Mathematical Modeling for Computer Applications

Biswadip Basu Mallik is a senior assistant professor of mathematics in the Department of Basic Sciences and Humanities at the Institute of Engineering and Management, India. He has been involved in teaching and research for more than 21 years and has published several research papers in various scientific journals along with book chapters with various publishers. He has authored five and has five patents to his credit. He is a managing editor of the Journal of Mathematical Sciences & Computational Mathematics and is an editorial board member and reviewer for several scientific journals.M. Niranjanamurthy, PhD, is an assistant professor in the Department of Computer Applications, M S Ramaiah Institute of Technology, Bangalore, Karnataka. He earned his PhD in computer science at JJTU, Rajasthan, India. He has over 11 years of teaching experience and two years of industry experience as a software engineer. He has published several books, and he is working on numerous books for Scrivener Publishing. He has published over 60 papers for scholarly journals and conferences, and he is working as a reviewer in 22 scientific journals. He also has numerous awards to his credit.Sharmistha Ghosh, PhD, is a professor at the Institute of Engineering and Management, India. She received her doctorate in mathematics from the Indian Institute of Technology, India. Her major field of study includes fuzzy and vague databases as well as computational fluid dynamics, and she has published several papers in scientific journals. She is also the editor of several scientific journals and works as reviewer of journals as well as doctoral theses in India as well abroad.Valentina Emilia Balas, PhD, is a full professor in the Department of Automatics and Applied Software at the Faculty of Engineering, "Aurel Vlaicu" University of Arad, Romania. She holds a PhD cum Laude in applied electronics and telecommunications from the Polytechnic University of Timisoara. She is the author of more than 350 research papers and is the editor-in-chief of two esteemed journals and is an editorial board member for several other national and international publications.Krishanu Deyasi is an associate professor in the Department of Basic Sciences and Humanities at the Institute of Engineering and Management, India. He earned his PhD from the Indian Institute of Science Education and Research, and he has postdoctoral experience from The Institute of Mathematical Sciences, India. He has written three books and has published papers in scientific journals. He is also an editor for several scientific journals.Santanu Das is as an assistant professor in the Department of Basic Sciences and Humanities at the Institute of Engineering and Management, India. He completed his undergraduate degree from and is pursuing his doctorate from Jadavpur University.

• Preface xxi1 Fermatean Fuzzy Entropy Measure with Application in Decision Making Using COPRAS Approach 1Mansi Bhatia, H. D. Arora, Anjali Naithani and Vijay Kumar1.1 Introduction 21.2 Preliminaries 41.3 Novel Fermatean Entropy Measure 51.4 Application of Entropy Measure Through COPRAS 71.5 Comparative Analysis 121.6 Conclusion 13References 132 Some Properties of Cartesian and Lexicographic Products of Soft Graphs 17Jinta Jose, Bobin George and Rajesh K. Thumbakara2.1 Introduction 172.2 Soft Graphs 182.3 Some Properties of Cartesian and Restricted Cartesian Products of Soft Graphs 202.4 Some Properties of Lexicographic and Restricted Lexicographic Products of Soft Graphs 232.5 Conclusion 26References 263 Advancements in Enhancing Car Object Detection in Complex and Adverse Environmental Conditions Through Deep Learning Techniques 29Rejuwan Shamim, Biswadip Basu Mallik and Trapty Agarwal3.1 Introduction 303.2 Literature Review 333.3 Methodology 353.4 Result 443.5 Discussion 493.6 Conclusion 54References 574 Approximation by Durrmeyer Type Operators Using Polya Distribution 61Prerna