Recent Advances in Mathematics for Engineering (Mathematical Engineering, Manufacturing, and Management Sciences)

Description

In recent years, mathematics has experienced amazing growth in the engineering sciences. Mathematics forms the common foundation of all engineering disciplines. This book provides a comprehensive range of mathematics applied in various fields of engineering for different tasks such as civil engineering, structural engineering, computer science, and electrical engineering, among others. It offers chapters that develop the applications of mathematics in engineering sciences, conveys the innovative research ideas, offers real-world utility of mathematics, and has a significance in the life of academics, practitioners, researchers, and industry leaders. Features Focuses on the latest research in the field of engineering applications Includes recent findings from various institutions Identifies the gaps in the knowledge in the field and provides the latest approaches Presents international studies and findings in modeling and simulation Offers various mathematical tools, techniques, strategies, and methods across different engineering fields Cover Half Title Series Page Title Page Copyright Page Table of Contents Preface Acknowledgments Editor Biography Contributors Chapter 1 Statistical Techniques and Stochastic Modeling in Public Health Surveillance Systems Engineering 1.1 Introduction 1.1.1 Preliminaries 1.1.2 Definition of Biosurveillance 1.1.3 Objectives of Biosurveillance 1.1.4 Biosurveillance Systems and Processes 1.1.5 Objectives, Goals, and Challenges 1.2 State of the Art 1.3 Statistical Framework 1.3.1 Sentinel Epidemiological Surveillance System 1.3.2 Two Season Influenza Historical Data 1.3.3 Research Methodology 1.3.3.1 The Standard CDC and ECDC Flu Detection Algorithm (Serfling’s Model) 1.3.3.2 An Extended Serfling’s Model 1.3.3.3 A Mixed Model Including Auto-Regressive Moving Average (ARMA) Terms 1.3.3.4 A Mixed Effects Periodic ARMA Model Based on Change-Point Detection 1.3.3.5 A Distribution-Free Control Charting Technique Based on Change-Point Detection 1.4 Comparative Study 1.5 Concluding Remarks Acknowledgments References Chapter 2 Assessment of Earthquake Hazard Based on Statistical Models, Probability Theory, and Nonlinear Analysis 2.1 Introduction 2.2 Earthquake Hazards 2.2.1 Strong Ground Motions 2.2.2 Seismic Wave Amplification 2.2.3 Liquefaction Hazard 2.3 Probabilistic Seismic Hazard Analysis 2.3.1 Assessment 2.3.2 Methods for Seismic Hazard Analysis 2.3.2.1 Deterministic Seismic Hazard Analysis (DSHA) 2.3.2.2 Probabilistic Seismic Hazard Analysis (PSHA) 2.3.3 Development of a Comprehensive Earthquake Catalogue 2.3.4 Catalogue Homogenization 2.3.5 De-clustering of Catalogue 2.3.6 Check for Completeness 2.3.7 Seismogenic Source Characterization 2.3.8 Seismicity Parameters 2.3.9 Ground Motion Prediction Equation (GMPE) 2.3.10 Formulation of PSHA 2.3.10.1 Spatial Uncertainty 2.3.10.2 Size Uncertainty 2.3.10.3 Temporal Uncertainty 2.3.10.4 Uncertainty in GMPE 2.3.10.5 Hazard Calculation Using Total Probability Theorem 2.3.10.6 Disaggregation 2.4 Ground Response Analysis (GRA) 2.4.1 Methods for Nonlinear Ground Response Analysis 2.4.1.1 One-Dimensional Approach 2.4.1.2 Two-Dimensional