Advanced applications of computational mathematics Preface xiii List of Figures xv List of Tables xix List of Contributors xxi List of Abbreviations xxv Chapter 1 Locating ROI in Iris Using Randomized Hough Transform 1 1.1 Introduction 1 1.2 Dataset Used 2 1.3 Segmentation Procedure 3 1.3.1 Reflection Mask Detection and Removal 3 1.3.2 Thresholding 3 1.3.3 Adaptive Thresholding 3 1.3.4 Edge and Border Mask Detection 5 1.3.5 Edge Detector of Canny 5 1.3.6 Working of Canny Edge Detector 6 1.3.7 Gaussian Mask (Filter) 6 1.3.8 Intensity Gradient 7 1.3.9 Non Maximum Suppression 7 1.3.10 Edge Tracking by Hysterics 8 1.4 Classical Hough Transform 9 1.4.1 Transformation for Circle Detection 9 1.4.2 Polar Transform 10 1.5 Conclusion 12 References 12 Chapter 2 Cross Diffusion Nonlinear Radiation and Newtonian Heating Effects of Third Grade Fluid Flow Over a Riga Plate With Entropy Generation Minimization 15 2.1 Introduction 16 2.2 Problem Development 16 2.3 Entropy Optimization 19 2.4 Solution Technique (HAM) 20 2.5 Computational Results and Discussion 22 2.6 Key Results 28 References 28 Chapter 3 Canonical Representation of Kogas Solution to the Dirac Equation 31 3.1 Introduction 31 3.2 Preliminaries 32 3.3 Canonical Representation of 35 3.4 Result 36 3.5 Discussions 37 3.6 Conclusions 37 References 37 Chapter 4 Bounds of Generalized Useful Information Measure With Application Jensens Inequality 39 4.1 Introduction 39 4.2 Lower and Upper Bounds for Jensens Inequality With Utility 42 4.3 Bounds on Useful Information Measure With Application of Bounds Obtained for Jensens Inequality 45 4.4 Results and Discussions 48 4.5 Conclusion 48 References 48 Chapter 5 Scalar Potential in Planar Filippov Systems 51 5.1 Introduction 51 5.2 Simple Planar Filippov System 52 5.3 Curve Integral in a Simple Planar Filippov System 59 5.4 Scalar Potential in a Simple Planar Filippov System 61 5.5 Scalar Potential on a Closed Region 62 5.6 Properties of Orthogonal Projections 64 5.7 Conditions of Conservativeness 66 5.8 Path Independence 68 5.9 Trajectories and Fall Lines 73 5.10 Examples 78 5.11 Conclusion 83 References 83 Chapter 6 Numerical Methods and Some of Their Applications 87 6.1 History of Numerical Analysis 88 6.2 Theory of Numerical Analysis 89 6.2.1 Theorem 90 6.3 Characterization of Numerical Methods 90 6.3.1 One Step or Single Step Method 90 6.3.2 Multi Step Method 91 6.4 Types of Numerical Methods 91 6.4.1 Explicit Method 91 6.4.2 Implicit Method 91 6.5 Factors 92 6.5.1 Consistency of Method 92 6.5.2 Convergence of Method 92 6.5.3 Stability of Method 93 6.6 Distinct Numerical Methods 93 6.6.1 Euler Method 93 6.6.2 Backward Euler Method 94 6.6.3 Runge Kutta Methods 95 6.6.3.1 Runge Kutta method of an order 2 95 6.6.3.1.1 Heuns method 96 6.6.3.1.2 Modified Euler method 96 6.6.3.1.3 Optimal Runge Kutta method 96 6.6.3.2 Runge Kutta method of an order 3 96 6.6.3.2.1 Nystrm̲ method 97 6.6.3.2.2 Classical Runge Kutta method 97 6.6.3.3 Runge Kutta method of an order 4 97 6.6.3.3.1 Classical Runge Kutta method 98 6.6.4 Adams Bashforth Method 99 6.6.4.1 Adams Bashforth method of an order 2 99 6.6.4.2 Adams Bashforth method of an order 3 99 6.6.4.3 Adams Bashforth method of an order 4 99 6.6.5 Milne Simpsons Method 99 6.6.5.1 Milne Simpsons method of an order 2 100 6.6.5.2 Milne Simpsons method of an order 3 100 6.6.5.3 Milne Simpsons method of an order 4 100 6.7 Numerical Solution in Aircraft Buffet 100 6.8 Numerical Solution in Degradation