Modern Discrete Mathematics and Analysis: With Applications in Cryptography, Information Systems and Modeling (Springer Optimization and Its Applications, 131)

✍ Scribed by Nicholas J. Daras (editor), Themistocles M. Rassias (editor)

• Publisher: Springer
• Year: 2018
• Tongue: English
• Leaves: 516
• Category: Library

✦ Synopsis

A variety of modern research in analysis and discrete mathematics is provided in this book along with applications in cryptographic methods and information security, in order to explore new techniques, methods, and problems for further investigation. Distinguished researchers and scientists in analysis and discrete mathematics present their research. Graduate students, scientists and engineers, interested in a broad spectrum of current theories, methods, and applications in interdisciplinary fields will find this book invaluable.

✦ Table of Contents

Preface
Contents
Contributors
Fixed Point Theorems in Generalized b-Metric Spaces
Introduction and Preliminaries
Linear Quasi-Contractions
Nonlinear Contractions
References
Orlicz Dual Brunn-Minkowski Theory: Addition, Dual Quermassintegrals and Inequalities
Introduction
Preliminaries
Mixed p-Quermassintegrals of Convex Bodies
Dual Mixed Quermassintegrals
Dual Mixed p-Quermassintegrals
Dual Mixed Harmonic p-Quermassintegrals
Orlicz Radial Harmonic Addition
Orlicz Dual Mixed Quermassintegral
Orlicz Dual Minkowski Inequality
Orlicz Dual Brunn-Minkowski Inequality
Dual Log-Minkowski Inequality
References
Modeling Cyber-Security
Introduction
Mathematical Definition of Cyberspace
Mathematical Description of Cyber-Attacks
Valuations and Vulnerabilities of Parts of a Node Constituent
Cyber-Effects and Cyber-Interactions
Description of Cyber Navigations and Protection from Unplanned Attacks
Cyber Navigations
Inadequacy of Cyber Nodes
Infected Cyber Nodes
Dangerous Navigations
Protection of Cyber Nodes from Unplanned Attacks
Description of Various Types of Cyber-Attacks and Protection
Passive Cyber-Attacks
Protected Cyber Nodes from Passive Attacks
Active Cyber-Attacks
Protected Cyber Nodes from Active Attacks
References
Solutions of Hard Knapsack Problems Using Extreme Pruning
Introduction
Lattices
Lenstra-Lenstra-Lovsz Algorithm (LLL)
Gram-Schmidt Orthogonalization (GSO)
LLL-Pseudocode
Analysis of LLL
Blockwise Korkine-Zolotarev (BKZ)
The Enumeration Subroutine
Extreme Pruning
Attacks to Subset Sum Problem
Birthday Attacks
Lattice Attacks
Experiments
Conclusions
Appendix
References
A Computational Intelligence System Identifying Cyber-Attacks on Smart Energy Grids
Introduction
Smart Energy Grids
Conceptual Framework
Conceptual Model
Cybersecurity for Smart Grid Systems
A New, Smart Era for the Energy Grids
Risks Involved
Threats
Types of Attacks
Cyber Attacks on Smart Grid
SCADA Systems
Methods of Attack
Literature Review
Power System Attack Datasets
SCADA Power System Architecture
Types of Scenarios
The Final Dataset
Methodology and Techniques
Extreme Learning Machines
Adaptive Elitist Differential Evolution (AEDE)
Adaptive Elitist Differential Evolution ELM (AEDE-ELM)
Results and Comparative Analysis
Discussion: Conclusions
References
Recent Developments of Discrete Inequalities for Convex Functions Defined on Linear Spaces with Applications
Introduction
Refinements of Jensen's Inequality
Preliminary Facts
General Results
Applications for f-Divergences
More General Results
A Lower Bound for Mean f-Deviation
Applications for f-Divergence Measures
Inequalities in Terms of Gâteaux Derivatives
Gâteaux Derivatives
A Refinement of Jensen's Inequality
A Reverse of Jensen's Inequality
Bounds for the Mean f-Deviation
Bounds for f-Divergence Measures
Inequalities of Slater's Type
Introduction
Slater's Inequality for Functions Defined on Linear Spaces
The Case of Finite Dimensional Linear Spaces
Some Applications for f-divergences
References
Extrapolation Methods for Estimating the Trace of the Matrix Inverse
Introduction
Overview of the Methods
Extrapolation of Moments
Prediction by the Aitken's Process
Estimation of Tr(A-1)
Hutchinson's Trace Estimation
Trace Estimation Through the Diagonal Approximation
Numerical Examples
Example 1: A Dense Matrix
Example 2: A Block Tridiagonal Matrix
Example 3: Application to Networks
Concluding Remarks
References
Moment Generating Functions and Moments of Linear Positive Operators
Preliminaries
M.G.F. and Moments of Exponential Type Operators
Bernstein Operators
Post-Widder Operators
Szász-Mirakyan Operators