Approach 2.4.1.3 Three-Dimensional Approach 2.4.2 Procedure of GRA 2.4.3 Geotechnical Site Characterization 2.4.3.1 Site Class 2.4.3.2 Bedrock Definition 2.4.4 Estimation of Dynamic Soil Properties 2.4.4.1 Low Strain Shear Modulus (G[sub(max)]) 2.4.4.2 Standard G/G[sub(max)]-(gamma) and D-(gamma) Curves 2.4.5 Selection of Input Earthquake Motion 2.4.6 Nonlinear Ground Response 2.4.6.1 Formulation of Ground Response 2.5 Liquefaction Potential 2.5.1 Simplified Procedure Based on SPT 2.5.1.1 Cyclic Stress Ratio (CSR) 2.5.1.2 Cyclic Resistance Ratio (CRR) 2.5.1.3 Factor of Safety (FS) and Liquefaction Potential Index (LPI) References Chapter 3 Multi-Model Approach in the Risk Assessment Tasks with Satellite Data Utilization 3.1 Introduction: On the Methodology of Satellite Data Utilization in Multi-Modeling Approach for Socio-Ecological Risks Assessment Tasks – A Problem Formulation 3.2 On the Methodology of Modeling: Selection of Variables to Assessing Risks 3.2.1 Data Utilization Approach to Variables Selection 3.2.2 Formal Models of Risk Assessment and Decision Support 3.3 Generalized Stochastic Model of Hydrological Threats 3.3.1 Analysis of Key Processes Forming Flood Emergency 3.3.2 Detailed Models of Moisture and Soil Water Content 3.4 Satellite Models: Spectral Response Models 3.4.1 Spectral Model of Surface Response to the Heat and Water Stress 3.4.2 Spectral Response to the Snow Melting: The Stochastic Approach 3.5 Satellite Data for Assessment of Hydrological Climate-Related Risks 3.5.1 Land Covers Classification Approach 3.5.2 Spectral Data Calibration Using in-Field Spectrometry Measurements 3.6 Risk Model: Method of to the Risk Assessments Using Bayes Approach 3.7 Conclusions Acknowledgments References Chapter 4 Integral Transforms and Parseval–Goldstein-Type Relationships 4.1 Introduction 4.2 A Parseval–Goldstein-Type Relationship 4.2.1 A Parseval–Goldstein-Type Relationship for Laplace Transforms 4.2.2 Some Illustrative Examples 4.3 The L2-Transform and its Applications 4.3.1 A Parseval–Goldstein-Type Relationship and its Corollaries 4.3.2 Some Illustrative Examples 4.4 Solving Classical Differential Equations with the L2-Transform 4.4.1 A Technique for Solving Bessel’s Differential Equation Using the L2-Transform 4.4.2 A Technique for Solving Hermite’s Differential Equation Using the L2-Transform References Chapter 5 Numerical Solution of Cauchy and Hypersingular Integral Equations 5.1 Introduction Singular Integral Equations with Cauchy Kernel 5.2 Method of Solution for CSIEs over [–1,1] 5.3 Error Analysis 5.3.1 Well Posedness 5.3.2 Existence and Uniqueness 5.4 Illustrative Examples 5.5 Introduction of Hypersingular Integral Equations 5.6 Method of Solution to the Problem 5.7 Convergence 5.7.1 Function Spaces 5.7.2 Error Analysis 5.7.3 Well Posedness of Linear System 5.7.4 Existence and Uniqueness 5.8 Illustrative Examples 5.9 Conclusion References Chapter 6 Krylov Subspace Methods for Numerically Solving Partial Differential Equations 6.1 Introduction 6.1.1 Types of PDEs 6.2 Solution of PDEs 6.3 Numerical Solutions 6.3.1 Finite Volume Method 6.3.2 Finite Element Methods 6.3.3 Finite Difference Methods 6.3.3.1 Explicit Method 6.3.3.2 Implicit Method 6.4 Stationary Iterative Methods 6.5 Non-Stationary Methods (Krylov Subspace Methods) 6.5.1 Conjugate Gradient (CG) Method 6.5.2 Generalized Minimum Residual (GMRES) Method 6.6 Conclusion Appendix References Chapter 7 The (2+1) Dimensional Nonlinear Sine–Gordon Soliton Waves and its Numerical Simulations 7.1 Introduction 7.2 Description of the Method 7.3 Implementation of Method to 2D SGE 7.4 Results and Discussion 7.4.1 Circular Ring Solitons 7.4.2 Elliptical Ring Solitons 7.4.3 Elliptical Breather 7.4.4 Superposition of Two Orthogonal Line Solitons 7.4.5 Line Solitonsin an Inhomogenous Medium 7.5 Conclusions References Chapter 8 Dynamical Complexity of Patchy Invasion in Prey–Predator Model 8.1 Introduction 8.1.1 Prey–Predator System 8.1.1.1 Cooperative Behavior of Hunting 8.2 Nonlinear Dynamics Preliminaries 8.2.1 Basics of Stability Analysis 8.2.1.1 Local Stability Analysis 8.2.2 Types of Bifurcations 8.3 Turing (Diffusive) Instability 8.4 Models Description 8.5 Spatiotemporal Model 8.5.1 Initial Density Distribution 8.5.2 Equilibria of System 8.5.3 Stability Analysis of System 8.6 Analysis of the Spatiotemporal Model 8.7 Numerical Simulations 8.8 Discussion and Conclusion References Chapter 9 Developments in Runge–Kutta Method to Solve Ordinary Differential Equations 9.1 Introduction 9.2 Development of Runge–Kutta Method 9.3 The Runge–Kutta Methods 9.4 Extension of Runge–Kutta Methods 9.5 Numerical Results 9.6 Conclusion References Chapter 10 A Criterion Space Decomposition Method for a Tri-objective Integer Program 10.1 Introduction 10.2 Literature Review 10.3 Preliminaries 10.3.1 Basic Concept 10.3.2 Review of Some Recent Approaches 10.3.2.1 The (epsilon)-Constraint Method 10.3.2.2 Boland, Charkhgard, and Savelsbergh Method (2017) 10.4 The Proposed Algorithm 10.4.1 Numerical Illustration 10.5 Computational Experiments 10.5.1 Before Relaxation 10.5.2 After Relaxation 10.6 Conclusion References Chapter 11 Link-Weight Modification for Network Optimization: Is it a Tool, Philosophy, or an Art? 11.1 Introduction 11.2 Broad Classification 11.3 Network Optimization by “Link-Weight Modified to Zero Value”: A Close Look at Some Problems in Category 1 11.3.1 A Classical Application: The Assignment Problem Solved by the Hungarian Method of Assignment 11.3.2 Unification of an Assignment and the Transportation Problems 11.3.3 Shortest Route in a Directed Network 11.3.4 Shortest Route in a Non-Directed Network 11.3.4.1 Label Associated with a Node 11.3.4.2 Notations and Definitions 11.3.4.3 Link-Weight Modification Using the Implied Direction 11.4 Link-Weight Modification Approach to Find a Minimum Spanning Tree with Node Index (Lesser than equal to) 2 11.4.1 Index Balancing Theorems 11.5 Numerical Illustrations 11.5.1 Unification of the Transportation and Assignment Models by the Hungarian Approach 11.5.2 Shortest Path in a Directed Network 11.5.3 Shortest Path in the Non-Directed Network by Labelling Approach 11.5.4 Minimum Spanning Tree 11.6 Concluding Remarks References Chapter 12 Residual Domain-Rich Models and their Application in Distinguishing Photo-Realistic and Photographic Images 12.1 Introduction 12.2 Need for Residual Domain 12.3 Rich Models of Noise Residual 12.3.1 Noise Residual 12.3.2 Truncation and Quantization 12.3.3 Co-Occurrences 12.4 Rich Models for Steganalysis of