of Components of Engine 101 6.9 Applications of Numerical Techniques 101 References 102 Chapter 7 On a Certain Subclass of Analytic Functions Defined by q Analogue Differential Operator 103 7.1 Introduction 103 7.2 Coefficient Bounds 107 7.3 Neighborhood Properties 110 7.4 Partial Sums 112 References 116 Chapter 8 Second Law Analysis of Williamson Nanofluid Flow in Attendance of Radiation and Heat Generation with Cattaneo Christov (C C) Heat Flux 119 8.1 Introduction 120 8.2 Problem Development 121 8.3 Formulation of Entropy Generation 123 8.4 HAM Solutions 124 8.5 Computational Results and Discussion 124 8.6 Code Validation 131 8.7 Key Results 132 References 132 Chapter 9 Computational Study of Double Diffusive MHD Buoyancy Induced Free Convection in Porous Media with Chemical Reaction and Internal Heating 135 9.1 Introduction 136 9.2 Mathematical Model 138 9.3 Similarity Transformation 140 9.4 Computational Solution 141 9.5 Computational Results and Their Interpretation 142 9.6 Conclusion 147 References 148 Chapter 10 Importance of Analytic Continuation in Complex Analysis 151 10.1 Introduction 151 10.2 Analytic Continuation 154 10.2.1 Direct Analytic Continuation 154 10.2.2 Indirect Analytic Continuation 157 10.2.3 Complete Analytic Functions 158 10.2.4 Analytic Continuation Along Arcs 159 10.3 Singularities 160 10.4 Riemann Surfaces 160 10.4.1 The Idea of a Riemann Surface 161 10.5 Conclusion 167 References 168 Chapter 11 Crime Prediction via Fuzzy Multi Criteria Decision Making Approach Under Hesitant Fuzzy Environment 171 11.1 Introduction 171 11.2 Preliminaries 173 11.3 Distance Measures 174 11.3.1 Some Well Known Distance Measures on Hesitant Fuzzy Sets 174 11.4 Multi Criteria Decision Making Approach for Crime Prediction 176 11.5 A Hypothetical Case Study 177 11.6 Conclusion and Discussion 180 References 181 Chapter 12 Variable Selection in Bioinformatics: Methods and Algorithms 183 12.1 Introduction 183 12.2 Classification Methods 184 12.2.1 Support Vector Machine 184 12.2.2 Random Forest Algorithm 185 12.3 Performance Measures 185 12.4 Classification of Feature Selection Methods 187 12.4.1 Filter Ranking Methods 187 12.4.2 Chi Square Test 188 12.4.3 Fishers Score 188 12.4.4 Correlation Coefficient 189 12.4.5 Mean Absolute Difference 189 12.4.6 Dispersion Ratio 189 12.4.7 Variance 190 12.4.8 Mutual Information 190 12.4.9 Wrapper Methods 190 12.4.10 Deterministic Wrappers 191 12.4.10.1 Forward selection 191 12.4.10.2 Backward selection 191 12.4.10.3 Bi directional elimination (stepwise selection) 192 12.4.11 Stochastic and Heuristic Wrapper Methods 192 12.4.11.1 Genetic algorithm 192 12.4.11.2 Ant colony optimization 196 12.4.11.3 Biogeography Based optimization 198 12.4.12 Embedded Methods 198 12.4.12.1 SVM RFE algorithm 198 12.4.12.2 Random forest mean decrease in accuracy 198 12.4.12.3 Random forest mean decrease in Gini 199 12.5 Bioinformatics Applications 199 12.5.1 Example Involving Quantitative Structure Activity Relationship Application 201 12.6 Final Remarks 210 References 210 Chapter 13 Bifurcation Analysis for COVID 19 Model With Inhibitory Effect 215 13.1 Introduction 216 13.2 Description of Mathematical Model 217 13.3 Basic Reproduction Number 220 13.3.1 Existence of Unique Endemic Equilibrium Point 221 13.4 Stability Analysis 222 13.5 Sensitivity Analysis 225 13.6 Numerical Simulation 226 13.7 Conclusion 230 13.8 Conflict of Interest 231 References 231 Index 235 About the Editors 239.