Mathematical Analysis II: Optimisation, Differential Equations and Graph Theory (eBook)

Dedicated to Professor Niranjan Singh 6
Preface 8
Contents 10
About the Editors 12
Exact Solution for Mixed Integral Equations by Method of Bernoulli Polynomials 13
1 Introduction 13
2 Bernoulli Polynomial Method 15
3 Matrix Representation of Bernoulli Polynomial 15
4 Method of Solution for Mixed Volterra–Fredholm Integral Equation of Second Kind 16
5 Algorithm of Bernoulli Polynomial Method 18
6 Numerical Examples 19
7 Conclusion and Result 20
References 20
Turing Patterns in a Cross Diffusive System 22
1 Introduction 22
2 Model Formulation 23
3 Stability Analysis 26
3.1 Temporal Model 26
3.2 Model with Self Diffusion 28
3.3 Model with Self Diffusion and Cross Diffusion 30
4 Numerical Simulations 34
5 Conclusion 38
References 38
On Multi-objective Optimization Problems and Vector Variational-Like Inequalities 40
1 Introduction 40
2 Preliminaries 41
3 Main Results 43
4 Conclusions 49
References 49
Controllability of Semilinear Control Systems with Fixed Delay in State 51
1 Introduction 51
2 Preliminaries 52
3 Main Results 54
4 Application 59
References 60
Computational Performance of Server Using the Mx/M/1 Queue Model 61
1 Introduction 61
2 Notations and Mathematical Description 62
2.1 Notations 62
2.2 Mathematical Model 63
3 Numerical Approach 69
4 Conclusion 75
References 76
Quantum Codes from the Cyclic Codes Over mathbbFp[v,w]/langlev2-1,w2-1,vw-wvrangle 77
1 Introduction 77
2 Preliminary 78
3 Linear Codes Over R 79
4 Cyclic Codes Over R 80
5 Quantum Codes Over mathbbFp 81
6 Conclusion 83
References 84
Effect of Sterile Insect Technique on Dynamics of Stage-Structured Model Under Immigration 85
1 Introduction 85
2 Mathematical Model Formulation 86
3 Dynamical Behaviour 88
3.1 Boundedness of Model 88
3.2 Equilibrium Points 88
4 Conclusion 95
References 95
Strict Practical Stability of Impulsive Differential System in Terms of Two Measures 97
1 Introduction 97
2 Preliminaries 98
3 Main Section 100
4 Conclusion 104
References 104
Free Vibration Analysis of Rigidly Fixed Axisymmetric Viscothermoelastic Cylinder 106
1 Introduction 106
1.1 Formulation of Problem 108
2 Boundary Conditions 109
2.1 Solution of Mathematical Problem 110
3 Series Solution 111
4 Dispersion Relations 114
4.1 Deduction of Results 116
5 Numerical Results and Discussion 116
6 Conclusion 120
References 120
Study on a Free Boundary Problem Arising in Porous Media 122
1 Introduction 122
2 Flow Problem 123
3 Solution of the Problem 126
4 Concluding Remarks 129
References 130
Effect of Habitat on Dynamic of Native and Exotic Prey–Predator Population 131
1 Introduction 131
2 Biological Background 132
3 Mathematical Model 133
4 Boundedness 134
5 Basic Feasible Equilibrium Points 135
6 Local Stability Analysis 136
7 Global Stability 138
8 Numerical Example 139
9 Conclusion 144
References 144
On Cliques and Clique Chromatic Numbers in Line, Lict and Lictact Graphs 145
1 Introduction 145
2 Main Results 147
References 151
Friendship-Like Graphs and It's Classiffication 152
1 Introduction 152
2 Main Results 154
2.1 Friendship-Like Graphs 155
3 Conclusion 161
References 161
Chaotic Maps: Applications to Cryptography and Network Generation for the Graph Laplacian Quantum States 162
1 Introduction 163
2 Analysis of Chaotic Maps 164
3 Modelling of One-Dimensional Chaotic Map into Networks 166
4 Quantum States 168
5 Conclusion 169
References 170
Consumer Behaviour Analysis for Purchasing a Passenger Car in Indian Context 172
1 Introduction 172
2 Problem Statement and Data Collection 174
3 Methodology 174
3.1 Crosstab Analysis 174
3.2 AHP 175
3.3 TOPSIS 176
4 Illustration 176
4.1 Crosstab Analysis 176
4.2 AHP 178
4.3 TOPSIS 182
5 Conclusion 183
References 184
A New Hybrid Model Based on Triple Exponential Smoothing and Fuzzy Time Series for Forecasting Seasonal Time Series 185
1 Introduction 185
2 Triple Exponential Smoothing 187
3 Basic Notions of Fuzzy Time Series 187
4 The Proposed Hybrid Model 188
5 Numerical Results 191
6 Conclusion 194
References 195
New Fuzzy Divergence Measure and Its Applications in Multi-criteria Decision-Making Using New Tool 197
1 Introduction 197
2 Preliminaries 198
2.1 Information Measures 198
2.2 Divergence Measures 198
2.3 Fuzzy Set Theory 199
2.4 Fuzzy Divergence Measures 199
3 Proposed Generalized Fuzzy Divergence Measure 200
4 Series of Fuzzy Divergence Measure 202
4.1 Some New Other Fuzzy Divergence Measures 204
5 Application of New Fuzzy Divergence Measure in Multi-criteria Decision-Making 206
5.1 Numerical Illustration 206
5.2 Comparison with the TOPSIS Method 208
5.3 Numerical Illustration 209
6 Conclusion 210
References 210
An SIRS Age-Structured Model for Vector-Borne Diseases with Infective Immigrants 212
1 Introduction 213
2 The SIRS Model Formulation 213
3 Feasibility of Solution 214
4 Existence of Equilibrium Points 215
4.1 Disease-Free Equilibrium Point 215
4.2 Endemic Equilibrium Point 215
5 Basic Reproduction Number R0 216
6 Local Stability Analysis of the Equilibrium Points 217
7 Numerical Simulation 219
8 Conclusion 223
References 223
Numerical Study of Conformable Space and Time Fractional Fokker–Planck Equation via CFDT Method 225
1 Introduction 225
2 Preliminaries 227
2.1 Description of CFDTM 229
3 Analytical Study of Conformable Fractional Fokker–Planck Equation 230
4 Conclusion 235
References 235
Multispectral Bayer Color Image Encryption 238
1 Introduction 238
2 Review of Literature Survey 240
2.1 Multispectral Color Image and Bayer Image 240
2.2 Elliptic Curve Cryptography for Images 240
2.3 Generalized Arnold Transformation for Images 241
3 Proposed Model for Image Encryption and Decryption 242
3.1 Image Encryption Procedure 243
3.2 Image Decryption Procedure 244
4 Security Analysis and Experimental Results 245
4.1 Statistical Analysis 246
4.2 Numerical Analysis 248
5 Conclusions 249
References 250
Investigation of Prospective Elementary Teachers’ Opinions About Problem Concept 252
1 Introduction 252
1.1 What Is a Problem? 252
1.2 Problem-Solving and Process of Problem-Solving 254
1.3 Nonroutine Problems 255
1.4 Importance of the Study 256
2 Method 256
2.1 Sample 256
2.2 Instruments 256
2.3 Reliability and Validity 257
3 Results 257
3.1 What Is a Problem? 257
3.2 Types of Problem 258
3.3 Conditions of Being Problem 258
3.4 Problem-Solving Steps of Polya 259
3.5 Right/Wrong Items 260
3.6 Multiple-Choice Items 261
4 Discussion and Conclusion 262
References 263