Digital Images 12.5 Rich Models for Distinguishing Photo-Realistic and Photographic Images 12.5.1 Existing Works 12.5.2 Feature Extraction 12.5.3 Classification 12.5.4 System Description 12.6 Experiments and Discussion 12.6.1 Datasets 12.6.2 Analysis for Different Color Channels 12.6.3 Robustness against Post-Processing Operations 12.6.4 Comparison with State of the Art 12.6.4.1 Comparison on Columbia Database 12.6.4.2 Comparison on RAISE versus Level-Design 12.7 Conclusion Acknowledgment References Chapter 13 Swirling Subsonic Annular Circular Jets 13.1 Introduction 13.2 Computational Model 13.2.1 Geometry 13.2.2 Meshing 13.2.3 Physics Definition 13.3 Results and Discussions 13.4 Conclusions References Chapter 14 Computations of Linear Programming Problems in Integers 14.1 Introduction 14.2 Review on Terms Related to Linear Programming Problems and Simplex Method 14.2.1 Convergence of Simplex Method 14.2.2 Programming for Simplex Method 14.2.3 Code to Perform Optimality Test 14.2.4 Code to Print Simplex Table for Each Iteration 14.3 Two-Phase Method 14.3.1 Code to Check Feasibility of the Solution 14.3.2 Code for Two-Phase Method 14.3.3 Code for Two Phase Method 14.4 Integer Cutting Planes 14.4.1 Basic Terminology for Integer Programming 14.4.2 Cutting-Plane Algorithm for Pure Integer Programming 14.4.3 Code for Gomory’s Cuts 14.4.4 Codes to Display Gomory’s Tables 14.5 Discussion and Summary Acknowledgment References Chapter 15 Fuzzy EOQ Model with Reliability-Induced Demand and Defuzzification by Graded Mean Integration 15.1 Introduction 15.2 Literature Review 15.3 Preliminaries 15.4 Notations and Assumptions 15.4.1 Notations 15.4.2 Assumptions 15.5 Formulation of Mathematical Model 15.5.1 Crisp Model 15.5.2 Fuzzy Model 15.6 Optimality Criteria 15.7 Numerical Example 15.8 Sensitivity Analysis 15.8.1 For Crisp Model 15.8.2 For Fuzzy Model 15.9 Conclusion Appendix References Chapter 16 Inventory Model for Decaying Products with Shortages and Inflation under Trade Credit in Two Warehouses 16.1 Introduction 16.2 Assumptions and Notations 16.2.1 Assumptions 16.2.2 Notations 16.3 Mathematical Formulation and Solution of the Model 16.4 Total Cost Calculations 16.4.1 Present Worth Ordering Cost 16.4.2 Present Worth Holding Cost for RW 16.4.2.1 Case 1: When Q (Lesser than equal to) W 16.4.2.2 Case 2: When Q > W 16.4.3 Present Worth Holding Cost for OW 16.4.3.1 Case 1: When Q (Lesser than equal to) W 16.4.3.2 Case 2: When Q > W 16.5 Present Worth Deterioration Cost 16.6 Present Worth Shortage Cost 16.7 Present Worth Opportunity Cost 16.8 Interest Payable 16.8.1 Case 1: 0 (Lesser than equal to) M (Lesser than equal to) t[sub(d)] 16.8.1.1 When Q (Lesser than equal to) W 16.8.1.2 When Q > W 16.8.2 Case 2: t[sub(d)] (Lesser than equal to) M (Lesser than equal to) t1 16.8.2.1 When Q (Lesser than equal to) W and Q > W 16.8.3 Case 3: When M (greater than equal to) t1 16.9 Interest Earned (I[sub(e)]) from Sales Revenue 16.9.1 Case 1: 0 W 16.9.2 Case 2: t[sub(d)] W 16.9.3 Case 3: M > t1 16.9.3.1 When Q (Lesser than equal to) W 16.9.3.2 When Q > W 16.10 Present Worth Total Cost 16.11 Numerical Illustrations and Analysis 16.11.1 Example 16.12 Sensitivity Analysis 16.13 Observations 16.14 Concluding Remarks Appendix I Appendix II References Index