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Mathematical Methods in Interdisciplinary Sciences

Release Date: 2020/07/01
ISBN: 9781119585503
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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.

Table of Contents

  1. Cover
  2. Notes on Contributors
  3. Preface
  4. Acknowledgments
  5. 1 Connectionist Learning Models for Application Problems Involving Differential and Integral Equations
    1. 1.1 Introduction
    2. 1.2 Methodology for Differential Equations
    3. 1.3 Methodology for Solving a System of Fredholm Integral Equations of Second Kind
    4. 1.4 Numerical Examples and Discussion
    5. 1.5 Conclusion
    6. References
  6. 2 Deep Learning in Population Genetics: Prediction and Explanation of Selection of a Population
    1. 2.1 Introduction
    2. 2.2 Literature Review
    3. 2.3 Dataset Description
    4. 2.4 Objective
    5. 2.5 Relevant Theory, Results, and Discussions
    6. 2.6 Conclusion
    7. References
  7. 3 A Survey of Classification Techniques in Speech Emotion Recognition
    1. 3.1 Introduction
    2. 3.2 Emotional Speech Databases
    3. 3.3 SER Features
    4. 3.4 Classification Techniques
    5. 3.5 Difficulties in SER Studies
    6. 3.6 Conclusion
    7. References
  8. 4 Mathematical Methods in Deep Learning
    1. 4.1 Deep Learning Using Neural Networks
    2. 4.2 Introduction to Neural Networks
    3. 4.3 Other Activation Functions (Variant Forms of ReLU)
    4. 4.4 Backpropagation Algorithm
    5. 4.5 Performance and Accuracy
    6. 4.6 Results and Observation
    7. References
  9. 5 Multimodal Data Representation and Processing Based on Algebraic System of Aggregates
    1. 5.1 Introduction
    2. 5.2 Basic Statements of ASA
    3. 5.3 Operations on Aggregates and Multi‐images
    4. 5.4 Relations and Digital Intervals
    5. 5.5 Data Synchronization
    6. 5.6 Fuzzy Synchronization
    7. 5.7 Conclusion
    8. References
  10. 6 Nonprobabilistic Analysis of Thermal and Chemical Diffusion Problems with Uncertain Bounded Parameters
    1. 6.1 Introduction
    2. 6.2 Preliminaries
    3. 6.3 Finite Element Formulation for Tapered Fin
    4. 6.4 Radon Diffusion and Its Mechanism
    5. 6.5 Radon Diffusion Mechanism with TFN Parameters
    6. 6.6 Conclusion
    7. References
  11. 7 Arbitrary Order Differential Equations with Fuzzy Parameters
    1. 7.1 Introduction
    2. 7.2 Preliminaries
    3. 7.3 Arbitrary Order Integral and Derivative for Fuzzy‐Valued Functions
    4. 7.4 Generalized Fuzzy Laplace Transform with Respect to Another Function
    5. References
  12. 8 Fluid Dynamics Problems in Uncertain Environment
    1. 8.1 Introduction
    2. 8.2 Preliminaries
    3. 8.3 Problem Formulation
    4. 8.4 Methodology
    5. 8.5 Application of HPM and HPTM
    6. 8.6 Results and Discussion
    7. 8.7 Conclusion
    8. References
  13. 9 Fuzzy Rough Set Theory‐Based Feature Selection: A Review
    1. 9.1 Introduction
    2. 9.2 Preliminaries
    3. 9.3 Fuzzy Rough Set‐Based Attribute Reduction
    4. 9.4 Approaches for Semisupervised and Unsupervised Decision Systems
    5. 9.5 Decision Systems with Missing Values
    6. 9.6 Applications in Classification, Rule Extraction, and Other Application Areas
    7. 9.7 Limitations of Fuzzy Rough Set Theory
    8. 9.8 Conclusion
    9. References
  14. 10 Universal Intervals: Towards a Dependency‐Aware Interval Algebra
    1. 10.1 Introduction
    2. 10.2 The Need for Interval Computations
    3. 10.3 On Some Algebraic and Logical Fundamentals
    4. 10.4 Classical Intervals and the Dependency Problem
