{"product_id":"mathematical-methods-in-interdisciplinary-sciences-isbn-9781119585503","title":"Mathematical Methods in Interdisciplinary Sciences","description":"\u003cp\u003e\u003cb\u003eBrings mathematics to bear on your real-world, scientific problems\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e\u003ci\u003eMathematical Methods in Interdisciplinary Sciences\u003c\/i\u003e provides a practical and usable framework for bringing a mathematical approach to modelling real-life scientific and technological problems. The collection of chapters Dr. Snehashish Chakraverty has provided describe in detail how to bring mathematics, statistics, and computational methods to the fore to solve even the most stubborn problems involving the intersection of multiple fields of study. Graduate students, postgraduate students, researchers, and professors will all benefit significantly from the author's clear approach to applied mathematics.\u003c\/p\u003e \u003cp\u003eThe book covers a wide range of interdisciplinary topics in which mathematics can be brought to bear on challenging problems requiring creative solutions. Subjects include:\u003c\/p\u003e \u003cul\u003e \u003cli\u003eStructural static and vibration problems\u003c\/li\u003e \u003cli\u003eHeat conduction and diffusion problems\u003c\/li\u003e \u003cli\u003eFluid dynamics problems\u003c\/li\u003e \u003c\/ul\u003e \u003cp\u003eThe book also covers topics as diverse as soft computing and machine intelligence. It concludes with examinations of various fields of application, like infectious diseases, autonomous car and monotone inclusion problems.\u003c\/p\u003e \u003cp\u003eNotes on Contributors xv\u003c\/p\u003e \u003cp\u003ePreface xxv\u003c\/p\u003e \u003cp\u003eAcknowledgments xxvii\u003c\/p\u003e \u003cp\u003e\u003cb\u003e1 Connectionist Learning Models for Application Problems Involving Differential and Integral Equations 1\u003cbr\u003e\u003c\/b\u003e\u003ci\u003eSusmita Mall, Sumit Kumar Jeswal, and Snehashish Chakraverty\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e1.1 Introduction 1\u003c\/p\u003e \u003cp\u003e1.1.1 Artificial Neural Network 1\u003c\/p\u003e \u003cp\u003e1.1.2 Types of Neural Networks 1\u003c\/p\u003e \u003cp\u003e1.1.3 Learning in Neural Network 2\u003c\/p\u003e \u003cp\u003e1.1.4 Activation Function 2\u003c\/p\u003e \u003cp\u003e1.1.4.1 Sigmoidal Function 3\u003c\/p\u003e \u003cp\u003e1.1.5 Advantages of Neural Network 3\u003c\/p\u003e \u003cp\u003e1.1.6 Functional Link Artificial Neural Network (FLANN) 3\u003c\/p\u003e \u003cp\u003e1.1.7 Differential Equations (DEs) 4\u003c\/p\u003e \u003cp\u003e1.1.8 Integral Equation 5\u003c\/p\u003e \u003cp\u003e1.1.8.1 Fredholm Integral Equation of First Kind 5\u003c\/p\u003e \u003cp\u003e1.1.8.2 Fredholm Integral Equation of Second Kind 5\u003c\/p\u003e \u003cp\u003e1.1.8.3 Volterra Integral Equation of First Kind 5\u003c\/p\u003e \u003cp\u003e1.1.8.4 Volterra Integral Equation of Second Kind 5\u003c\/p\u003e \u003cp\u003e1.1.8.5 Linear Fredholm Integral Equation System of Second Kind 6\u003c\/p\u003e \u003cp\u003e1.2 Methodology for Differential Equations 6\u003c\/p\u003e \u003cp\u003e1.2.1 FLANN-Based General Formulation of Differential Equations 6\u003c\/p\u003e \u003cp\u003e1.2.1.1 Second-Order Initial Value Problem 6\u003c\/p\u003e \u003cp\u003e1.2.1.2 Second-Order Boundary Value Problem 7\u003c\/p\u003e \u003cp\u003e1.2.2 Proposed Laguerre Neural Network (LgNN) for Differential Equations 7\u003c\/p\u003e \u003cp\u003e1.2.2.1 Architecture of Single-Layer LgNN Model 7\u003c\/p\u003e \u003cp\u003e1.2.2.2 Training Algorithm of Laguerre Neural Network (LgNN) 8\u003c\/p\u003e \u003cp\u003e1.2.2.3 Gradient Computation of LgNN 9\u003c\/p\u003e \u003cp\u003e1.3 Methodology for Solving a System of Fredholm Integral Equations of Second Kind 9\u003c\/p\u003e \u003cp\u003e1.3.1 Algorithm 10\u003c\/p\u003e \u003cp\u003e1.4 Numerical Examples and Discussion 11\u003c\/p\u003e \u003cp\u003e1.4.1 Differential Equations and Applications 11\u003c\/p\u003e \u003cp\u003e1.4.2 Integral Equations 16\u003c\/p\u003e \u003cp\u003e1.5 