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

ICRAPAM 2018, New Delhi, India, October 23–25

Naokant Deo, Vijay Gupta, Ana Maria Acu, P. N. Agrawal (Herausgeber)

eBook Download: PDF

2020 | 1st ed. 2020
XI, 261 Seiten
Springer Singapore (Verlag)
978-981-15-1157-8 (ISBN)

Infos

This book collects original research papers and survey articles presented at the International Conference on Recent Advances in Pure and Applied Mathematics (ICRAPAM), held at Delhi Technological University, India, on 23-25 October 2018. Divided into two volumes, it discusses major topics in mathematical analysis and its applications, and demonstrates the versatility and inherent beauty of analysis. It also shows the use of analytical techniques to solve problems and, wherever possible, derive their numerical solutions. This volume addresses major topics, such as multi-objective optimization problems, impulsive differential equations, mathematical modelling, fuzzy mathematics, graph theory, and coding theory. It is a valuable resource to students as well as researchers in mathematical sciences.

Naokant Deo, Ph.D., is a Professor at the Department of Applied Mathematics, Delhi Technological University, India. He is an active member of various scientific organizations. 

His main research interests include approximation theory and real analysis.

Vijay Gupta is a Professor in the Department of Mathematics at the Netaji Subhas University of Technology, New Delhi, India. He holds a Ph.D. from the Indian Institute of Technology Roorkee (formerly, the University of Roorkee), and his area of research is approximation theory, with a focus on linear positive operators. The author of 5 books, 15 book chapters, and over 300 research papers, he is actively involved in editing over 25 international scientific research journals.

Ana Maria Acu is a Professor at the Department of Mathematics and Computer Science, Lucian Blaga University of Sibiu, Romania. She earned her Ph.D. in Mathematics from the Technical University of Cluj-Napoca, Romania. She is an active member of various scientific organizations, editorial boards of scientific journals, and scientific committees, and her main research interest is approximation theory.

P.N. Agrawal is a Professor at the Department of Mathematics, Indian Institute of Technology Roorkee, India. He received his Ph.D. degree from the Indian Institute of Technology Kanpur, India, in 1980. Professor Agrawal has published 110 research papers in various respected journals, has presented papers at a number of international conferences in India and abroad and also delivered invited lectures. His research interests include approximation theory, numerical methods, and complex analysis.

Inhalt

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

Produkt-Details

• Erscheint lt. Verlag: 11.3.2020
• Reihe/Serie: Springer Proceedings in Mathematics & Statistics
• Reihe/Serie: Springer Proceedings in Mathematics & Statistics
• Zusatzinfo: XI, 261 p. 76 illus., 64 illus. in color.
• Sprache: englisch
• Themenwelt: Informatik ► Netzwerke ► Sicherheit / Firewall
• Themenwelt: Informatik ► Theorie / Studium ► Kryptologie
• Themenwelt: Mathematik / Informatik ► Mathematik ► Analysis
• Themenwelt: Mathematik / Informatik ► Mathematik ► Angewandte Mathematik
• Themenwelt: Mathematik / Informatik ► Mathematik ► Finanz- / Wirtschaftsmathematik
• Themenwelt: Mathematik / Informatik ► Mathematik ► Graphentheorie
• Themenwelt: Naturwissenschaften
• Schlagworte: Analysis • cryptography • graph theory • ICRAPAM • optimisation • Ordinary differential equations • Partial differential equations
• ISBN-10: 981-15-1157-8 / 9811511578
• ISBN-13: 978-981-15-1157-8 / 9789811511578