Оглавление
Группа авторов. Mathematics in Computational Science and Engineering
Table of Contents
List of Illustrations
List of Table
Guide
Pages
Mathematics in Computational Science and Engineering
Dedication
Preface
1. Brownian Motion in EOQ
1.1 Introduction
1.2 Assumptions in EOQ. 1.2.1 Model Formulation
1.2.1.1 Assumptions
1.2.1.2 Notations
1.2.1.3 Inventory Ordering Cost
1.2.1.4 Inventory Holding Cost
1.2.1.5 Inventory Total Cost in EOQ
1.2.2 Example
1.2.3 Inventory Control Commodities in Instantaneous Demand Method Under Development of the Stock
1.2.3.1 Assumptions
1.2.3.2 Notations
1.2.3.3 Model Formulation
1.2.3.4 Numerical Examples
1.2.3.5 Sensitivity Analysis
1.2.4 Classic EOQ Method in Inventory
1.2.4.1 Assumptions
1.2.4.2 Notations
1.2.4.3 Mathematical Model
1.3 Methodology
1.3.1 Brownian Motion
1.4 Results
1.4.1 Numerical Examples
1.4.2 Sensitivity Analysis
1.4.3 Brownian Path in Hausdorff Dimension
1.4.4 The Hausdorff Measure
1.4.5 Levy Processes
1.5 Discussion
1.5.1 Future Research
1.6 Conclusions
References
2. Ill-Posed Resistivity Inverse Problems and its Application to Geoengineering Solutions
2.1 Introduction
2.2 Fundamentals of Ill-Posed Inverse Problems
2.3 Brief Historical Development of Resistivity Inversion
2.4 Overview of Inversion Schemes
2.5 Theoretical Basis for Multi-Dimensional Resistivity Inversion Technqiues
2.6 Mathematical Concept for Application to Geoengineering Problems
2.7 Mathematical Quantification of Resistivity Resolution and Detection
2.8 Scheme of Resistivity Data Presentation
2.9 Design Strategy for Monitoring Processes of IOR Projects, Geo-Engineering, and Geo-Environmental Problems
2.10 Final Remarks and Conclusions
References
3. Shadowed Set and Decision-Theoretic Three-Way Approximation of Fuzzy Sets
3.1 Introduction
3.2 Preliminaries on Three-Way Approximation of Fuzzy Sets. 3.2.1 Shadowed Set Approximation
3.2.2 Decision-Theoretic Three-Way Approximation
3.3 Theoretical Foundations of Shadowed Sets
3.3.1 Uncertainty Balance Models
3.3.1.1 Pedrycz’s (Pd) Model
3.3.1.2 Tahayori-Sadeghian-Pedrycz (TSP) Model
3.3.1.3 Ibrahim-William-West-Kana-Singh (IWKS) Model
3.3.2 Minimum Error or Deng-Yao (DY) Model
3.3.3 Average Uncertainty or Ibrahim-West (IW) Model
3.3.4 Nearest Quota of Uncertainty (WIK) Model
3.3.5 Algorithm for Constructing Shadowed Sets
3.3.6 Examples on Shadowed Set Approximation
3.4 Principles for Constructing Decision-Theoretic Approximation
3.4.1 Deng and Yao Special Decision-Theoretic (DYSD) Model
3.4.2 Zhang, Xia, Liu and Wang (ZXLW) Generalized Decision-Theoretic Model
3.4.3 A General Perspective to Decision-Theoretic Three-Way Approximation
3.4.3.1 Determination of n, m and p for Decision-Theoretic Three-Way Approximation
3.4.3.2 A General Decision-Theoretic Three-Way Approximation Partition Thresholds
3.4.4 Example on Decision-Theoretic Three-Way Approximation
3.5 Concluding Remarks and Future Directions
References
4. Intuitionistic Fuzzy Rough Sets: Theory to Practice
4.1 Introduction
4.2 Preliminaries
4.2.1 Rough Set Theory
4.2.2 Intuitionistic Fuzzy Set Theory
4.2.3 Intuitionistic Fuzzy-Rough Set Theory
4.3 Intuitionistic Fuzzy Rough Sets
4.4 Extension and Hybridization of Intuitionistic Fuzzy Rough Sets
4.4.1 Extension
4.4.1.1 Dominance-Based Intuitionistic Fuzzy Rough Sets
4.4.1.2 Covering-Based Intuitionistic Fuzzy Rough Sets
4.4.1.3 Kernel Intuitionistic Fuzzy Rough Sets
4.4.1.4 Tolerance-Based Intuitionistic Fuzzy Rough Sets
4.4.1.5 Interval-Valued Intuitionistic Fuzzy Rough Sets
4.4.2 Hybridization
4.4.2.1 Variable Precision Intuitionistic Fuzzy Rough Sets
4.4.2.2 Intuitionistic Fuzzy Neighbourhood Rough Sets
4.4.2.3 Intuitionistic Fuzzy Multigranulation Rough Sets
