Algorithms as a Basis of Modern Applied Mathematics

Preface
Contents
Numerical Computation in Spiky Domain
	1 Introduction
	2 Near-Consistent Linear Systems: Nclinsolver Versus Matlab Solvers
		2.1 Numerical Experiments
		2.2 Remarks: Matlab Commands, Large Systems, Pruning, Rank, and Complexity
		2.3 Linear Optimization Problems with Near-Linearly Dependent Constraints
	3 Solving a Nonlinear Equation in One Variable Having Root-Clusters and/or Multiple Roots
	4 A Sensitive Nonlinear BVP: A Model for Gas Flow Through a Porus Medium
		4.1 Lower, Upper, and ODE Solutions and Matlab Program
		4.2 Numerical Results and Their Graphical Visualization
		4.3 Critical Observations for Sensitive BVPs
	5 Conclusions
	References
Modeling the Relationship Between Energy, Carbon and Water Efficiency of the Most Sustainable Corporations in the World
	1 Introduction
	2 Methodology
	3 Results
	4 Conclusion
	References
Multi-objective Evolutionary Algorithms: Decomposition Versus Indicator-Based Approach
	1 Introduction
	2 Theory
		2.1 Background
	3 Results
		3.1 Test Instances
		3.2 Performance Indicators
		3.3 Parameter Settings
		3.4 Experimental Results
	4 Conclusion and Perspectives
	References
The Hopf-Levi-Civita Data of Two-Dimensional Metrics
	1 Introduction
	2 The Hopf-Levi-Civita Data for Two-Dimensional Riemannian Metrics
	3 The Second-Hopf and Hopf-Shape Data for a Regular Surface
	4 The Hopf-Levi-Civita Data for Two Dimensional Kähler Geometry
	5 The Hopf-Levi-Civita Data for Two-Dimensional Hessian Geometry
	6 Subgeodesic Correspondence of Metrics and Connections
	7 Conclusion
	References
Some Applications of Fibonacci  and Lucas Numbers
	1 Introduction
	2 Preliminaries
	3 Main Results
	4 Conclusion
	References
Some Remarks Regarding Finite Bounded Commutative BCK-Algebras
	1 Introduction
	2 Connections Between Finite Bounded Commutative BCK-Algebras and Wajsberg Algebras
	3 The Algorithm
	4 Examples of Finite Commutative Bounded BCK-Algebras
	5 Conclusions
	References
Revisiting Fixed Point Results with a Contractive Iterative at a Point
	1 Introduction and Preliminaries
		1.1 Results in the Setting of Complete Metric Spaces
		1.2 Results in the Setting of Complete b-Metric Spaces
		1.3 Results in the Setting of Complete Dislocated b-Metric Spaces
		1.4 Branciari b-Metric Space
	2 Extension of Matkowski Theorem
	3 Conclusion
	References
An Algorithmic Perspective on the Thermoelasticity of the Micromorphic Materials Using Fractional Order Strain
	1 Introduction
	2 Theory
	3 Result
	4 Discussions and Conclusions
	References
Numerical Algorithms in Mechanics  of Generalized Continua
	1 Introduction
	2 Preliminaries
		2.1 The Finite Element Method
		2.2 The Mathematical Model to Be Discretized by the Finite Element Method
	3 Variational Formulation
	4 Numerical Simulations
	5 Discussion and Conclusion
	References
A Practical Review on Intrusion Detection Systems by Known Data Mining Methods
	1 Introduction
	2 Preliminaries
		2.1 Intrusion Detection Systems (IDSs)
		2.2 Traditional Approaches
		2.3 New Approaches
	3 Classification
		3.1 Artificial Neural Networks
		3.2 Support Vector Machines (SVMs)
		3.3 Decision Trees
		3.4 Lazy Learners
		3.5 Bayesian Methods
	4 Clustering
		4.1 Partitioning Methods
		4.2 Hierarchical Methods
		4.3 Density–Based Methods
		4.4 Model–Based Methods
	5 Experiment and Results
		5.1 Data Set Analysis
		5.2 Evaluation Measures
		5.3 Results and Analysis
	6 Conclusions
	References
Leaf Recognition Based on Image Processing
	1 Introduction
	2 Extractable Features
		2.1 Leaf Shape Features
		2.2 Leaf Texture Features
		2.3 Leaf Color Features
	3 Features Evaluation
	4 Methods Classification
		4.1 Methods Based on Leaf Shape
		4.2 Methods Based on Leaf Texture
		4.3 Methods Based on Leaf Color
		4.4 Methods Summarization
	5 Conclusion
	References
A Hypercomplex Method for Solving Boundary Value Problems for Biharmonic Functions
	1 Main Boundary Value Problems for Biharmonic functions
	2 Monogenic Functions in a Biharmonic Algebra
	3 Schwarz-Type Boundary Value Problems for Monogenic Functions
	4 Solutions Represented by Means Hypercomplex Cauchy-Type Integrals
	5 Auxiliary Statements
	6 Reducing the (1-3)-Problem to a System of Integral Equations
	7 Reducing the (1-4)-Problem to a System of Integral Equations
	References
On Algorithms Related to Expressibility of Functions of Diagonalizable Algebras
	1 Introduction
	2 Preliminaries
		2.1 Diagonalizable Algebras
		2.2 Propositional Provability Logics Associated to Diagonalizable Algebras
		2.3 Iterative Post Algebras
		2.4 Relations on Diagonalizable Algebras
	3 Preliminary Results
		3.1 Representation of 4-Valued Functions by Terms of Diagonalizable Algebra mathfrakB2
	4 Important Properties of Some Sequences of Diagonalizable Algebras
	5 Results
		5.1 On Existence of an Algorithm for Determination of Functional Expressibility in Local Tabular Diagonalizable Algebras
		5.2 Completeness Relative to Expressibility of Terms for an Infinite Sequence of Diagonalizable Algebras
		5.3 Conditions for Expressibility of Constants in mathfrakBinfty
	6 Conclusions
	References
An Algorithm for Solving the Sylvester s-Conjugate Elliptic Quaternion Matrix Equations
	1 Introduction
	2 Elliptic Quaternions
	3 Elliptic Quaternion Matrices
	4 Real Representations of Elliptic Quaternion Matrices
	5 Solving the Sylvester s-Conjugate Elliptic Quaternion Matrix Equations
	6 Numerical Algorithms
	7 Numerical Examples
	References
Deterministic Actions on Stochastic Ensembles of Particles Can Replicate Wavelike Behaviour of Quantum Mechanics: Does It Matter?
	1 Introduction
	2 Origins of Wave Mechanics in Relativity and Paradoxes of Measurement
	3 De Broglie–Bohm Pilot Wave Theory and Contextuality
	4 Illustration by a Numerical Experiment
	5 Conclusion: Why Does It Matter?
	References
Modeling of Selected Physical Phenomena Under Explosion Welding the Laminate AA2519-Ti6Al4V
	1 Introduction
	2 Problem Statement
	3 Derivation of the Problem’s Solution
		3.1 Case 1: Subsonic Detonation Velocity  ( M12