Table of Contents

Cover

Title Page

Dedication

Preface

1 Brownian Motion in EOQ

1.1 Introduction
1.2 Assumptions in EOQ
1.3 Methodology
1.4 Results
1.5 Discussion
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
3.3 Theoretical Foundations of Shadowed Sets
3.4 Principles for Constructing Decision-Theoretic Approximation
3.5 Concluding Remarks and Future Directions
References

4 Intuitionistic Fuzzy Rough Sets: Theory to Practice

4.1 Introduction
4.2 Preliminaries
4.3 Intuitionistic Fuzzy Rough Sets
4.4 Extension and Hybridization of Intuitionistic Fuzzy Rough Sets
4.5 Applications of Intuitionistic Fuzzy Rough Sets
4.6 Work Distribution of IFRS Country-Wise and Year-Wise
4.7 Conclusion
Acknowledgement
References

5 Satellite-Based Estimation of Ambient Particulate Matters (PM_2.5) 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
6.2 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
8.4 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
10.3 Work Flow of Artificial Intelligence & Application 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
11.4 Comparative Study of Mathematical Model in the Time of Covid-19 – A Review
11.5 Corona Epidemic in the Context of West Bengal: Predictive Mathematical Model
References

12 Application of Mathematical Modeling in Various Fields in Light of Fuzzy Logic

12.1 Introduction
12.2 Fuzzy Logic
12.3 Literature Review
12.4 Applications of Fuzzy Logic
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
13.5 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
15.6 Reproduction Module
15.7 Example
15.8 Schema Theorem
15.9 Conclusion
15.10 Future Scope
References

16 Mathematically Enhanced Corrosion Detection

16.1 Introduction
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
18.4 Synchronization of Modified Chaotic Colpitts Oscillator
18.5 The Synchronization of Colpitts Oscillator via Backstepping Control
18.6 Circuit Implementation
18.7 Conclusion
References

Index

Also of Interest

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List of Illustrations

Chapter 1

Figure 1.1 Optimal result of the order quantity in EOQ.
Figure 1.2 Graphical representation of Inventory Instantaneous demand in Brownia...
Figure 1.3 Trapezoidal rule in brownian movement.

Chapter 2

Figure 2.1 This is a vertical cross-section of a 3-D model. The model represents...
Figure 2.2 Schematic diagram of the new method for sampling and measuring potent...
Figure 2.3 Computation of changes in the potential field response with increasin...
Figure 2.4 Electrode array for landfill monitoring.
Figure 2.5 Electrode array for monitoring EOR/IOR processes using subsurface cur...

Chapter 4

Figure 4.1 Lower and upper approximation of set X.
Figure 4.2 Intuitionistic fuzzy set as a generalization of fuzzy set.
Figure 4.3 Intuitionistic fuzzy rough set.
Figure 4.4 Application of IF rough sets in various fields.
Figure 4.5 The country-wise distribution for the number of works in the field of...
Figure 4.6 The year-wise distribution for the number of works in the field of IF...

Chapter 5

Figure 5.1 Residual plot for linear regression model of Set I.
Figure 5.2 Residual plot for linear regression model of Set II.
Figure 5.3 Residual plot for linear regression model of Set III.
Figure 5.4 Residual plot for linear regression model of Set IV.
Figure 5.5 Residual plot for linear regression model of Set V.
Figure 5.6 Residual plot for linear regression model of Set VI.

Chapter 6

Figure 6.1 Schematic representation of simulation.

Chapter 7

Figure 7.1 Graph for flow value of cement mortar with nano silica.
Figure 7.2 Graph for flow value of cement mortar with nano Alumina.
Figure 7.3 Graph for flow value of cement mortar with nano zinc oxide.
Figure 7.4 Graph for flow value of cement mortar with PVA.
Figure 7.5 Graph for flow value of cement mortar with nano silica + PVA.
Figure 7.6 Graph for flow value of cement mortar with nano Alumina + PVA.
Figure 7.7 Graph for flow value of cement mortar with nano Zinc oxide + PVA.
Figure 7.8 Graph for flow value of cement mortar with nano silica + nano alumina...