Conclusion 20\u003c\/p\u003e \u003cp\u003eReferences 20\u003c\/p\u003e \u003cp\u003e\u003cb\u003e2 Deep Learning in Population Genetics: Prediction and Explanation of Selection of a Population \u003c\/b\u003e\u003cb\u003e23\u003cbr\u003e\u003c\/b\u003e\u003ci\u003eRomila Ghosh and Satyakama Paul\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e2.1 Introduction 23\u003c\/p\u003e \u003cp\u003e2.2 Literature Review 23\u003c\/p\u003e \u003cp\u003e2.3 Dataset Description 25\u003c\/p\u003e \u003cp\u003e2.3.1 Selection and Its Importance 25\u003c\/p\u003e \u003cp\u003e2.4 Objective 26\u003c\/p\u003e \u003cp\u003e2.5 Relevant Theory, Results, and Discussions 27\u003c\/p\u003e \u003cp\u003e2.5.1 automl 27\u003c\/p\u003e \u003cp\u003e2.5.2 Hypertuning the Best Model 28\u003c\/p\u003e \u003cp\u003e2.6 Conclusion 30\u003c\/p\u003e \u003cp\u003eReferences 30\u003c\/p\u003e \u003cp\u003e\u003cb\u003e3 A Survey of Classification Techniques in Speech Emotion Recognition \u003c\/b\u003e\u003cb\u003e33\u003cbr\u003e\u003c\/b\u003e\u003ci\u003eTanmoy Roy, Tshilidzi Marwala, and Snehashish Chakraverty\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e3.1 Introduction 33\u003c\/p\u003e \u003cp\u003e3.2 Emotional Speech Databases 33\u003c\/p\u003e \u003cp\u003e3.3 SER Features 34\u003c\/p\u003e \u003cp\u003e3.4 Classification Techniques 35\u003c\/p\u003e \u003cp\u003e3.4.1 Hidden Markov Model 36\u003c\/p\u003e \u003cp\u003e3.4.1.1 Difficulties in Using HMM for SER 37\u003c\/p\u003e \u003cp\u003e3.4.2 Gaussian Mixture Model 37\u003c\/p\u003e \u003cp\u003e3.4.2.1 Difficulties in Using GMM for SER 38\u003c\/p\u003e \u003cp\u003e3.4.3 Support Vector Machine 38\u003c\/p\u003e \u003cp\u003e3.4.3.1 Difficulties with SVM 39\u003c\/p\u003e \u003cp\u003e3.4.4 Deep Learning 39\u003c\/p\u003e \u003cp\u003e3.4.4.1 Drawbacks of Using Deep Learning for SER 41\u003c\/p\u003e \u003cp\u003e3.5 Difficulties in SER Studies 41\u003c\/p\u003e \u003cp\u003e3.6 Conclusion 41\u003c\/p\u003e \u003cp\u003eReferences 42\u003c\/p\u003e \u003cp\u003e\u003cb\u003e4 Mathematical Methods in Deep Learning \u003c\/b\u003e\u003cb\u003e49\u003cbr\u003e\u003c\/b\u003e\u003ci\u003eSrinivasa Manikant Upadhyayula and Kannan Venkataramanan\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e4.1 Deep Learning Using Neural Networks 49\u003c\/p\u003e \u003cp\u003e4.2 Introduction to Neural Networks 49\u003c\/p\u003e \u003cp\u003e4.2.1 Artificial Neural Network (ANN) 50\u003c\/p\u003e \u003cp\u003e4.2.1.1 Activation Function 52\u003c\/p\u003e \u003cp\u003e4.2.1.2 Logistic Sigmoid Activation Function 52\u003c\/p\u003e \u003cp\u003e4.2.1.3 tanh or Hyperbolic Tangent Activation Function 53\u003c\/p\u003e \u003cp\u003e4.2.1.4 ReLU (Rectified Linear Unit) Activation Function 54\u003c\/p\u003e \u003cp\u003e4.3 Other Activation Functions (Variant Forms of ReLU) 55\u003c\/p\u003e \u003cp\u003e4.3.1 Smooth ReLU 55\u003c\/p\u003e \u003cp\u003e4.3.2 Noisy ReLU 55\u003c\/p\u003e \u003cp\u003e4.3.3 Leaky ReLU 55\u003c\/p\u003e \u003cp\u003e4.3.4 Parametric ReLU 56\u003c\/p\u003e \u003cp\u003e4.3.5 Training and Optimizing a Neural Network Model 56\u003c\/p\u003e \u003cp\u003e4.4 Backpropagation Algorithm 56\u003c\/p\u003e \u003cp\u003e4.5 Performance and Accuracy 59\u003c\/p\u003e \u003cp\u003e4.6 Results and Observation 59\u003c\/p\u003e \u003cp\u003eReferences 61\u003c\/p\u003e \u003cp\u003e\u003cb\u003e5 Multimodal Data Representation and Processing Based on Algebraic System of Aggregates \u003c\/b\u003e\u003cb\u003e63\u003cbr\u003e\u003c\/b\u003e\u003ci\u003eYevgeniya Sulema and Etienne Kerre\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e5.1 Introduction 63\u003c\/p\u003e \u003cp\u003e5.2 Basic Statements of ASA 64\u003c\/p\u003e \u003cp\u003e5.3 Operations on Aggregates and Multi-images 65\u003c\/p\u003e \u003cp\u003e5.4 Relations and Digital Intervals 72\u003c\/p\u003e \u003cp\u003e5.5 Data Synchronization 75\u003c\/p\u003e \u003cp\u003e5.6 Fuzzy Synchronization 92\u003c\/p\u003e \u003cp\u003e5.7 Conclusion 96\u003c\/p\u003e \u003cp\u003eReferences 96\u003c\/p\u003e \u003cp\u003e\u003cb\u003e6 