Advanced Applications of Computational Mathematics

Front Cover
Advanced Applications of Computational Mathematics
Contents
Preface
List of Figures
List of Tables
List of Contributors
List of Abbreviations
1 Locating ROI in Iris Using Randomized Hough Transform
	1.1 Introduction
	1.2 Dataset Used
	1.3 Segmentation Procedure
		1.3.1 Reflection Mask Detection and Removal
		1.3.2 Thresholding
		1.3.3 Adaptive Thresholding
		1.3.4 Edge and Border Mask Detection
		1.3.5 Edge Detector of Canny
		1.3.6 Working of Canny Edge Detector
		1.3.7 Gaussian Mask (Filter)
		1.3.8 Intensity Gradient
		1.3.9 Non-Maximum Suppression
		1.3.10 Edge Tracking by Hysterics
	1.4 Classical Hough Transform
		1.4.1 Transformation for Circle Detection
		1.4.2 Polar Transform
	1.5 Conclusion
	References
2 Cross-Diffusion, Nonlinear Radiation, and Newtonian Heating Effects of Third-Grade Fluid Flow Over a Riga Plate With Entropy Generation Minimization
	2.1 Introduction
	2.2 Problem Development
	2.3 Entropy Optimization
	2.4 Solution Technique (HAM)
	2.5 Computational Results and Discussion
	2.6 Key Results
	References
3 Canonical Representation of Koga’s Solution to the Dirac Equation
	3.1 Introduction
	3.2 Preliminaries
	3.3 Canonical Representation of
	3.4 Result
	3.5 Discussions
	3.6 Conclusions
	Acknowledgements
	References
4 Bounds of Generalized ‘Useful’ Information Measure With Application Jensen’s Inequality
	4.1 Introduction
	4.2 Lower and Upper Bounds for Jensen’s Inequality With Utility
	4.3 Bounds on ‘Useful’ Information Measure With Application of Bounds Obtained for Jensen’s Inequality
	4.4 Results and Discussions
	4.5 Conclusion
	References
5 Scalar Potential in Planar Filippov Systems
	5.1 Introduction
	5.2 Simple Planar Filippov System
	5.3 Curve Integral in a Simple Planar Filippov System
	5.4 Scalar Potential in a Simple Planar Filippov System
	5.5 Scalar Potential on a Closed Region
	5.6 Properties of Orthogonal Projections
	5.7 Conditions of Conservativeness
	5.8 Path Independence
	5.9 Trajectories and Fall Lines
	5.10 Examples
	5.11 Conclusion
	References
6 Numerical Methods and Some of Their Applications
	6.1 History of Numerical Analysis
	6.2 Theory of Numerical Analysis
		6.2.1 Theorem
	6.3 Characterization of Numerical Methods
		6.3.1 One-Step or Single-Step Method
		6.3.2 Multi-Step Method
	6.4 Types of Numerical Methods
		6.4.1 Explicit Method
		6.4.2 Implicit Method
	6.5 Factors
		6.5.1 Consistency of Method
		6.5.2 Convergence of Method
		6.5.3 Stability of Method
	6.6 Distinct Numerical Methods
		6.6.1 Euler Method
		6.6.2 Backward Euler Method
		6.6.3 Runge–Kutta Methods
		6.6.3.1 Runge–Kutta method of an order 2
			6.6.3.1.1 Heun’s method
			6.6.3.1.2 Modified Euler method
			6.6.3.1.3 Optimal Runge–Kutta method
		6.6.3.2 Runge–Kutta method of an order 3
			6.6.3.2.1 Nyström method
			6.6.3.2.2 Classical Runge–Kutta method
		6.6.3.3 Runge–Kutta method of an order 4
			6.6.3.3.1 Classical Runge–Kutta method
		6.6.4 Adam’s Bashforth Method
			6.6.4.1 Adam’s Bashforth method of an order 2
			6.6.4.2 Adam’s Bashforth method of an order 3
			6.6.4.3 Adam’s Bashforth method of an order 4
		6.6.5 Milne-Simpson’s Method
			6.6.5.1 Milne-Simpson’s method of an order 2
			6.6.5.2 Milne-Simpson’s method of an order 3
