Advances in mathematics : theory, methods & applications /
This book is an excellent collection of various topics of mathematics which include numerical methods, integral equations, and differential equations. The book is recommended to readers to refresh their understanding of applied mathematics with theory and applications. It will be useful to students,...
| Main Authors: | , |
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| Corporate Author: | |
| Format: | eBook |
| Language: | English |
| Published: |
[United States] :
River Publishers,
[2025]
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| Series: | River Publishers series in mathematical, statistical and computational modelling for engineering.
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| Subjects: | |
| Online Access: | Connect to the full text of this electronic book |
Table of Contents:
- Preface xi Acknowledgement xiii List of Figures xv List of Tables xvii List of Contributors xix List of Abbreviations xxiii List of Notations xxv 1 Natural Concept of the Foundations of Mathematics 1 1.1 Introduction 1 1.2 Main Concepts of the Foundation of Mathematics 2 1.3 Polymetric Analysis as a Natural Concept of the Foundations of Mathematics 10 1.4 Conclusion 20 2 Versatile Applications of the Burgers Equation Across Diverse Disciplines 23 2.1 Introduction 23 2.2 Application of the Burgers Equation 26 2.2.1 Viscous flow and turbulence 27 2.2.2 Shock theory 28 2.2.3 Gas dynamics 30 2.2.4 Cosmology 30 2.2.5 Traffic flow 31 2.2.6 Quantum field 32 2.3 Conclusion 33 3 Modeling Crude Oil Transport With a Variable-Diameter Pipeline System 39 3.1 Introduction 40 3.2 Numerical Model 42 3.3 Data Collection and Analysis 44 3.3.1 Description of the entries 45 3.3.2 Data analysis 45 3.3.3 Linear regression model 45 3.4 Results and Discussions 50 3.5 Conclusion 53 4 An Alternate Approach to Solve Two-Stage Transportation ProblemsWith Uncertain Parameters 57 4.1 Introduction 58 4.2 Preliminaries 61 4.2.1 Fuzzy (uncertain) number 61 4.2.2 Trapezoidal uncertain number 61 4.2.3 Membership function of trapezoidal fuzzy number 61 4.2.4 De-fuzzification of trapezoidal uncertain numbers 61 4.2.5 Algebraic operations on trapezoidal uncertain numbers 62 4.3 Two-Stage Fuzzy Transportation Problem 62 4.4 Proposed Approach 63 4.5 Illustrative Examples 64 4.6 Result Comparison 67 4.7 Conclusion 67 5 A Note on Existence and Controllability Results on Fractional Sobolev-type Differential System of Order Îł ⁸́⁸ (0, 1) in a Banach Space 71 5.1 Introduction 72 5.2 Preliminaries 73 5.3 Controllability Results 75 5.4 An Example 83 5.5 Conclusion 84 6 Mathematical Modeling using Fuzzy Petri Nets and its Classifications 89 6.1 Introduction 89 6.2 Preliminaries 90 6.3 Classifications of Fuzzy Petri Net 94 6.3.1 Fuzzy time Petri net 94 6.3.2 Fuzzy stochastic Petri net 95 6.3.3 Fuzzy colored Petri net 95 6.3.4 Fuzzy continuous Petri nets (FCPNs) 96 6.4 Applications 97 6.5 Conclusion and Future Scope 97 7 Exploring New Exact Solutions of (2 + 1)-Dimensional Date⁰́₃Jimbo⁰́₃Kashiwara⁰́₃Miwa Equation with tan -Expansion Method 101 7.1 Introduction 101 7.2 Methodology 103 7.3 (2 + 1)-Dimensional Date⁸́₂Jimbo⁸́₂Kashiwara⁸́₂Miwa Equation 105 7.4 Conclusion 111 8 Unveiling Dynamics of Solutions for Variable Killing Rate Brain Tumor ModelWith Lie Symmetry Analysis 115 8.1 Introduction 116 8.2 Lie Symmetry Analysis of Brain Tumor Model 117 8.3 Establishing Exact Solutions via Power Series Method 119 8.3.1 Exact solution of eqn (2.6) 120 8.3.2 Exact solution of eqn (2.7) 121 8.3.3 Exact solution via traveling wave transformation 122 8.4 Convergence of Power Series Solution 124 8.5 Conclusion 126 9 Convergence of Generalized Sz©Łsz⁰́₃Mirakjan⁰́₃Kantorovich Operators on Different Function Spaces 129 9.1 Introduction 129 9.2 Literature Review 131 9.3 Generalizing Jakimovski⁰́₃Leviatan Operators 134 9.4 Preliminaries 135 9.5 Approximation Properties 137 9.6 Conclusion 142 10 Herd Behavior in Prey and Cooperative Hunting in Predators With Holling Type-II: A Dynamical Approach 145 10.1 Introduction 146 10.2 Mathematical Model Formulation and Preliminaries 149 10.2.1 Existence and uniqueness 150 10.2.2 Positivity and boundedness 151 10.3 Linear Stability Analysis for Non-spatial Model 152 10.4 Hopf Bifurcation 154 10.5 Spatial Model 156 10.6 Diffusion-driven Instability 157 10.7 Weakly Nonlinear Analysis 159 10.8 Numerical Simulations 164 10.8.1 Pattern selection 166 10.9 Conclusion 172 11 Aryabhata⁰́₉s Contribution to Advancement in Arithmetic 177 11.1 Introduction 177 11.2 Aryabhatiya: Treatise of Aryabhata 178 11.3 Seeding of Arithmetic by Aryabhata 179 11.3.1 Using the Sanskrit alphabet for enumeration 179 11.3.2 Sanskrit 179 11.3.3 Square 180 11.3.4 Square root 180 11.3.5 Cube 181 11.3.6 Cube root 181 11.3.7 Method of inversion 184 11.4 Significance of the Work in Modern Technology 184 11.5 Some of the Honors in the Name of Aryabhata 184 11.6 Conclusion 185 12 A Brief Account of Ancient Indian Astronomy and Mathematics 189 12.1 Introduction 189 12.2 Brief History of Ancient Indian Astronomy 190 12.3 Some Comments on Ancient Indian Astronomy 194 12.4 A Brief Description of Ancient Indian Mathematics 195 12.4.1 The decimal system 197 12.4.2 Numerals and zero symbols 198 12.5 Concluding Remarks 199 12.6 Future Scope 200 13 Identification of Leak LocationsWith Mathematical Modeling: A Case ofWater Distribution Network 203 13.1 Introduction 204 13.2 Materials and Methods 205 13.3 Result and Discussion 207 13.4 Conclusion 209 Index 213 About the Editors 215.