Nonprobabilistic Analysis of Thermal and Chemical Diffusion Problems with Uncertain Bounded Parameters \u003c\/b\u003e\u003cb\u003e99\u003cbr\u003e\u003c\/b\u003e\u003ci\u003eSukanta Nayak, Tharasi Dilleswar Rao, and Snehashish Chakraverty\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e6.1 Introduction 99\u003c\/p\u003e \u003cp\u003e6.2 Preliminaries 99\u003c\/p\u003e \u003cp\u003e6.2.1 Interval Arithmetic 99\u003c\/p\u003e \u003cp\u003e6.2.2 Fuzzy Number and Fuzzy Arithmetic 100\u003c\/p\u003e \u003cp\u003e6.2.3 Parametric Representation of Fuzzy Number 101\u003c\/p\u003e \u003cp\u003e6.2.4 Finite Difference Schemes for PDEs 102\u003c\/p\u003e \u003cp\u003e6.3 Finite Element Formulation for Tapered Fin 102\u003c\/p\u003e \u003cp\u003e6.4 Radon Diffusion and Its Mechanism 105\u003c\/p\u003e \u003cp\u003e6.5 Radon Diffusion Mechanism with TFN Parameters 107\u003c\/p\u003e \u003cp\u003e6.5.1 EFDM to Radon Diffusion Mechanism with TFN Parameters 108\u003c\/p\u003e \u003cp\u003e6.6 Conclusion 112\u003c\/p\u003e \u003cp\u003eReferences 112\u003c\/p\u003e \u003cp\u003e\u003cb\u003e7 Arbitrary Order Differential Equations with Fuzzy Parameters \u003c\/b\u003e\u003cb\u003e115\u003cbr\u003e\u003c\/b\u003e\u003ci\u003eTofigh Allahviranloo and Soheil Salahshour\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e7.1 Introduction 115\u003c\/p\u003e \u003cp\u003e7.2 Preliminaries 115\u003c\/p\u003e \u003cp\u003e7.3 Arbitrary Order Integral and Derivative for Fuzzy-Valued Functions 116\u003c\/p\u003e \u003cp\u003e7.4 Generalized Fuzzy Laplace Transform with Respect to Another Function 118\u003c\/p\u003e \u003cp\u003eReferences 122\u003c\/p\u003e \u003cp\u003e\u003cb\u003e8 Fluid Dynamics Problems in Uncertain Environment \u003c\/b\u003e\u003cb\u003e125\u003cbr\u003e\u003c\/b\u003e\u003ci\u003ePerumandla Karunakar, Uddhaba Biswal, and Snehashish Chakraverty\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e8.1 Introduction 125\u003c\/p\u003e \u003cp\u003e8.2 Preliminaries 126\u003c\/p\u003e \u003cp\u003e8.2.1 Fuzzy Set 126\u003c\/p\u003e \u003cp\u003e8.2.2 Fuzzy Number 126\u003c\/p\u003e \u003cp\u003e8.2.3 \u003ci\u003e𝛿\u003c\/i\u003e-Cut 127\u003c\/p\u003e \u003cp\u003e8.2.4 Parametric Approach 127\u003c\/p\u003e \u003cp\u003e8.3 Problem Formulation 127\u003c\/p\u003e \u003cp\u003e8.4 Methodology 129\u003c\/p\u003e \u003cp\u003e8.4.1 Homotopy Perturbation Method 129\u003c\/p\u003e \u003cp\u003e8.4.2 Homotopy Perturbation Transform Method 130\u003c\/p\u003e \u003cp\u003e8.5 Application of HPM and HPTM 131\u003c\/p\u003e \u003cp\u003e8.5.1 Application of HPM to Jeffery–Hamel Problem 131\u003c\/p\u003e \u003cp\u003e8.5.2 Application of HPTM to Coupled Whitham–Broer–Kaup Equations 134\u003c\/p\u003e \u003cp\u003e8.6 Results and Discussion 136\u003c\/p\u003e \u003cp\u003e8.7 Conclusion 142\u003c\/p\u003e \u003cp\u003eReferences 142\u003c\/p\u003e \u003cp\u003e\u003cb\u003e9 Fuzzy Rough Set Theory-Based Feature Selection: A Review \u003c\/b\u003e\u003cb\u003e145\u003cbr\u003e\u003c\/b\u003e\u003ci\u003eTanmoy Som, Shivam Shreevastava, Anoop Kumar Tiwari, and Shivani Singh\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e9.1 Introduction 145\u003c\/p\u003e \u003cp\u003e9.2 Preliminaries 146\u003c\/p\u003e \u003cp\u003e9.2.1 Rough Set Theory 146\u003c\/p\u003e \u003cp\u003e9.2.1.1 Rough Set 146\u003c\/p\u003e \u003cp\u003e9.2.1.2 Rough Set-Based Feature Selection 147\u003c\/p\u003e \u003cp\u003e9.2.2 Fuzzy Set Theory 147\u003c\/p\u003e \u003cp\u003e9.2.2.1 Fuzzy Tolerance Relation 148\u003c\/p\u003e \u003cp\u003e9.2.2.2 Fuzzy Rough Set Theory 149\u003c\/p\u003e \u003cp\u003e9.2.2.3 Degree of Dependency-Based Fuzzy Rough Attribute Reduction 149\u003c\/p\u003e \u003cp\u003e9.2.2.4 Discernibility Matrix-Based Fuzzy Rough Attribute Reduction 149\u003c\/p\u003e \u003cp\u003e9.3 Fuzzy Rough Set-Based Attribute Reduction 149\u003c\/p\u003e \u003cp\u003e9.3.1 Degree of Dependency-Based Approaches 150\u003c\/p\u003e \u003cp\u003e9.3.2 Discernibility Matrix-Based Approaches 154\u003c\/p\u003e \u003cp\u003e9.4 Approaches for Semisupervised