Chapter 8

Figure 8.1 Crystal structure of half-Heusler alloys; (a) LiZnP and (b) LiCdP.
Figure 8.2 Total energy vs. volume for half-Heusler alloys; (a) LiZnP and (b) Li...
Figure 8.3 (a-b) Band structure of half-Heusler alloys; (a) LiZnP and (b) LiCdP.
Figure 8.4 Total density of states (a−b) and Partial density of states (c−d) of ...
Figure 8.5 Charge density plots for half-Heusler alloys; (a) LiZnP and (b) LiCdP...
Figure 8.6 Variation of Debye temperature with temperature for (a) LiZnP and (b)...
Figure 8.7 Variation of Gruneisen parameter with temperature for (a) LiZnP and (...
Figure 8.8 Variation of bulk modulus with temperature for (a) LiZnP and (b) LiCd...
Figure 8.9 Variation of specific heat capacity with temperature for (a) LiZnP an...
Figure 8.10 Variation of thermal expansion coefficient with temperature for (a) ...
Figure 8.11 Variation of entropy with temperature for (a) LiZnP and (b) LiCdP.

Chapter 10

Figure 10.1 Mathematical topics covered.
Figure 10.2 Cost function.
Figure 10.3 Various types of losses.
Figure 10.4 Statistical concepts.
Figure 10.5 Descriptive statistics.
Figure 10.6 Data visualizations.
Figure 10.7 Work flow of building an artificial intelligence model.
Figure 10.8 Steps of processing the dataset.
Figure 10.9 Application areas.
Figure 10.10 Trending areas.

Chapter 12

Figure 12.1 An elementary representation of the world’s scientific method is con...
Figure 12.2 The conceptual approach to creating a model relates to the developme...
Figure 12.3 A socioeconomic model can be constructed based on issues related to ...
Figure 12.4 Some fields related to fuzzy logic and fuzzy set theory [2, 3, 5].
Figure 12.5 The working process of the air conditioner [21].
Figure 12.6 Use of fuzzy logic for decision making during car driving [18].

Chapter 13

Figure 13.1 An overview of recommendation techniques [13].
Figure 13.2 Content-based filtering technique [5].
Figure 13.3 Collaborative filtering technique [5].

Chapter 14

Figure 14.1 Screenshot for the shear capacity prediction program.
Graph 14.1 The comparison of testing result for Neural Networks.
Graph 14.2 The comparison of testing result for Genetic Programming.
Graph 14.3 Coefficient of determination (the results of ANN).
Graph 14.4 Coefficient of determination (the results for GEP).

Chapter 16

Figure 16.1 (a) Concrete beam specimen. (b) Three small holes in sound steel rei...
Figure 16.2 Raw magnetic field data from the surface of the drilled reinforced c...
Figure 16.3 Raw magnetic field data from the surface of sound reinforced concret...
Figure 16.4 Eigensignals of sound steel reinforcement.
Figure 16.5 Eigensignals of drilled steel reinforcement.
Figure 16.6 Subtraction of Eigensignal from threshold Eigensignal. Red line show...

Chapter 17

Figure 17.1 Flow diagram of EGPLC model.
Figure 17.2 Pictorial representation of EGPLC.
Figure 17.3 Stability of deterministic EGPLC model.
Figure 17.4 Stochastic of EGPLC model.

Chapter 18

Figure 18.1 The circuit diagram.
Figure 18.2 Lyapunov exponents of the Modified Colpitts oscillator. (a) The Lyap...
Figure 18.3 Portrait of Colpitts. (a) Chaotic nature between x₁ and x₂. (b) Poin...
Figure 18.4 The parameter estimation of the modified Colpitts oscillator.
Figure 18.5 The stability of the modified Colpitts oscillator.
Figure 18.6 Synchronization of the modified colpitts oscillator. (a) Synchroniza...
Figure 18.7 Error dynamics of chaotic colspitts oscillator.
Figure 18.8 Synchronization of identical modified Colpitts oscillator, error plo...
Figure 18.9 Op amp circuit diagram of chaotic variable x₁.
Figure 18.10 Op amp circuit diagram of chaotic variable x₂.
Figure 18.11 Op amp circuit diagram of chaotic variable x₃.
Figure 18.12 Op amp circuit diagram of chaotic variable x₄.