    5. 10.5 Interval Dependency: A Logical Treatment
    6. 10.6 Interval Enclosures Under Functional Dependence
    7. 10.7 Parametric Intervals: How Far They Can Go
    8. 10.8 Universal Intervals: An Interval Algebra with a Dependency Predicate
    9. 10.9 The S‐Field Algebra of Universal Intervals
    10. 10.10 Guaranteed Bounds or Best Approximation or Both?
    11. Supplementary Materials
    12. Acknowledgments
    13. References
  15. 11 Affine‐Contractor Approach to Handle Nonlinear Dynamical Problems in Uncertain Environment
    1. 11.1 Introduction
    2. 11.2 Classical Interval Arithmetic
    3. 11.3 Interval Dependency Problem
    4. 11.4 Affine Arithmetic
    5. 11.5 Contractor
    6. 11.6 Proposed Methodology
    7. 11.7 Numerical Examples
    8. 11.8 Conclusion
    9. References
  16. 12 Dynamic Behavior of Nanobeam Using Strain Gradient Model
    1. 12.1 Introduction
    2. 12.2 Mathematical Formulation of the Proposed Model
    3. 12.3 Review of the Differential Transform Method (DTM)
    4. 12.4 Application of DTM on Dynamic Behavior Analysis
    5. 12.5 Numerical Results and Discussion
    6. 12.6 Conclusion
    7. Acknowledgment
    8. References
  17. 13 Structural Static and Vibration Problems
    1. 13.1 Introduction
    2. 13.2 One‐parameter Groups
    3. 13.3 Infinitesimal Transformation
    4. 13.4 Canonical Coordinates
    5. 13.5 Algorithm for Lie Symmetry Point
    6. 13.6 Reduction of the Order of the ODE
    7. 13.7 Solution of First‐Order ODE with Lie Symmetry
    8. 13.8 Identification
    9. 13.9 Vibration of a Microcantilever Beam Subjected to Uniform Electrostatic Field
    10. 13.10 Contact Form for the Equation
    11. 13.11 Reducing in the Order of the Nonlinear ODE Representing the Vibration of a Microcantilever Beam Under Electrostatic Field
    12. 13.12 Nonlinear Pull‐in Voltage
    13. 13.13 Nonlinear Analysis of Pull‐in Voltage of Twin Microcantilever Beams
    14. 13.14 Nonlinear Analysis of Pull‐in Voltage of Twin Microcantilever Beams of Different Thicknesses
    15. References
  18. 14 Generalized Differential and Integral Quadrature: Theory and Applications
    1. 14.1 Introduction
    2. 14.2 Differential Quadrature
    3. 14.3 General View on Differential Quadrature
    4. 14.4 Generalized Integral Quadrature
    5. 14.5 General View: The Two‐Dimensional Case
    6. References
  19. 15 Brain Activity Reconstruction by Finding a Source Parameter in an Inverse Problem
    1. 15.1 Introduction
    2. 15.2 Methodology
    3. 15.3 Implementation
    4. 15.4 Numerical Results and Discussion
    5. 15.5 Conclusion
    6. References
  20. 16 Optimal Resource Allocation in Controlling Infectious Diseases
    1. 16.1 Introduction
    2. 16.2 Mobility‐Based Resource Distribution
    3. 16.3 Connection–Strength Minimization
    4. 16.4 Risk Minimization
    5. 16.5 Conclusion
    6. References
  21. 17 Artificial Intelligence and Autonomous Car
    1. 17.1 Introduction
    2. 17.2 What Is Artificial Intelligence?
    3. 17.3 Natural Language Processing
    4. 17.4 Robotics
    5. 17.5 Image Processing
    6. 17.6 Problem Solving
    7. 17.7 Optimization
    8. 17.8 Autonomous Systems
    9. 17.9 Conclusion
    10. References
  22. 18 Different Techniques to Solve Monotone Inclusion Problems
    1. 18.1 Introduction
    2. 18.2 Preliminaries
    3. 18.3 Proximal Point Algorithm
    4. 18.4 Splitting Algorithms
    5. 18.5 Inertial Methods
    6. 18.6 Numerical Experiments
    7. References
  23. Index
  24. End User License Agreement
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