4.4.2.4 Intuitionistic Fuzzy Decision-Theoretic Rough Sets
4.4.2.5 Intuitionistic Fuzzy Rough Sets and Soft Intuitionistic Fuzzy Rough Sets
4.4.2.6 Multi-Adjoint Intuitionistic Fuzzy Rough Sets
4.4.2.7 Intuitionistic Fuzzy Quantified Rough Sets
4.4.2.8 Genetic Algorithm and IF Rough Sets
4.5 Applications of Intuitionistic Fuzzy Rough Sets
4.5.1 Attribute Reduction
4.5.2 Decision Making
4.5.3 Other Applications
4.6 Work Distribution of IFRS Country-Wise and Year-Wise
4.6.1 Country-Wise Work Distribution
4.6.2 Year-Wise Work Distribution
4.6.3 Limitations of Intuitionistic Fuzzy Rough Set Theory
4.7 Conclusion
Acknowledgement
References
5. Satellite-Based Estimation of Ambient Particulate Matters (PM2.5) Over a Metropolitan City in Eastern India
5.1 Introduction
5.2 Methodology
5.3 Result and Discussions
5.4 Conclusion
References
6. Computational Simulation Techniques in Inventory Management
6.1 Introduction. 6.1.1 Inventory Management
6.1.2 Simulation
6.2 Conclusion
References
7. Workability of Cement Mortar Using Nano Materials and PVA
7.1 Introduction
7.2 Literature Survey
7.3 Materials and Methods
7.4 Results and Discussion
7.5 Conclusion
References
8. Distinctive Features of Semiconducting and Brittle Half-Heusler Alloys; LiXP (X=Zn, Cd)
8.1 Introduction
8.2 Computation Method
8.3 Result and Discussion. 8.3.1 Structural Properties
8.3.2 Elastic Properties
8.3.3 Electronic Properties
8.3.4 Thermodynamic Properties
8.4 Conclusions
Acknowledgement
References
9. Fixed Point Results with Fuzzy Sets
9.1 Introduction
9.2 Definitions and Preliminaries
9.3 Main Results
References
10. Role of Mathematics in Novel Artificial Intelligence Realm
10.1 Introduction
10.2 Mathematical Concepts Applied in Artificial Intelligence
10.2.1 Linear Algebra
10.2.1.1 Matrix and Vectors
10.2.1.2 Eigen Value and Eigen Vector
10.2.1.3 Matrix Operations
10.2.1.4 Artificial Intelligence Algorithms That Use Linear Algebra
10.2.2 Calculus
10.2.2.1 Objective Function
10.2.2.2 Loss Function & Cost Function
10.2.2.2.1 Types of Loss Functions
10.2.2.3 Artificial Intelligence Algorithms That Use Calculus
10.2.3 Probability and Statistics
10.2.3.1 Population Versus Sample
10.2.3.2 Descriptive Statistics
10.2.3.3 Distributions
10.2.3.4 Probability
10.2.3.5 Correlation
10.2.3.6 Data Visualization Using Statistics
10.2.3.7 Artificial Intelligence Algorithms That Use Probability and Statistics
10.3 Work Flow of Artificial Intelligence & Application Areas
10.3.1 Application Areas
10.3.2 Trending Areas
10.4 Conclusion
References
11. Study of Corona Epidemic: Predictive Mathematical Model
11.1 Mathematical Modelling
11.2 Need of Mathematical Modelling
11.3 Methods of Construction of Mathematical Models. 11.3.1 Mathematical Modelling with the Help of Geometry
11.3.2 Mathematical Modelling with the Help of Algebra
11.3.3 Mathematical Modelling Using Trignometry
11.3.4 Mathematical Modelling with the Help of Ordinary Differential Equation (ODE)
11.3.5 Mathematical Modelling Using Partial Differential Equation (PDE)
11.3.6 Mathematical Modelling Using Difference Equation
11.4 Comparative Study of Mathematical Model in the Time of Covid-19 – A Review. 11.4.1 Review
11.4.2 Case Study
11.5 Corona Epidemic in the Context of West Bengal: Predictive Mathematical Model. 11.5.1 Overview
11.5.2 Case Study
11.5.3 Methodology
11.5.3.1 Exponential Model
11.5.3.2 Model Based on Geometric Progression (G.P.)
11.5.3.2.1 Without Implementation of Lockdown
11.5.3.2.2 With the Implementation of Lockdown
11.5.3.3 Model for Stay At Home
11.5.4 Discussion
References
12. Application of Mathematical Modeling in Various Fields in Light of Fuzzy Logic
12.1 Introduction. 12.1.1 Mathematical Modeling