List of Table

Chapter 2

Table 1.1 Effect of Q at various price.
Table 1.2 Optimal instantaneous demand solution of the order policy.
Table 1.3 Optimal results of the Inventory in Various Parameters
Table 1.4 Optimum results of the ordering processes.
Table 1.5 Optimum results of the number of integer cycles.
Table 1.6 Optimum results of the effective lead time.
Table 1.7 Optimal solution of the TCU(Y).
Table 1.8 Optimum results of the reorder in L_e D.
Table 1.9 The optimal results of the inventory in trapezoidal rule.

Chapter 3

Table 3.1 Fuzziness of elements in F.

Chapter 4

Table 4.1 Intuitionistic fuzzy rough sets.
Table 4.2 Applications of Intuitionistic fuzzy rough sets.

Chapter 5

Table 5.1 Statistical summary.
Table 5.2 Correlation matrix of dependent (PM_2.5) and independent parameters.
Table 5.3 Details of regression models.

Chapter 7

Table 7.1 Flow value of control mortar.
Table 7.2 Flow value of mortar with nano silica.
Table 7.3 Flow value of admixture with nano alumina.
Table 7.4 Flow value of cement mortar with nano Zinc oxide.
Table 7.5 Flow value of admixture with PVA.
Table 7.6 Flow value of admixture with nano silica + PVA.
Table 7.7 Flow value of admixture with nano alumina + PVA.
Table 7.8 Flow value of admixture with nano ZnO + PVA.
Table 7.9 Flow value of admixture with nano alumina + nano silica + PVA.

Chapter 8

Table 8.1 Ground state structural properties of transition metal-based Li half-H...
Table 8.2 Elastic properties of transition metal-based Li-half-Heusler alloys.
Table 8.3 Energy band gap (eV) of transition metal-based Li half-Heusler compoun...
Table 8.4 Thermodynamic properties of transition metal-based Li half-Heusler all...

Chapter 13

Table 13.1 User-movie rating matrix.
Table 13.2 Number coding of web pages for CTI dataset.
Table 13.3 Web navigational dataset.
Table 13.4 Similarity matrix for the sequences.
Table 13.5 Sample response matrix for User.
Table 13.6 Recommendations based on weight.

Chapter 14

Table 14.1 Data range of model parameters.
Table 14.2 Statistical data for the selected model.
Table 14.3 Statistical data for the selected model.
Table 14.4 List of the parameters of the model developed.
Table 14.5 Model comparison.

Chapter 16

Table 16.1 Geometry information for the three holes in the steel reinforcement.

Chapter 18

Table 18.1 LEs of system (1) for observation time (T) = 500, sampling time (Δt) ...

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Library of Congress Cataloging-in-Publication Data

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10 9 8 7 6 5 4 3 2 1

Preface

Chapter 1
The main aim of Inventory EOQ model is to reduce the Ordering Cost and Holding Cost in the Company. Based on Numerical Example, three proposed models are applied in EOQ. This leads to Brownian Path, which is based on Hausdroff Measure and Levy processes. Hence it is Fractals.

Chapter 2
This chapter gives a good description of ill-posed inverse problems encountered in the field of electrical geophysics. It begins with an overview of the present state of knowledge about electrical resistivity methods for mapping and monitoring in-situ processes that cannot be accessed directly. Based on reciprocity and perturbation analysis, an attempt has been made to introduce generalized multi-dimensional resistivity inversion methods. It may be found highly useful in environmental geophysics and geoengineering discipline to mapping and monitoring in-situ processes where electrical resistivity contrast is encountered.

Chapter 3
In this chapter, theoretical formulations of shadowed sets approximations (SSA) which hinge on ideas of uncertainty balance, average uncertainty and minimum approximation error are presented. Also, decision-theoretic three-way approximation (DTA) models which anchor on principles of minimum distance and least cost are revisited. Subsequently, we give a modified generalized model of decision-theoretic three-way approximation, called system, which does not impose values for and as against the trend in literature where and are chosen to be and respectively. A suitable formula for computing viable threshold from cost-sensitive and minimum distance-based models is derived.