Baskakov Operators
Lupaş Operators
Jain and Pethe Operators
Modified Baskakov Operators
Kantorovich-Type Operators
Bernstein-Kantorovich Operators
Szász-Mirakyan-Kantorovich Operators
Baskakov-Kantorovich Operators
Lupaş-Kantorovich Operators
Miheşan-Kantorovich Operators
References
Approximation by Lupaṣ–Kantorovich Operators
Introduction
Auxiliary Results
Main Results
References
Enumeration by e
Introduction and Summary of the Results
Proofs
Further Enumerative Formulas Related to e
References
Fixed Point and Nearly m-Dimensional Euler–Lagrange-Type Additive Mappings
Introduction and Preliminaries
RN-Approximation of Functional Equation (4)
References
Discrete Mathematics for Statistical and Probability Problems
Introduction
Discrete Mathematics and Statistics
Introduction
Latin Squares
Finite Geometry and Design Theory
Applications of Experimental Design
Discrete Mathematics and Probability
Algebraic Approach to Concept
Discrete Distance Measures
Fuzzy Logic Approach
Discussion
Appendix
References
On the Use of the Fractal Box-Counting Dimensionin Urban Planning
Introduction
Box-Counting Dimension and Urban Planning
Conclusions
References
Additive-Quadratic ρ-Functional Equations in Banach Spaces
Introduction and Preliminaries
Additive-Quadratic ρ-Functional Equation (1) in Banach Spaces
Additive-Quadratic ρ-Functional Equation (2) in Banach Spaces
References
De Bruijn Sequences and Suffix Arrays: Analysis and Constructions
Introduction
Preliminaries
Boolean Functions
Keystream Generators
Sequences and Suffix Arrays
De Bruijn Sequences
Properties of Suffix Arrays of De Bruijn Sequences
The Longest Common Prefix Array of a De Bruijn Sequence
Construction of De Bruijn Sequences Through Suffix Arrays
Suffix Arrays and Cross-Join Pairs
Conclusions
References
Fuzzy Empiristic Implication, A New Approach
Introduction
Preliminaries
Classical Implication
Fuzzy Implication
Construction of Fuzzy Implication Functions
S-N Implications
Reciprocal Implications
R Implications
QL Implications
f and g Implications
Convex Combinations
Symmetric Implication Functions
Approximate Reasoning
Choosing Fuzzy Implication Function
Empiristic Fuzzy Implications
Empiricism and Fuzzy Implication
Defining Empiristic Fuzzy Implication
Computation of Fuzzy Empiristic Implication Relation
Application
Selection of Logical Fuzzy Implication Through the Empiricist
Algorithm
Conclusions and Further Research
References
Adaptive Traffic Modelling for Network Anomaly Detection
Introduction
Network Monitoring
Traffic Modelling Detail Levels
Traffic Modelling Categories and Uses
Network Traffic Model Identification
SARIMA Traffic Modelling
State-Space Traffic Modelling
The Multi-Model Partitioning Algorithm (MMPA)
Detection Results Using Real Traffic Data
Conclusions
References
Bounds Involving Operator s-Godunova-Levin-Dragomir Functions
Introduction
Preliminary Results
Main Results
References
Closed-Form Solutions for Some Classes of Loaded Difference Equations with Initial and Nonlocal Multipoint Conditions
Introduction
Linear Difference Equations
Initial Value Problems
Problems with Nonlocal Conditions
Loaded Difference Equations
Loaded Problems with Homogeneous Conditions
Loaded Problems with Nonhomogeneous Conditions
Example Problems
References
Cauchy's Functional Equation, Schur's Lemma, One-dimensional Special Relativity, and Möbius's Functional Equation
Cauchy's Functional Equations
One-Dimensional Special Relativity
Möbius's Functional Equations
References
Plane-Geometric Investigation of a Proof of the Pohlke's Fundamental Theorem of Axonometry
Introduction
Ellipses Through Affine Geometry
The Four Ellipses Problem
The Circular Case
The Noncircular Case
Discussion
Appendix
References
Diagonal Fixed Points of Geometric Contractions
Introduction
Dependent Choice Principles
Conv-Cauchy Structures
Admissible Functions
Meir-Keeler Relations
Main Result
Particular Versions
Cirić-Presić Approach
Further Aspects
References
A More Accurate Hardy–Hilbert-Type Inequalitywith Internal Variables
Introduction
Some Lemmas
Main Results and Operator Expressions
Some More Accurate Reverses
References
An Optimized Unconditionally Stable Approach for the Solution of Discretized Maxwell's Equations
Introduction
Development of the Proposed Methodology
The Basic Algorithm
Performance Improvement
Theoretical Assessment
Numerical Validation
Conclusions
References
Author Correction to: Moment Generating Functionsand Moments of Linear Positive Operators