book

Mathematical Methods in Interdisciplinary Sciences

by Snehashish Chakraverty

July 2020

Intermediate to advanced

464 pages

17h 2m

English

Wiley

Read now

Unlock full access

1.1 Introduction1.2 Methodology for Differential Equations1.3 Methodology for Solving a System of Fredholm Integral Equations of Second Kind1.4 Numerical Examples and Discussion1.5 ConclusionReferences
2.1 Introduction2.2 Literature Review2.3 Dataset Description2.4 Objective2.5 Relevant Theory, Results, and Discussions2.6 ConclusionReferences
3.1 Introduction3.2 Emotional Speech Databases3.3 SER Features3.4 Classification Techniques3.5 Difficulties in SER Studies3.6 ConclusionReferences
4.1 Deep Learning Using Neural Networks4.2 Introduction to Neural Networks4.3 Other Activation Functions (Variant Forms of ReLU)4.4 Backpropagation Algorithm4.5 Performance and Accuracy4.6 Results and ObservationReferences
5.1 Introduction5.2 Basic Statements of ASA5.3 Operations on Aggregates and Multi‐images5.4 Relations and Digital Intervals5.5 Data Synchronization5.6 Fuzzy Synchronization5.7 ConclusionReferences
6.1 Introduction6.2 Preliminaries6.3 Finite Element Formulation for Tapered Fin6.4 Radon Diffusion and Its Mechanism6.5 Radon Diffusion Mechanism with TFN Parameters6.6 ConclusionReferences

7.1 Introduction7.2 Preliminaries7.3 Arbitrary Order Integral and Derivative for Fuzzy‐Valued Functions7.4 Generalized Fuzzy Laplace Transform with Respect to Another FunctionReferences
8.1 Introduction8.2 Preliminaries8.3 Problem Formulation8.4 Methodology8.5 Application of HPM and HPTM8.6 Results and Discussion8.7 ConclusionReferences
9.1 Introduction9.2 Preliminaries9.3 Fuzzy Rough Set‐Based Attribute Reduction9.4 Approaches for Semisupervised and Unsupervised Decision Systems9.5 Decision Systems with Missing Values9.6 Applications in Classification, Rule Extraction, and Other Application Areas9.7 Limitations of Fuzzy Rough Set Theory9.8 ConclusionReferences
10.1 Introduction10.2 The Need for Interval Computations10.3 On Some Algebraic and Logical Fundamentals10.4 Classical Intervals and the Dependency Problem10.5 Interval Dependency: A Logical Treatment10.6 Interval Enclosures Under Functional Dependence10.7 Parametric Intervals: How Far They Can Go10.8 Universal Intervals: An Interval Algebra with a Dependency Predicate10.9 The S‐Field Algebra of Universal Intervals10.10 Guaranteed Bounds or Best Approximation or Both?Supplementary MaterialsAcknowledgmentsReferences
11.1 Introduction11.2 Classical Interval Arithmetic11.3 Interval Dependency Problem11.4 Affine Arithmetic11.5 Contractor11.6 Proposed Methodology11.7 Numerical Examples11.8 ConclusionReferences
12.1 Introduction12.2 Mathematical Formulation of the Proposed Model12.3 Review of the Differential Transform Method (DTM)12.4 Application of DTM on Dynamic Behavior Analysis12.5 Numerical Results and Discussion12.6 ConclusionAcknowledgmentReferences
13.1 Introduction13.2 One‐parameter Groups13.3 Infinitesimal Transformation13.4 Canonical Coordinates13.5 Algorithm for Lie Symmetry Point13.6 Reduction of the Order of the ODE13.7 Solution of First‐Order ODE with Lie Symmetry13.8 Identification13.9 Vibration of a Microcantilever Beam Subjected to Uniform Electrostatic Field13.10 Contact Form for the Equation13.11 Reducing in the Order of the Nonlinear ODE Representing the Vibration of a Microcantilever Beam Under Electrostatic Field13.12 Nonlinear Pull‐in Voltage13.13 Nonlinear Analysis of Pull‐in Voltage of Twin Microcantilever Beams13.14 Nonlinear Analysis of Pull‐in Voltage of Twin Microcantilever Beams of Different ThicknessesReferences
14.1 Introduction14.2 Differential Quadrature14.3 General View on Differential Quadrature14.4 Generalized Integral Quadrature14.5 General View: The Two‐Dimensional CaseReferences
15.1 Introduction15.2 Methodology15.3 Implementation15.4 Numerical Results and Discussion15.5 ConclusionReferences
16.1 Introduction16.2 Mobility‐Based Resource Distribution16.3 Connection–Strength Minimization16.4 Risk Minimization16.5 ConclusionReferences
17.1 Introduction17.2 What Is Artificial Intelligence?17.3 Natural Language Processing17.4 Robotics17.5 Image Processing17.6 Problem Solving17.7 Optimization17.8 Autonomous Systems17.9 ConclusionReferences
18.1 Introduction18.2 Preliminaries18.3 Proximal Point Algorithm18.4 Splitting Algorithms18.5 Inertial Methods18.6 Numerical ExperimentsReferences

Overview

Brings mathematics to bear on your real-world, scientific problems

Mathematical Methods in Interdisciplinary Sciences 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.

The book covers a wide range of interdisciplinary topics in which mathematics can be brought to bear on challenging problems requiring creative solutions. Subjects include:

Structural static and vibration problems
Heat conduction and diffusion problems
Fluid dynamics problems

The 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.