Chapter 4
This chapter depicts a wide survey on Intuitionistic Fuzzy Rough Set theory. Several extensions of intuitionistic fuzzy rough sets and hybridization of intuitionistic fuzzy rough sets with other theories dealing with uncertainties are thoroughly looked over. A detailed discussion on intuitionistic fuzzy rough set theory in various real-world application fields is also presented.

Chapter 5
Air quality of different metropolitan cities of India has worsened over the last decade. Kolkata is among the most polluted urban areas of the country. Particulate matter smaller than 2.5μm (PM_2.5) is considered as one of the significant parameters for indicating the air quality. Ground based monitoring stations for PM _2.5 are limited over Kolkata. So, Aerosol optical depth (AOD) obtained by Aqua satellites and Moderate Resolution Imaging Spectroradiometer (MODIS) onboard EOS Terra are used to evaluate the local PM_2.5 concentration over Kolkata. This work attempts to develop a statistical model to estimate PM_2.5 concentration using AOD_MODIS and meteorological parameters (Temperature, Relative Humidity, Planetary Boundary Layer Height, Total Cloud Cover, Wind speed). The concentration of PM_2.5 is found to be influenced by various meteorological parameters. It is found that 52% of the variability of the dependent variable PM_2.5 is explained by the 6 explanatory variables (i.e., AOD_MODIS, temperature, relative humidity, average total cloud, planetary boundary layer height and wind speed) whereas only 3.9% of the variability of the dependent variable PM_2.5 is explained by AOD alone as explanatory variable.

Chapter 6
In this chapter we would see inventory systems and learn to manage it with simulation technique. We would study simulation which is performed manually for better understanding of the topic. Then some merits and demerits of it, Monte Carlo simulation technique and its application in a real life problem would be delved in. We would use Excel software to generate random numbers and perform simulation with it. Inventory sales for a confectionary bakery shop would be predicted for next few days. At the end we would compare and plot a graph so as to see and understand simulation better.

Chapter 7
The chapter gives an idea about change in characteristics of cement mortar while adding some nano admixtures and polymer PVA. Workability of mortar is measured in terms of flow value that is necessary to know how the mortar will behave with these additives. Final strength is dependent on various factors out of which workability is one factor. Also the handling with mortar in the field while mixing, transporting, pouring and compacting the workability plays important role hence various additives are added to achieve proper workability. In this article various nano materials like nano alumina, nano silica, nano zinc oxide, and polyvinyl alcohol has been tried for changing the workability.

Chapter 8
This chapter explores various properties of half-Heusler alloys; LiZnP and LiCdP. All the calculations are carried out based on the density functional theory using pseudopotential plane-wave method as implemented in the Quantum espresso package. The structural and electronic features are well described in result and discussion part along with thermodynamic properties. This chapter exposes the semiconductor and brittle behavior of LiZnP and LiCdP alloys.

Chapter 9
In this chapter, we establish a new common fixed point theorem satisfying the digital topology with Contractive mappings in fuzzy sets. Rather than focussing on mathematical details, we will concentrate on making the concepts as clear as possible. There are several useful technical introductions in fuzzy sets and fuzzy logic with digital space. fuzzy set theory is an analytic framework for handling concepts that are simultaneously categorical and dimensional. starting with a rational for fuzzy sets. in this chapter we provide some basic definitions and results for fuzzy sets. In this chapter we shall discuss two important categories of fuzzy logic with linear applications “digital” and “contractions “ with respect to fuzzy digital applications.

Chapter 10
This chapter discusses the bond between mathematics & Artificial intelligence. Mathematics helps to solve the challenging task of hypothetical problems in artificial intelligence using traditional methods and techniques. In the first part the main concern is to demonstrate the mathematical concepts like Linear Algebra in dimensionality reduction of large datasets, Eigen Vectors in ranking of features of dataset, Calculus in optimization task, Statistics for data visualization and so on. The later part discusses the work flow of artificial intelligence and the application areas where Artificial Intelligence is using now a days.