			6.6.5.3 Milne-Simpson’s method of an order 4
	6.7 Numerical Solution in Aircraft Buffet
	6.8 Numerical Solution in Degradation of of Engine
	6.9 Applications of Numerical Techniques
	References
7 On a Certain Subclass of Analytic Functions by q-Analogue Differential Operator
	7.1 Introduction
	7.2 Coefficient Bounds
	7.3 Neighborhood Properties
	7.4 Partial Sums
	References
8 Second Law Analysis of Williamson Nanofluid in Attendance of Radiation and Heat with Cattaneo–Christov (C–C) Heat Flux
	8.1 Introduction
	8.2 Problem Development
	8.3 Formulation of Entropy Generation
	8.4 HAM Solutions
	8.5 Computational Results and Discussion
	8.6 Code Validation
	8.7 Key Results
	References
9 Computational Study of Double Diffusive MHD Induced Free Convection in Porous Media with Reaction and Internal Heating
	9.1 Introduction
	9.2 Mathematical Model
	9.3 Similarity Transformation
	9.4 Computational Solution
	9.5 Computational Results and Their Interpretation
	9.6 Conclusion
	References
10 Importance of Analytic Continuation in Complex Analysis
	10.1 Introduction
	10.2 Analytic Continuation
		10.2.1 Direct Analytic Continuation
		10.2.2 Indirect Analytic Continuation
		10.2.3 Complete Analytic Functions
		10.2.4 Analytic Continuation Along Arcs
	10.3 Singularities
	10.4 Riemann Surfaces
		10.4.1 The Idea of a Riemann Surface
	10.5 Conclusion
	Acknowledgement
	References
11 Crime Prediction via Fuzzy Multi-Criteria Decision-Making Approach Under Hesitant Fuzzy Environment
	11.1 Introduction
	11.2 Preliminaries
	11.3 Distance Measures
		11.3.1 Some Well-Known Distance Measures on Fuzzy Sets
	11.4 Multi-Criteria Decision-Making for Crime Prediction
	11.5 A Hypothetical Case Study
	11.6 Conclusion and Discussion
	References
12 Variable Selection in Bioinformatics: Methods and Algorithms
	12.1 Introduction
	12.2 Classification Methods
		12.2.1 Support Vector Machine
		12.2.2 Random Forest Algorithm
	12.3 Performance Measures
	12.4 Classification of Feature Selection Methods
		12.4.1 Filter Ranking Methods
		12.4.2 Chi-Square Test
		12.4.3 Fisher’s Score
		12.4.4 Correlation Coefficient
		12.4.5 Mean Absolute Difference
		12.4.6 Dispersion Ratio
		12.4.7 Variance
		12.4.8 Mutual Information
		12.4.9 Wrapper Methods
		12.4.10 Deterministic Wrappers
			12.4.10.1 Forward selection
			12.4.10.2 Backward selection
			12.4.10.3 Bi-directional elimination (stepwise selection)
		12.4.11 Stochastic and Heuristic Wrapper Methods
			12.4.11.1 Genetic algorithm
			12.4.11.2 Ant colony optimization
			12.4.11.3 Biogeography-Based optimization
		12.4.12 Embedded Methods
			12.4.12.1 SVM-RFE algorithm
			12.4.12.2 Random forest mean in accuracy
			12.4.12.3 Random forest mean decrease in Gini
	12.5 Bioinformatics Applications
		12.5.1 Example Involving Quantitative Structure Relationship Application
	12.6 Final Remarks
	References
13 Bifurcation Analysis for COVID-19 With Inhibitory Effect
	13.1 Introduction
	13.2 Description of Mathematical Model
	13.3 Basic Reproduction Number
		13.3.1 Existence of Unique Endemic Equilibrium Point
	13.4 Stability Analysis
	13.5 Sensitivity Analysis
	13.6 Numerical Simulation
	13.7 Conclusion
	Acknowledgement
	13.8 Conflict of Interest
	References
Index
About the Editors
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