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 3.2 Case 2: Transonic Detonation Velocity ( M12 <1 3.3 Case 3: Supersonic Detonation Velocity 1 4 Finite Element Simulation of Elastic–Plastic Deformations Under Explosion Welding
4.1 Finite Element Simulation of Clad Plate Deformation Under Explosion Welding
5 Simplified Analytical Model of Deformation of the Clad Plate
6 The Analysis of Deformation of the Clad Plate Falling on a Wavy Surface
7 Conclusions
References
Modelling of the Stress–Strain State of a Viscoelastic Rectangular Plate in Condition Combine Load
1 Introduction
2 Conclusions
References
Formulas for the Sums of the Series of Reciprocals of the Polynomial of Degree Two with Non-zero Integer Roots
1 Introduction and Basic Notions
2 Integer Roots of the Reduced Quadratic Equations
3 The Sum of the Series of Reciprocals of the Quadratic Polynomials with Different Non-zero Integer Roots with the Same Signs
4 The Sum of the Series of Reciprocals of the Quadratic Polynomials with Double Non-zero Integer Roots
5 The Sum of the Series of Reciprocals of the Quadratic Polynomials with One Negative and One Positive Integer Root
6 Numerical Verification
7 Conclusion
References
Life Expectancy at Birth and Its Socioeconomic Determinants: An Application of Random Forest Algorithm
1 Introduction
2 Literature Review
3 Method
4 Data
4.1 Description and Contextualization of Data
4.2 Random Forests Implementation
5 Discussion
6 Conclusions
Appendix
References
The Role of the Communication and Information in Decision-Making Problems
1 Introduction
2 Behavioural Effect on Intertemporal Discounting
2.1 Standard Discount Model
2.2 Positive Effects of Emotions
2.3 Negative Effects of Emotions
3 The Importance of Mental Models
3.1 Thaler and Shefrin Model
4 The Influence of Information in a Multi-agent Decision Process
4.1 Lack of Information
4.2 Excess of Information
4.3 Erroneous Information
5 The Influence of Communication: BOR (Behavioral Operational Research)
5.1 Behavioural Perspective in Decision Analysis
5.2 Role of Communication and System Perspective
6 Cooperative and Non-cooperative Multi-agent Decision Problem in BOR Perspective
References
Parameter Estimation of Fuzzy Linear Regression Utilizing Fuzzy Arithmetic and Fuzzy Inverse Matrix
1 Introduction
2 Preliminary
3 Calculating Fuzzy Inverse Matrix
3.1 Fuzzy Linear Equation Systems
3.2 Calculating Fuzzy Inverse Matrix
4 Parameter Estimation in Fuzzy Linear Regression
5 Conclusion
References
Integrated Approach to Risk Management for Public Administrations: The Healthcare System
1 The Framework
2 Aims of the Application: State of the Art and Individuation of Risk Factors
3 Methodology
4 Case Study
5 Conclusion
References
A Memetic Algorithm for Solving the Rank Aggregation Problem
1 Introduction
2 Rank Aggregation Problem
3 A Memetic Algorithm for Consensus Ranking
3.1 Solution Encoding
3.2 Fitness Function
3.3 Genetic Operators
3.4 Local Search Phase
3.5 Termination Criteria
4 Experiments and Results
4.1 Datasets
4.2 Experimental Settings
4.3 Results
5 Conclusions
References
Mathematical Optimization and Application of Nonlinear Programming
1 Introduction
2 Optimization Process
2.1 Mathematical Optimization
3 Application of Nonlinear Programming to Optimize Technological Process of Electrolytic Alkaline Zinc Plating
3.1 Analysis of Zinc Plating Process
3.2 Experimental Part
3.3 Results of Experiments
3.4 Optimization of Zinc Plating Process in Matlab
4 Application of Nonlinear Programming to Anodic Oxidation Process
4.1 Experimental—Anodic Oxidation of Specimens
4.2 Results of Experiments
5 Conclusion
References
Applicability of Selected Mathematical Statistics Methods During Decision Activities Within Joint CBRN Defence COE
1 Introduction
2 Chosen Methods in Support of Decision Activities Within Joint CBRN Defence COE
2.1 Statistical Conception and Risk Processing
2.2 Numerically Expressed Risk
3 Methods of Useful Cost Analyze
3.1 Cost Minimization Analyze
3.2 Costs and Benefits Analyze
3.3 Cost Efficiency Analyze
3.4 Cost Utility Analyze
4 Application of CBA During Decision Activities Within Joint CBRN Defence COE
4.1 Utilization of Indicators NPV and NPV/I on Instances from Budgetary Restrictive Practice
5 Conclusion
References
Counting the Number of Fuzzy Subgroups of Abelian Group G= mathbbZpntimesmathbbZpm
1 Introduction
2 Preliminaries
3 Fuzzy Subgroups Enumeration
3.1 Counting Fuzzy Subgroups of mathbbZpntimesmathbbZp
3.2 Counting Fuzzy Subgroups of mathbbZpn timesmathbbZp2
4 Counting Distinct Fuzzy Subgroups of G=mathbbZpn timesmathbbZpm
References