and Unsupervised Decision Systems 154\u003c\/p\u003e \u003cp\u003e9.5 Decision Systems with Missing Values 158\u003c\/p\u003e \u003cp\u003e9.6 Applications in Classification, Rule Extraction, and Other Application Areas 158\u003c\/p\u003e \u003cp\u003e9.7 Limitations of Fuzzy Rough Set Theory 159\u003c\/p\u003e \u003cp\u003e9.8 Conclusion 160\u003c\/p\u003e \u003cp\u003eReferences 160\u003c\/p\u003e \u003cp\u003e\u003cb\u003e10 Universal Intervals: Towards a Dependency-Aware Interval Algebra \u003c\/b\u003e\u003cb\u003e167\u003cbr\u003e\u003c\/b\u003e\u003ci\u003eHend Dawood and Yasser Dawood\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e10.1 Introduction 167\u003c\/p\u003e \u003cp\u003e10.2 The Need for Interval Computations 169\u003c\/p\u003e \u003cp\u003e10.3 On Some Algebraic and Logical Fundamentals 170\u003c\/p\u003e \u003cp\u003e10.4 Classical Intervals and the Dependency Problem 174\u003c\/p\u003e \u003cp\u003e10.5 Interval Dependency: A Logical Treatment 176\u003c\/p\u003e \u003cp\u003e10.5.1 Quantification Dependence and Skolemization 177\u003c\/p\u003e \u003cp\u003e10.5.2 A Formalization of the Notion of Interval Dependency 179\u003c\/p\u003e \u003cp\u003e10.6 Interval Enclosures Under Functional Dependence 184\u003c\/p\u003e \u003cp\u003e10.7 Parametric Intervals: How Far They Can Go 186\u003c\/p\u003e \u003cp\u003e10.7.1 Parametric Interval Operations: From Endpoints to Convex Subsets 186\u003c\/p\u003e \u003cp\u003e10.7.2 On the Structure of Parametric Intervals: Are They Properly Founded? 188\u003c\/p\u003e \u003cp\u003e10.8 Universal Intervals: An Interval Algebra with a Dependency Predicate 192\u003c\/p\u003e \u003cp\u003e10.8.1 Universal Intervals, Rational Functions, and Predicates 193\u003c\/p\u003e \u003cp\u003e10.8.2 The Arithmetic of Universal Intervals 196\u003c\/p\u003e \u003cp\u003e10.9 The S-Field Algebra of Universal Intervals 201\u003c\/p\u003e \u003cp\u003e10.10 Guaranteed Bounds or Best Approximation or Both? 209\u003c\/p\u003e \u003cp\u003eSupplementary Materials 210\u003c\/p\u003e \u003cp\u003eAcknowledgments 211\u003c\/p\u003e \u003cp\u003eReferences 211\u003c\/p\u003e \u003cp\u003e\u003cb\u003e11 Affine-Contractor Approach to Handle Nonlinear Dynamical Problems in Uncertain Environment \u003c\/b\u003e\u003cb\u003e215\u003cbr\u003e\u003c\/b\u003e\u003ci\u003eNisha Rani Mahato, Saudamini Rout, and Snehashish Chakraverty\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e11.1 Introduction 215\u003c\/p\u003e \u003cp\u003e11.2 Classical Interval Arithmetic 217\u003c\/p\u003e \u003cp\u003e11.2.1 Intervals 217\u003c\/p\u003e \u003cp\u003e11.2.2 Set Operations of Interval System 217\u003c\/p\u003e \u003cp\u003e11.2.3 Standard Interval Computations 218\u003c\/p\u003e \u003cp\u003e11.2.4 Algebraic Properties of Interval 219\u003c\/p\u003e \u003cp\u003e11.3 Interval Dependency Problem 219\u003c\/p\u003e \u003cp\u003e11.4 Affine Arithmetic 220\u003c\/p\u003e \u003cp\u003e11.4.1 Conversion Between Interval and Affine Arithmetic 220\u003c\/p\u003e \u003cp\u003e11.4.2 Affine Operations 221\u003c\/p\u003e \u003cp\u003e11.5 Contractor 223\u003c\/p\u003e \u003cp\u003e11.5.1 SIVIA 223\u003c\/p\u003e \u003cp\u003e11.6 Proposed Methodology 225\u003c\/p\u003e \u003cp\u003e11.7 Numerical Examples 230\u003c\/p\u003e \u003cp\u003e11.7.1 Nonlinear Oscillators 230\u003c\/p\u003e \u003cp\u003e11.7.1.1 Unforced Nonlinear Differential Equation 230\u003c\/p\u003e \u003cp\u003e11.7.1.2 Forced Nonlinear Differential Equation 232\u003c\/p\u003e \u003cp\u003e11.7.2 Other Dynamic Problem 233\u003c\/p\u003e \u003cp\u003e11.7.2.1 Nonhomogeneous Lane–Emden Equation 233\u003c\/p\u003e \u003cp\u003e11.8 Conclusion 236\u003c\/p\u003e \u003cp\u003eReferences 236\u003c\/p\u003e \u003cp\u003e\u003cb\u003e12 Dynamic Behavior of Nanobeam Using Strain Gradient Model \u003c\/b\u003e\u003cb\u003e239\u003cbr\u003e\u003c\/b\u003e\u003ci\u003eSubrat Kumar Jena, Rajarama Mohan Jena, and Snehashish Chakraverty\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e12.1 Introduction 239\u003c\/p\u003e \u003cp\u003e12.2 Mathematical Formulation