Computational Mathematics and Variational Analysis

Preface
Contents
Scattering Relations of Elastic Waves by a Multi-Layered Thermoelastic Body
	1 Introduction
	2 Formulation
	3 Integral Representations and Far-Field Patterns
	4 Scattering Relations
	References
Blind Transfer of Personal Data Achieving Privacy
	1 Introduction
	2 System Infrastructure
	3 The Proposed Protocol
		3.1 Cryptographic Concerns
		3.2 Anonymization of the Header
	4 Security Considerations
		4.1 Privacy in Regard to TS
		4.2 Privacy in Regard to PC
		4.3 Generalized Discrete Logarithm of Order s
	5 A Case Study
	6 Conclusion
	References
Equilibria of Parametrized N-Player Nonlinear Games Using Inequalities and Nonsmooth Dynamics
	1 Introduction
	2 N-Player Games, Inequalities and Nonsmooth Dynamics
	3 Results—Changes in Game Equilibria Using Variational Inequalities
		3.1 Theoretical Approach
		3.2 Computational Approach for Non-unique Nash Equilibria
	4 Discussion of Results on Examples
	5 Conclusions
	References
Numerical Approximation of a Class of Time-Fractional Differential Equations
	1 Introduction
	2 Preliminaries
		2.1 Fractional Derivatives
		2.2 Some Function Spaces
		2.3 Problem Formulation
	3 A Priori Estimates
		3.1 Case 0 < β< α< 1
		3.2 Case 1 < β< α< 2
		3.3 Case 0 < β< 1 < α< 2
	4 Numerical Approximation
		4.1 Case  0<β<α<1
		4.2 Case 1< β<α<2
		4.3 Case  0<β<1<α<2
	5 Convergence of Finite Difference Schemes
		5.1 Case  0<β<α<1
		5.2 Case  1<β<α<2
		5.3 Case  0<β<1<α<2
	6 Numerical Examples
		6.1 Case 0<β<α<1
		6.2 Case 1<β<α<2
		6.3 Case 0<β< 1< α< 2
	References
Approximating the Integral of Analytic Complex Functions on Paths from Convex Domains in Terms of Generalized Ostrowski and Trapezoid Type Rules
	1 Introduction
	2 Ostrowski and Trapezoid Type Equalities
	3 Error Bounds for Ostrowski\'s Rule
	4 Error Bounds for Trapezoid Rule
	References
Szász–Durrmeyer Operators and Approximation
	1 Some Operators
	2  Lemmas
	3 Estimates for Polynomially Bounded Functions
	4 Exponential Growth
	5 Difference Between Operators
	References
Leibniz\'s Rule and Fubini\'s Theorem Associated with a General Quantum Difference Operator
	1 Introduction
	2 Preliminaries
	3 Quantum Leibniz\'s Rule and Fubini\'s Theorem
	4 Conclusion
	References
Some New Ostrowski Type Integral Inequalities via General Fractional Integrals
	1 Introduction
	2 Main Result
	3 Applications to Special Means and Some New Error Estimates for Midpoint Formula
	References
Some New Integral Inequalities via General Fractional Operators
	1 Introduction
	2 Main Results
	3 Applications and New Error Estimates
	References
Asymptotic Statistical Results: Theory and Practice
	1 Introduction
	2 First-Order Autoregression Model
	3 Stochastic Approximation
	4 Asymptotic Statistical Results for Percentiles
	5 Discussion
	Appendix
	References
On the Computational Methods in Non-linear Design of Experiments
	1 Background
	2 Optimality Criteria
	3 A Computational Approach for the Cancer Bioassay
	4 Measuring Non-linearity in Models
	5 Conclusions
	Appendix
	References
Geometric Derivation and Analysis of Multi-Symplectic Numerical Schemes for Differential Equations
	1 Introduction and Motivation
	2 Review of Variational Integrators
	3 Exponential Integrators
		3.1 Exponential High Order Variational Integrators
		3.2 Frequency Estimation for Mass Points Motion in Three Dimensions
	4 Triangle and Square Discretization
		4.1 Triangle Discretization
		4.2 Square Discretization
	5 Numerical Examples Using Triangle Discretization
		5.1 Linear Wave Equation
		5.2 Laplace Equation
		5.3 Poisson Equation
	6 Numerical Examples Using Square Discretization
		6.1 Klein–Gordon
	7 Analysis of the Proposed Schemes
		7.1 Dispersion Analysis
		7.2 Convergence Experiments
	8 Summary and Conclusions
	Appendix
	References
Additive (ρ1, ρ2)-Functional Inequalities in Complex Banach Spaces
	1 Introduction and Preliminaries
	2 Additive (ρ1, ρ2)-Functional Inequality (1): A Fixed Point Method
	3 Additive (ρ1, ρ2)-Functional Inequality (1): A Direct Method
	4 Additive (ρ1, ρ2)-Functional Inequality (2): A Fixed Point Method
	5 Additive (ρ1, ρ2)-Functional Inequality (2): A Direct Method
	References
First Study for Ramp Secret Sharing Schemes Through Greatest Common Divisor of Polynomials
	1 Introduction
	2 Ramp Secret Sharing Scheme
	3 Computation of The Greatest Common Divisor of Polynomials
	4 Hybrid Implementation
	5 Synopsis and Concluding Remarks
	References
From Representation Theorems to Variational Inequalities
	1 Introduction
	2 Preliminary Results
	3 Main Results
	4 Iterative Methods
	5 Conclusion and Future Research
	References