Chapter 11
In this chapter three mathematical models have been used. One is model based on Geometric Progression (G.P.). The second is SIR model and the third one is constructed using differential equations. The model based on G.P. shows how coronavirus is spread using tree chart, assuming that an infected person is capable of infecting two persons who come in contact with the former. It can also be observed that there is a significant difference between the number of covid patients with and without the lockdown.

Chapter 12
This chapter describes about the application of Fuzzy Logic in Mathematical modelling. The chapter is started with explanation about Mathematical modelling with definition and examples. With the help of principles of Mathematical Models, how real world problems can be solved by it, is described. Fuzzy logic is widely accepted and used term in the light of development for application, tools, techniques as Fuzzy Cognitive Maps, Fuzzy Cluster Means, etc. Here Fuzzy Logic Concept has been studied and tried to explain applications of the concept in various fields as Mathematics, Science, Business, Finance, Controller of Temperature, Home appliances, Aeronautics, Defence, Medical Science and Bioinformatics, Engineering Fields such as Mechanical, Industrial, Production, Electronics, Chemical, Automotives, Signal Processing and Communication, Robotics.

Chapter 13
This chapter explores the different types of recommender techniques with its mathematical foundation and also discusses some of the problems in the prevailing system. It discusses use of sequential patterns of web navigation along with the content information and is based on set and sequence similarity measure (S3M), principle of upper approximation and singular value decomposition for generating recommendations on web data. This chapter makes use of mathematics involved in finding the set and sequence similarity for recommendation to user on CTI news dataset.

Chapter 14
The adhesive anchors are usually installed into un-cracked hardened concrete. The Artificial Intelligence methodology of Neural Network (NN) and Genetic Expression Programming (GEP) are used to develop an explicit equation for estimating and predicting the shear capacity of a single adhesive anchor post. The main objective in this chapter is to provide a mathematical tool to predict shear capacity or shear strength of an anchor without any expansive laboratory testing. The Artificial Intelligence (AI) techniques are well-suited for assessment and prediction purposes.

Chapter 15
Genetic Algorithms is an easy form of learning and improvising design of Algorithm. The foundation of the principle is Darwin’s Natural selection, which states survival of the fittest. It offers solutions to various problems and helps to evaluate the value and also permits to combine with each other. This chapter gives confidence to reproduce good solutions, it will steadily produce enhanced solutions. It proves that any range of problem can be supported and solved. Gene is generally made up of a cells which represents individual problems and it represents individual solution of the problem.

Chapter 16
Defects play a key role in the mechanical behavior of reinforced concrete structures during loading. These defects are mainly cracks or small holes. These are usually the results of steel rebar corrosion caused by electrochemical and chemical processes. Defect detections are the prime goal of Non Destructive Testing (NDT) methods. This chapter is mainly focused on the Passive Magnetic Inspection (PMI) method. This is an innovative NDT method, which is highly used to inspect a reinforced concrete sample with three holes, in three different positions and locations of steel reinforcement. Principal Component Analysis (PCA) technique is one of the several signal processing techniques is used herein for corrosion detection.

Chapter 17
This chapter focuses on the control of Plasmodium parasite by studying the stages in the cycle. Backstepping control technique is applied to breakup the life cycle of plasmodium parasites. Lyapunov function is derived for the recursive procedure for the entire system to reduce the energy rate of reproduction among plasmodium parasites. Depending upon the concerned state in the system, ‘pseudo controls’ are introduced so as to achieve global stability of plasmodium life cycle.

Chapter 18
The purpose of this paper is to introduce a new chaotic oscillator. Although different chaotic systems have been formulated by earlier researchers, only a few chaotic systems exhibit chaotic behaviour. In this work, a new chaotic system with chaotic attractor is introduced for triangular wave non-linearity. It is worth noting that this striking phenomenon rarely occurs in respect of chaotic systems. The system proposed in this paper has been realized with numerical simulation. The results emanating from the numerical simulation indicate the feasibility of the proposed chaotic system. More over, chaos control, stability, diffusion and synchronization of such a system have been dealt with.