of the Proposed Model 240\u003c\/p\u003e \u003cp\u003e12.3 Review of the Differential Transform Method (DTM) 241\u003c\/p\u003e \u003cp\u003e12.4 Application of DTM on Dynamic Behavior Analysis 242\u003c\/p\u003e \u003cp\u003e12.5 Numerical Results and Discussion 244\u003c\/p\u003e \u003cp\u003e12.5.1 Validation and Convergence 244\u003c\/p\u003e \u003cp\u003e12.5.2 Effect of the Small-Scale Parameter 245\u003c\/p\u003e \u003cp\u003e12.5.3 Effect of Length-Scale Parameter 247\u003c\/p\u003e \u003cp\u003e12.6 Conclusion 248\u003c\/p\u003e \u003cp\u003eAcknowledgment 249\u003c\/p\u003e \u003cp\u003eReferences 250\u003c\/p\u003e \u003cp\u003e\u003cb\u003e13 Structural Static and Vibration Problems \u003c\/b\u003e\u003cb\u003e253\u003cbr\u003e\u003c\/b\u003e\u003ci\u003eM. Amin Changizi and Ion Stiharu\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e13.1 Introduction 253\u003c\/p\u003e \u003cp\u003e13.2 One-parameter Groups 254\u003c\/p\u003e \u003cp\u003e13.3 Infinitesimal Transformation 254\u003c\/p\u003e \u003cp\u003e13.4 Canonical Coordinates 254\u003c\/p\u003e \u003cp\u003e13.5 Algorithm for Lie Symmetry Point 255\u003c\/p\u003e \u003cp\u003e13.6 Reduction of the Order of the ODE 255\u003c\/p\u003e \u003cp\u003e13.7 Solution of First-Order ODE with Lie Symmetry 255\u003c\/p\u003e \u003cp\u003e13.8 Identification 256\u003c\/p\u003e \u003cp\u003e13.9 Vibration of a Microcantilever Beam Subjected to Uniform Electrostatic Field 258\u003c\/p\u003e \u003cp\u003e13.10 Contact Form for the Equation 259\u003c\/p\u003e \u003cp\u003e13.11 Reducing in the Order of the Nonlinear ODE Representing the Vibration of a Microcantilever Beam Under Electrostatic Field 260\u003c\/p\u003e \u003cp\u003e13.12 Nonlinear Pull-in Voltage 261\u003c\/p\u003e \u003cp\u003e13.13 Nonlinear Analysis of Pull-in Voltage of Twin Microcantilever Beams 266\u003c\/p\u003e \u003cp\u003e13.14 Nonlinear Analysis of Pull-in Voltage of Twin Microcantilever Beams of Different Thicknesses 268\u003c\/p\u003e \u003cp\u003eReferences 272\u003c\/p\u003e \u003cp\u003e\u003cb\u003e14 Generalized Differential and Integral Quadrature: Theory and Applications \u003c\/b\u003e\u003cb\u003e273\u003cbr\u003e\u003c\/b\u003e\u003ci\u003eFrancesco Tornabene and Rossana Dimitri\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e14.1 Introduction 273\u003c\/p\u003e \u003cp\u003e14.2 Differential Quadrature 274\u003c\/p\u003e \u003cp\u003e14.2.1 Genesis of the Differential Quadrature Method 274\u003c\/p\u003e \u003cp\u003e14.2.2 Differential Quadrature Law 275\u003c\/p\u003e \u003cp\u003e14.3 General View on Differential Quadrature 277\u003c\/p\u003e \u003cp\u003e14.3.1 Basis Functions 278\u003c\/p\u003e \u003cp\u003e14.3.1.1 Lagrange Polynomials 281\u003c\/p\u003e \u003cp\u003e14.3.1.2 Trigonometric Lagrange Polynomials 282\u003c\/p\u003e \u003cp\u003e14.3.1.3 Classic Orthogonal Polynomials 282\u003c\/p\u003e \u003cp\u003e14.3.1.4 Monomial Functions 291\u003c\/p\u003e \u003cp\u003e14.3.1.5 Exponential Functions 291\u003c\/p\u003e \u003cp\u003e14.3.1.6 Bernstein Polynomials 291\u003c\/p\u003e \u003cp\u003e14.3.1.7 Fourier Functions 292\u003c\/p\u003e \u003cp\u003e14.3.1.8 Bessel Polynomials 292\u003c\/p\u003e \u003cp\u003e14.3.1.9 Boubaker Polynomials 292\u003c\/p\u003e \u003cp\u003e14.3.2 Grid Distributions 293\u003c\/p\u003e \u003cp\u003e14.3.2.1 Coordinate Transformation 293\u003c\/p\u003e \u003cp\u003e14.3.2.2 \u003ci\u003e𝛿\u003c\/i\u003e-Point Distribution 293\u003c\/p\u003e \u003cp\u003e14.3.2.3 Stretching Formulation 293\u003c\/p\u003e \u003cp\u003e14.3.2.4 Several Types of Discretization 293\u003c\/p\u003e \u003cp\u003e14.3.3 Numerical Applications: Differential Quadrature 297\u003c\/p\u003e \u003cp\u003e14.4 Generalized Integral Quadrature 310\u003c\/p\u003e \u003cp\u003e14.4.1 Generalized Taylor-Based Integral Quadrature 312\u003c\/p\u003e \u003cp\u003e14.4.2 Classic Integral Quadrature Methods 314\u003c\/p\u003e \u003cp\u003e14.4.2.1 Trapezoidal Rule with Uniform Discretization 314\u003c\/p\u003e \u003cp\u003e14.4.2.2 Simpson’s Method (One-third Rule) with Uniform Discretization 