Unsupervised Stochastic Learning for User Profiles
	1 Introduction to Profiling and Contributions
	2 Unsupervised Learning with Stochastic Hierarchical Clustering
		2.1 Preliminaries: The Markovian Process and its Transient Behaviour
		2.2 Markovian State Space Partition: The Convergence Process on the Eigenvectors of the One Step Transition Probability Matrix
		2.3 The Initial Conditions as Random Variables and Their Covariance
	3 Unsupervised Learning of User Profiles
		3.1 The Distance Between User Profiles
		3.2 Hierarchical Clustering of User Profiles
		3.3 Working Example of Unsupervised Learning Through Hierarchical Clustering
	References
On the Solution of Boundary Value Problems for Ordinary Differential Equations of Order n and 2n with General Boundary Conditions
	1 Introduction
	2 Preliminaries and Definitions
	3 BVPs of Order n with Homogeneous Conditions
	4 BVPs of Order n with Nonhomogeneous Conditions
	5 BVPs of Order 2n of Special Form
	6 Example Problems
	7 Concluding Remarks
	References
Additive-Quadratic Functional Inequalities
	1 Introduction and Preliminaries
	2 Stability of the Additive-Quadratic s-Functional Inequality (1): A Direct Method
	3 Stability of the Additive-Quadratic s-Functional Inequality (2): A Direct Method
	4 Stability of the Additive-Quadratic s-Functional Inequality (1): A Fixed Point Method
	5 Stability of the Additive-Quadratic s-Functional Inequality (2): A Fixed Point Method
	References
Time-Delay Multi-Agent Systems for a Movable Cloud
	1 Introduction
	2 Literature
	3 Algorithms
		3.1 Single-Agent System
		3.2 Neighbor-Agent System
		3.3 Multi-Agent System
	4 Results
	5 Simulation
	6 Conclusion
	References
The Global-Local Transformation
	1 Prologue
	2 The Global-Local Transformation in a Single Dimension
	3 The Generalized Global-Local Transformation in Multiple Dimensions
	4 GL-Landmarks on 1D Manifolds
		4.1 The Global-Local Properties
		4.2 Encoding Curvature into Global Descriptors of the GL Surface
		4.3 Encoding Global Curve Descriptors into Curvature
	5 Performance Evaluation: Matching Benchmark Shapes with the GL-Transform
	6 Targeted Application: SAR Radar Shadow Analysis
		6.1 VAR vs LAII
		6.2 VAR vs LAII as Noise Resistant Shape Descriptors
		6.3 VAR vs LAII in Matching Noisy Shapes
	References
On Algorithms for Difference of Monotone Operators
	1 Introduction
	2 DC Programming and DCA
	3 Proximal Point Algorithm for DC Program
	4 Inertial Proximal Algorithm for Difference of Two Maximal Monotone Operators
	References
A Mathematical Model for Simulation of Intergranular μ-Capacitance as a Function of Neck Growth in Ceramic Sintering
	1 Introduction
	2 Model System Topology
		2.1 Domain Structure
		2.2 Domain Displacement
		2.3 Skeleton Structure
	3 Process Modeling
		3.1 Intergranular μ-Capacitance
		3.2 Neck Growth
		3.3 Time-Dependent Intergranular μ-Capacitance
	4 Process Simulation
		4.1 μ-Capacitor Connection Models
			μ-Capacitors in Series
			μ-Capacitors in Parallel
		4.2 Time-Dependent Intergranular Capacitance
	5 Conclusion
	Appendix 1: Neck Radius Computation
	Appendix 2: Delta to Star Transformation
	Appendix 3: Star to Delta Transformation
	References
Variational Inequalities in Semi-inner Product Spaces
	1 Introduction
	2 Variational Inequalities in Banach Space
	3 Introduction to Semi-inner Product
	4 Variational Inequalities in Banach Spaces in the Frame Work of Semi-inner Product
	5 System of Multivariate Variational Inequalities in Uniformly Convex Banach Spaces in the Frame Work of Semi-inner Product
		5.1 Main Results
	References
Results Concerning Certain Linear Positive Operators
	1 Preliminaries
	2 Ordinary and Simultaneous Approximation
	3 Rate of Convergence
	4 Quantum Calculus
	5 Post-quantum Calculus
	References
Behavior of the Solutions of Functional Equations
	1 Introduction
	2 Delay Equation
		2.1 Preliminaries and Problem Description
		2.2 Oscillation Criteria
		2.3 Example
	3 Difference Equation
		3.1 Introduction and Problem Description
		3.2 Oscillation Criteria for Difference Equation (50)
		3.3 Oscillation Criteria for Difference Equation (51)
		3.4 Example
	References
The Isometry Group of n-Dimensional Einstein Gyrogroup
	1 Introduction
	2 Main Results
	References
Function Variational Principles and Normed Minimizers
	1 Introduction
	2 Metrical Ordering Principles
	3 Extension of (EAOP)
	4 Differential Versions
	5 Existence of Minimizers
	6 Dependent Choice Principles
	7 Equivalence Results
	References
Nadler-Liu Functional Contractions in Metric Spaces
	1 Introduction
	2 Dependent Choice Principles
	3 Conv-Cauchy Structures
	4 Admissible Functions
	5 Main Result
	6 Particular Versions
	References