sets in a Hilbert space.
Graduate students, scientists, engineers and researchers in pure and applied mathematical sciences, operations research, engineering, and cyber security will find the interdisciplinary scientific perspectives useful to their overall understanding and further research.

Operations Research, Engineering, and Cyber Security: Trends in Applied Mathematics and Technology 1st Table of contents:

1. Complementarity Problem and Variational Inequalities in Electronics

• The Complementarity Relation
• The Complementarity Relation in Electronics
• The Complementarity Problem
• The Complementarity Problem in Electronics
• A Clipping Circuit with Ideal Diode
• On the Use of Variational Inequalities in Electronics
• The Convex Subdifferential Relation
• The Convex Subdifferential Relation and the Complementarity Relation
• The Convex Subdifferential Relation in Electronics
• The Variational Inequality Model
• The Variational Inequality Model in Electronics
• A General Clipping Circuit
• A Rectifier-Stabilizer Circuit
• A General Framework
• A Sampling Gate
• Non-regular Dynamical Systems
• Assumption (G1) and Kalman–Yakubovich–Popov Lemma
• A Non-regular Circuit

2. Diode and Transistor Models

• Ideal Diode Model
• Practical Diode Model
• Complete Diode Model
• Zener Diode Models
• Varistor Model
• Transistor Models

3. Electromagnetic Scattering and Compatibility

• Electromagnetic Scattering by a Chiral Impedance Screen
  • Introduction
  • Setting Up the Problem
  • Uniqueness Results
  • Existence of the Solution
  • Conclusions
• Electromagnetic Compatibility (EMC) in Challenging Environments
  • Introduction
  • EMC in the Context of Electromagnetic System Design
  • EMI Sources, Coupling Paths, and Potential Victims
  • Shielding, Non-linear Protection, and Filtering
  • Analysis and Design Tools: Simulation and Testing
  • Uncertainty and Lifetime Compliance
  • Conclusions

4. Optimization and Network Security

• Cybersecurity Investments with Nonlinear Budget Constraints: Analysis of the Marginal Expected Utility
  • Introduction
  • The Model
  • Equivalent Formulation of the Variational Inequality
  • Numerical Example
  • Conclusions
• A Review of Several Optimization Problems Related to Security in Networked Systems
  • Introduction
  • Application of Convex Optimization in Network Security
  • Application of Multi-Objective Distributed Constraint Optimization
  • Optimization Problems in Security for Power Networks
  • Conclusion

5. Co-polynomials and Spectral Transformations

• On Co-polynomials on the Real Line and the Unit Circle
  • Introduction
  • Orthogonal Polynomials on the Real Line and Spectral Transformations
  • Co-Polynomials on the Real Line
  • Zeros and Inequalities
  • A Transfer Matrix Approach
  • Spectral Transformations of COPRL
  • Co-polynomials on the Unit Circle
  • Verblunsky Coefficients and LU Factorization

6. Geometric Approaches and Information Geometry

• On Some Information Geometric Approaches to Cyber Security
  • The Fisher Information Metric
  • Information Geometry of Gaussians
  • Neighbourhoods of Uniformity in the Log-Gamma Manifold
  • Statistics of Finite Random Spacing Sequences
  • Protecting Devices with Obscuring Techniques
  • Dimensionality Reduction Methods

7. Mathematical Optimization and Control Theory

• From Elliptic Multiobjective Optimal Control to Jointly Convex Generalized Nash Equilibria
  • The Concept of Jointly Convex Generalized Nash Equilibrium Problems
  • Primal Formulation of Elliptic Multiobjective Optimal Control Problems
  • Reduced Multicontrol Formulation
• A Direct Approach to Lagrange Multipliers for Variational Inequalities
• Strong and Weak Convexity of Closed Sets in a Hilbert Space
  • Strongly Convex Sets
  • Uniform Strong Convexity
  • Local Strong Convexity

8. Non-Equilibrium Solutions and Hybrid Systems

• Non-equilibrium Solutions of Dynamic Networks: A Hybrid System Approach
  • Equilibrium Problems: Variational Inequalities and Projected Differential Equations
  • Hybrid Systems
  • A Dynamic Traffic Network Example
  • DLD Non-equilibrium Solution

9. Quality Assurance and Image Watermarking

• Measuring Ballistic Dispersion for the Purpose of Ammunition Quality Assurance
• Region-Based Watermarking for Images
  • Introduction to Image Watermarking and Geometric Distortions
  • Proposed Approach: Invariant Watermarking of Image Regions
  • Testing Watermark Retrieval Under Common Attacks

10. Inventory Management and Optimization

• Optimal Inventory Policies for Finite Horizon Inventory Models with Time-Varying Demand
  • A Specific Optimization Problem
  • Inventory Models with Time Varying Demand
  • Assumptions for Infinite and Finite Replenishment Rates

11. Pareto Efficiency and Scalarizing Functions

• Metrical Pareto Efficiency and Monotone EVP
  • Monotone EVP
  • Metrical Efficiency
  • Uniform Pareto Efficiency
• New Two-Slope Parameterized Achievement Scalarizing Functions for Nonlinear Multiobjective Optimization

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