314\u003c\/p\u003e \u003cp\u003e14.4.2.3 Chebyshev–Gauss Method (Chebyshev of the First Kind) 314\u003c\/p\u003e \u003cp\u003e14.4.2.4 Chebyshev–Gauss Method (Chebyshev of the Second Kind) 314\u003c\/p\u003e \u003cp\u003e14.4.2.5 Chebyshev–Gauss Method (Chebyshev of the Third Kind) 315\u003c\/p\u003e \u003cp\u003e14.4.2.6 Chebyshev–Gauss Method (Chebyshev of the Fourth Kind) 315\u003c\/p\u003e \u003cp\u003e14.4.2.7 Chebyshev–Gauss–Radau Method (Chebyshev of the First Kind) 315\u003c\/p\u003e \u003cp\u003e14.4.2.8 Chebyshev–Gauss–Lobatto Method (Chebyshev of the First Kind) 315\u003c\/p\u003e \u003cp\u003e14.4.2.9 Gauss–Legendre or Legendre–Gauss Method 315\u003c\/p\u003e \u003cp\u003e14.4.2.10 Gauss–Legendre–Radau or Legendre–Gauss–Radau Method 315\u003c\/p\u003e \u003cp\u003e14.4.2.11 Gauss–Legendre–Lobatto or Legendre–Gauss–Lobatto Method 316\u003c\/p\u003e \u003cp\u003e14.4.3 Numerical Applications: Integral Quadrature 316\u003c\/p\u003e \u003cp\u003e14.4.4 Numerical Applications: Taylor-Based Integral Quadrature 320\u003c\/p\u003e \u003cp\u003e14.5 General View: The Two-Dimensional Case 324\u003c\/p\u003e \u003cp\u003eReferences 340\u003c\/p\u003e \u003cp\u003e\u003cb\u003e15 Brain Activity Reconstruction by Finding a Source Parameter in an Inverse Problem \u003c\/b\u003e\u003cb\u003e343\u003cbr\u003e\u003c\/b\u003e\u003ci\u003eAmir H. Hadian-Rasanan and Jamal Amani Rad\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e15.1 Introduction 343\u003c\/p\u003e \u003cp\u003e15.1.1 Statement of the Problem 344\u003c\/p\u003e \u003cp\u003e15.1.2 Brief Review of Other Methods Existing in the Literature 345\u003c\/p\u003e \u003cp\u003e15.2 Methodology 346\u003c\/p\u003e \u003cp\u003e15.2.1 Weighted Residual Methods and Collocation Algorithm 346\u003c\/p\u003e \u003cp\u003e15.2.2 Function Approximation Using Chebyshev Polynomials 349\u003c\/p\u003e \u003cp\u003e15.3 Implementation 353\u003c\/p\u003e \u003cp\u003e15.4 Numerical Results and Discussion 354\u003c\/p\u003e \u003cp\u003e15.4.1 Test Problem 1 355\u003c\/p\u003e \u003cp\u003e15.4.2 Test Problem 2 357\u003c\/p\u003e \u003cp\u003e15.4.3 Test Problem 3 358\u003c\/p\u003e \u003cp\u003e15.4.4 Test Problem 4 359\u003c\/p\u003e \u003cp\u003e15.4.5 Test Problem 5 362\u003c\/p\u003e \u003cp\u003e15.5 Conclusion 365\u003c\/p\u003e \u003cp\u003eReferences 365\u003c\/p\u003e \u003cp\u003e\u003cb\u003e16 Optimal Resource Allocation in Controlling Infectious Diseases \u003c\/b\u003e\u003cb\u003e369\u003cbr\u003e\u003c\/b\u003e\u003ci\u003eA.C. Mahasinghe, S.S.N. Perera, and K.K.W.H. Erandi\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e16.1 Introduction 369\u003c\/p\u003e \u003cp\u003e16.2 Mobility-Based Resource Distribution 370\u003c\/p\u003e \u003cp\u003e16.2.1 Distribution of National Resources 370\u003c\/p\u003e \u003cp\u003e16.2.2 Transmission Dynamics 371\u003c\/p\u003e \u003cp\u003e16.2.2.1 Compartment Models 371\u003c\/p\u003e \u003cp\u003e16.2.2.2 SI Model 371\u003c\/p\u003e \u003cp\u003e16.2.2.3 Exact Solution 371\u003c\/p\u003e \u003cp\u003e16.2.2.4 Transmission Rate and Potential 372\u003c\/p\u003e \u003cp\u003e16.2.3 Nonlinear Problem Formulation 373\u003c\/p\u003e \u003cp\u003e16.2.3.1 Piecewise Linear Reformulation 374\u003c\/p\u003e \u003cp\u003e16.2.3.2 Computational Experience 374\u003c\/p\u003e \u003cp\u003e16.3 Connection–Strength Minimization 376\u003c\/p\u003e \u003cp\u003e16.3.1 Network Model 376\u003c\/p\u003e \u003cp\u003e16.3.1.1 Disease Transmission Potential 376\u003c\/p\u003e \u003cp\u003e16.3.1.2 An Example 376\u003c\/p\u003e \u003cp\u003e16.3.2 Nonlinear Problem Formulation 377\u003c\/p\u003e \u003cp\u003e16.3.2.1 Connection Strength Measure 377\u003c\/p\u003e \u003cp\u003e16.3.2.2 Piecewise Linear Approximation 378\u003c\/p\u003e \u003cp\u003e16.3.2.3 Computational Experience 379\u003c\/p\u003e \u003cp\u003e16.4 Risk Minimization 379\u003c\/p\u003e \u003cp\u003e16.4.1 Novel Strategies for Individuals 379\u003c\/p\u003e \u003cp\u003e16.4.1.1 Epidemiological Isolation 380\u003c\/p\u003e \u003cp\u003e16.4.1.2 Identifying Objectives 380\u003c\/p\u003e \u003cp\u003e16.4.2 Minimizing the High-Risk Population 381\u003c\/p\u003e \u003cp\u003e16.4.2.1 An Example 381\u003c\/p\u003e \u003cp\u003e16.4.2.2 Model Formulation 382\u003c\/p\u003e \u003cp\u003e16.4.2.3 Linear Integer Program 383\u003c\/p\u003e \u003cp\u003e16.4.2.4 Computational Experience 383\u003c\/p\u003e \u003cp\u003e16.4.3 Minimizing the Total Risk 384\u003c\/p\u003e \u003cp\u003e16.4.4 Goal Programming Approach 384\u003c\/p\u003e \u003cp\u003e16.5 Conclusion 386\u003c\/p\u003e \u003cp\u003eReferences 387\u003c\/p\u003e \u003cp\u003e\u003cb\u003e17 Artificial Intelligence and Autonomous Car \u003c\/b\u003e\u003cb\u003e391\u003cbr\u003e\u003c\/b\u003e\u003ci\u003eMerve Ar\u003c\/i\u003eı\u003ci\u003etürk, S\u003c\/i\u003eı\u003ci\u003erma Yavuz, and Tofigh Allahviranloo\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e17.1 Introduction 391\u003c\/p\u003e \u003cp\u003e17.2 What is Artificial Intelligence? 391\u003c\/p\u003e \u003cp\u003e17.3 Natural Language Processing 391\u003c\/p\u003e \u003cp\u003e17.4 Robotics 393\u003c\/p\u003e \u003cp\u003e17.4.1 Classification by Axes 393\u003c\/p\u003e \u003cp\u003e17.4.1.1 Axis Concept in Robot Manipulators 393\u003c\/p\u003e \u003cp\u003e17.4.2 Classification of Robots by Coordinate Systems 394\u003c\/p\u003e \u003cp\u003e17.4.3 Other Robotic Classifications 394\u003c\/p\u003e \u003cp\u003e17.5 Image Processing 395\u003c\/p\u003e \u003cp\u003e17.5.1 Artificial Intelligence in Image Processing 395\u003c\/p\u003e \u003cp\u003e17.5.2 Image Processing Techniques 395\u003c\/p\u003e \u003cp\u003e17.5.2.1 Image Preprocessing and Enhancement 396\u003c\/p\u003e \u003cp\u003e17.5.2.2 Image Segmentation 396\u003c\/p\u003e \u003cp\u003e17.5.2.3 Feature Extraction 396\u003c\/p\u003e \u003cp\u003e17.5.2.4 Image Classification 396\u003c\/p\u003e \u003cp\u003e17.5.3 Artificial Intelligence Support in Digital Image Processing 397\u003c\/p\u003e \u003cp\u003e17.5.3.1 Creating a Cancer Treatment Plan 397\u003c\/p\u003e \u003cp\u003e17.5.3.2 Skin Cancer Diagnosis 397\u003c\/p\u003e \u003cp\u003e17.6 Problem Solving 397\u003c\/p\u003e \u003cp\u003e17.6.1 Problem-solving Process 397\u003c\/p\u003e \u003cp\u003e17.7 Optimization 399\u003c\/p\u003e \u003cp\u003e17.7.1 Optimization Techniques in Artificial Intelligence 399\u003c\/p\u003e \u003cp\u003e17.8 Autonomous Systems 400\u003c\/p\u003e \u003cp\u003e17.8.1 History of Autonomous System 400\u003c\/p\u003e \u003cp\u003e17.8.2 What is an Autonomous Car? 401\u003c\/p\u003e \u003cp\u003e17.8.3 Literature of Autonomous Car 402\u003c\/p\u003e \u003cp\u003e17.8.4 How Does an Autonomous Car Work? 405\u003c\/p\u003e \u003cp\u003e17.8.5 Concept of Self-driving Car 406\u003c\/p\u003e \u003cp\u003e17.8.5.1 Image Classification 407\u003c\/p\u003e \u003cp\u003e17.8.5.2 Object Tracking 407\u003c\/p\u003e \u003cp\u003e17.8.5.3 Lane Detection 408\u003c\/p\u003e \u003cp\u003e17.8.5.4 Introduction to Deep Learning 408\u003c\/p\u003e \u003cp\u003e17.8.6 Evaluation 409\u003c\/p\u003e \u003cp\u003e17.9 Conclusion 410\u003c\/p\u003e \u003cp\u003eReferences 410\u003c\/p\u003e \u003cp\u003e\u003cb\u003e18 Different Techniques to Solve Monotone Inclusion Problems \u003c\/b\u003e\u003cb\u003e413\u003cbr\u003e\u003c\/b\u003e\u003ci\u003eTanmoy Som, Pankaj Gautam, Avinash Dixit, and D. R. Sahu\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e18.1 Introduction 413\u003c\/p\u003e \u003cp\u003e18.2 Preliminaries 414\u003c\/p\u003e \u003cp\u003e18.3 Proximal Point Algorithm 415\u003c\/p\u003e \u003cp\u003e18.4 Splitting Algorithms 415\u003c\/p\u003e \u003cp\u003e18.4.1 Douglas–Rachford Splitting Algorithm 416\u003c\/p\u003e \u003cp\u003e18.4.2 Forward–Backward Algorithm 416\u003c\/p\u003e \u003cp\u003e18.5 Inertial Methods 418\u003c\/p\u003e \u003cp\u003e18.5.1 Inertial Proximal Point Algorithm 419\u003c\/p\u003e \u003cp\u003e18.5.2 Splitting Inertial Proximal Point Algorithm 421\u003c\/p\u003e \u003cp\u003e18.5.3 Inertial Douglas–Rachford Splitting Algorithm 421\u003c\/p\u003e \u003cp\u003e18.5.4 Pock and Lorenz’s Variable Metric Forward–Backward Algorithm 422\u003c\/p\u003e \u003cp\u003e18.5.5 Numerical Example 428\u003c\/p\u003e \u003cp\u003e18.6 Numerical Experiments 429\u003c\/p\u003e \u003cp\u003eReferences 430\u003c\/p\u003e \u003cp\u003eIndex 433\u003c\/p\u003e  \u003cp\u003e\u003cb\u003ePROFESSOR SNEHASHISH CHAKRAVERTY,\u003c\/b\u003e is working in the Department of Mathematics (Applied Mathematics Group), National Institute of Technology Rourkela, Odisha, India as a Senior (Higher Administrative Grade) Professor. Prior to this he was with CSIR-Central Building Research Institute, Roorkee, India. Prof. Chakraverty received his Ph. D. from University of Roorkee (now IIT Roorkee). There after he did his post-doctoral research at Institute of Sound and Vibration Research (ISVR), University of Southampton, U.K. and at the Faculty of Engineering and Computer Science, Concordia University, Canada. He has authored\/co-authored 20 books, published 356 research papers in journals and conferences. Prof. Chakraverty is the Chief Editor of \"\u003ci\u003eInternational Journal of Fuzzy Computation and Modelling\"\u003c\/i\u003e (IJFCM), Inderscience Publisher, Switzerland (http:\/\/www.inderscience.com\/ijfcm) and Associate Editor of \"Computational Methods in Structural Engineering, Frontiers in Built Environment\". He has been the President of the Section of Mathematical sciences (including Statistics) of \"Indian Science Congress\" (2015-2016) and was the Vice President – \"Orissa Mathematical Society\" (2011-2013). Prof. Chakraverty is recipient of prestigious awards viz. Indian National Science Academy (INSA) nomination under International Collaboration\/Bilateral Exchange Program, Platinum Jubilee ISCA Lecture Award (2014), CSIR Young Scientist (1997), BOYSCAST (DST), UCOST Young Scientist (2007, 2008), Golden Jubilee Director's (CBRI) Award (2001), Roorkee University Gold Medals (1987, 1988) etc. His present research area includes Differential Equations (Ordinary, Partial and Fractional), Numerical Analysis and Computational Methods, Structural Dynamics (FGM, Nano) and Fluid Dynamics, Mathematical Modeling and Uncertainty Modeling, Soft Computing and Machine Intelligence (Artificial Neural Network, Fuzzy, Interval and Affine Computations).   \u003c\/p\u003e\u003cp\u003e\u003cb\u003eBrings mathematics to bear on your real-world, scientific problems\u003c\/b\u003e \u003c\/p\u003e\u003cp\u003e\u003ci\u003eMathematical Methods in Interdisciplinary Sciences\u003c\/i\u003e provides a practical and usable framework for bringing a mathematical approach to modelling real-life scientific and technological problems. The collection of chapters Dr. Snehashish Chakraverty has provided describe in detail how to bring mathematics, statistics, and computational methods to the fore to solve even the most stubborn problems involving the intersection of multiple fields of study. Graduate students, postgraduate students, researchers, and professors will all benefit significantly from the author's clear approach to applied mathematics. \u003c\/p\u003e\u003cp\u003eThe book covers a wide range of interdisciplinary topics in which mathematics can be brought to bear on challenging problems requiring creative solutions. Subjects include: \u003c\/p\u003e\u003cul\u003e \u003cli\u003eStructural static and vibration problems\u003c\/li\u003e \u003cli\u003eHeat conduction and diffusion problems\u003c\/li\u003e \u003cli\u003eFluid dynamics problems\u003c\/li\u003e \u003c\/ul\u003e \u003cp\u003eThe book also covers topics as diverse as soft computing and machine intelligence. It concludes with examinations of various fields of application, like infectious diseases, autonomous car and monotone inclusion problems.\u003c\/p\u003e","brand":"Wiley","offers":[{"title":"Default Title","offer_id":47989586788581,"sku":"NP9781119585503","price":128.95,"currency_code":"USD","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/1842\/7735\/files\/9781119585503.jpg?v=1761784706","url":"https:\/\/k12savings.com\/products\/mathematical-methods-in-interdisciplinary-sciences-isbn-9781119585503","provider":"K12savings","version":"1.0","type":"link"}