12.1.2 Principles of Mathematical Models
12.2 Fuzzy Logic
12.2.1 Fuzzy Cognitive Maps & Induced Fuzzy Cognitive Maps
12.2.2 Fuzzy Cluster Means
12.3 Literature Review
12.4 Applications of Fuzzy Logic
12.4.1 Controller of Temperature
12.4.2 Usage of Fuzzy Logic in a Washing Machine
12.4.3 Air Conditioner
12.4.4 Aeronautics
12.4.5 Automotive Field
12.4.6 Business
12.4.7 Finance
12.4.8 Chemical Engineering
12.4.9 Defence
12.4.10 Electronics
12.4.11 Medical Science and Bioinformatics
12.4.12 Robotics
12.4.13 Signal Processing and Wireless Communication
12.4.14 Transportation Problems
12.5 Conclusion
References
13. A Mathematical Approach Using Set & Sequence Similarity Measure for Item Recommendation Using Sequential Web Data
13.1 Introduction
13.2 Measures of Assessment for Recommendation Engines
13.3 Related Work
13.4 Methodology/Research Design
13.4.1 Web Data Collection Through Web Logs
13.4.2 Web User Sessions Classification
13.5 Finding or Result
13.6 Conclusion and Future Work
References
14. Neural Network and Genetic Programming Based Explicit Formulations for Shear Capacity Estimation of Adhesive Anchors
14.1 General Introduction
14.2 Research Significance
14.3 Biological Nervous System
14.4 Constructing Artificial Neural Network Model
14.5 Genetic Programming (GP)
14.6 Administering Genetic Programming Scheme
14.7 Genetic Programming In Details
14.8 Genetic Expression Programming
14.9 Developing Model With Genexpo Software
14.10 Comparing NN and GEP Results
14.11 Conclusions
References
15. Adaptive Heuristic - Genetic Algorithms
15.1 Introduction
15.2 Genetic Algorithm
15.3 The Genetic Algorithm
15.4 Evaluation Module
15.5 Populace Module. 15.5.1 Introduction
15.5.2 Initialisation Technique
15.5.3 Deletion Technique
15.5.4 Parent Selection Procedure
15.5.5 Fitness Technique
15.5.6 Populace Size
15.5.7 Elitism
15.6 Reproduction Module. 15.6.1 Introduction
15.6.2 Operators
15.6.3 Mutation
15.6.4 Mutation Rate
15.6.5 Crossover Rate
15.6.6 Dynamic Mutation and Crossover Rates
15.7 Example
15.8 Schema Theorem. 15.8.1 Introduction
15.9 Conclusion
15.10 Future Scope
References
16. Mathematically Enhanced Corrosion Detection
16.1 Introduction
16.1.1 Mathematics in NDT
16.1.2 Principal Component Analysis (PCA)
16.2 Case Study: PCA Applied to PMI Data for Defect Detection
16.3 PCA Feature Extraction for PMI Method
16.4 Experimental Setup and Test
16.5 Results
16.6 Conclusions
References
17. Dynamics of Malaria Parasite with Effective Control Analysis
17.1 Introduction
17.2 The Mathematical Structure of EGPLC
17.3 The Modified EGPLC Model
17.4 Equilibria and Local Stability Analysis
17.5 Analysis of Global Stability
17.6 Global Stability Analysis with Back Propagation
17.7 Stability Analysis of Non-Deterministic EGPLC Model
17.8 Discussion on Numerical Simulation
17.9 Conclusion
17.10 Future Scope of the Work
References
18. Dynamics, Control, Stability, Diffusion and Synchronization of Modified Chaotic Colpitts Oscillator with Triangular Wave Non-Linearity Depending on the States
18.1 Introduction
18.2 The Mathematical Model of Chaotic Colpitts Oscillator
18.3 Adaptive Backstepping Control of the Modified Colpitts Oscillator with Unknown Parameters. 18.3.1 Proposed System
18.3.2 Numerical Simulation
18.4 Synchronization of Modified Chaotic Colpitts Oscillator
18.4.1 Synchronization of Modified Chaotic Colpitts Oscillator using Non-Linear Feedback Method
18.4.2 Numerical Simulation
18.5 The Synchronization of Colpitts Oscillator via Backstepping Control
18.5.1 Analysis of the Error Dynamics
18.5.2 Numerical Simulation
18.6 Circuit Implementation
18.7 Conclusion
References
Index
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