Sharma and Diwaker Sharma4.1 Introduction 614.2 Basic Outcomes 634.3 Direct Results 654.4 Discussion 73Disclaimer 73References 735 Solution of Pollutant Dispersion in Porous Medium Under Linear Sorption Using Finite Element Method 75Rashmi Radha, Tapan Paul, Rakesh Kumar Singh, Nav Kumar Mahato and Mritunjay Kumar Singh5.1 Introduction 765.2 Mathematical Formulation 775.3 Numerical Derivation of the Proposed Model Problem by FEM Method 795.4 Analytical Derivation of the Proposed Model Equation 815.5 Results and Discussion 835.6 Conclusion 87References 886 A Comparative Analysis of Fuzzy and Neutrosophic Database Models in Handling Imprecise Queries 91Doyel Sarkar and Sharmistha Ghosh6.1 Introduction 926.2 Basic Definitions 936.3 Processing Imprecise Query using Fuzzy and Neutrosophic Sets 946.4 Results and Discussion 986.5 Concluding Remarks 98References 997 Tweaked Portfolio Estimation Regarding Indian Securities Exchange: An Empirical Study 101Abhijit Biswas and Meghdoot Ghosh7.1 Introduction 1027.2 Literature Review in Financial Market 1027.3 Method 1037.4 Results 1077.5 Discussion 116References 1168 Fixed Point Results Related to Graph Theory 117Aditya Bhattacharya, Özen Özer, Sonendra Gupta, Ramakant Bhardwaj and Sonam8.1 Introduction 1178.2 Preliminaries 1188.3 Main Results 119References 1289 Unleashing GPT-3’s Potential in Automatic Text Generation: A Comprehensive Study and Analysis 131Rejuwan Shamim and Biswadip Basu Mallik9.1 Introduction 1329.2 Literature Review 1339.3 Methodology 1359.4 Evaluation Metrics 1409.5 Experimental Results 1439.6 Discussion 1479.7 Exploration of the Strengths and Weaknesses of GPT-3 for Automatic Text Generation 148Conclusion 150References 15110 Optimization Techniques and Their Applications in Science and Engineering 153Ravi Kiran Bagadi, Eali Stephen Neal Joshua, T. Pavankumar, S. NagaMallik Raj and Debnath Bhattacharyya10.1 Introduction 15410.2 Related Work 15910.3 Metaheuristic Optimization Techniques 16710.4 Multi-Objective Optimization 17210.5 Stochastic Optimization 17610.6 Robust Optimization 18010.7 Applications of Robust Optimization in Science and Engineering 18210.8 Applications of Optimization Techniques in Science and Engineering 18310.9 Challenges and Future Directions in Optimization 189Conclusion 194References 19511 On Sum 3-Equitable Labeling of Some Graphs 197Sarang Sadawarte and Sweta Srivastav11.1 Introduction 19711.2 Terminology and Notation 19811.3 Results 19911.4 Conclusions and Perspectives 205References 20512 An Application of Invariant Point Theory in G-Metric Spaces with Special Emphasis on Alpha-Psi Contraction 207Samriddhi Ghosh, Sonam, Deb Sarkar, Poulami Halder and Ramakant Bhardwaj12.1 Introduction 20712.2 Elementaries 21012.3 Main Result 211Acknowledgement 216Collision of Interest 216References 21713 Fixed Point Results for Compatible Mapping of Type (α) in Fuzzy Metric Spaces 219Poulami Halder, Samriddhi Ghosh, Ramakant Bhardwaj, Sonam and Satyendra Narayan13.1 Introduction 21913.2 Preliminaries 22013.3 Compatible Mappings of Type (α) 22213.4 Main Results 223Acknowledgement 229Conflict of Interest 229References 22914 Combined Matrices Associated with Soft Digraphs 231Bobin George, Jinta Jose and Rajesh K. Thumbakara14.1 Introduction 23114.2 Soft Digraphs 23214.3 Combined Adjacency Matrix of a Soft Digraph 23414.4 Combined Incidence Matrix of a Soft Digraph 23614.5 Conclusion 238References 23815 Refining Medical Text Query Responses: Tailoring Hugging Face’s BERT Model for Precise and Swift Medical Question Answering 241Rejuwan Shamim, Badria Sulaiman Alfurhood and Biswadip Basu Mallik15.1 Introduction 24215.2 Related Work 24415.3 Methodology 24815.4 Result 25315.5 Strengths and Weaknesses of the Fine-Tuned BERT Model 25515.6 Applications 25715.7 Conclusion 258References 26016 Machine Learning Mathematics: A Study on Concepts of Processing Knowledge 263Prasad Kaviti, Eali Stephen Neal Joshua, N. Venkatram, Dinesh Reddy and Debnath Bhattacharyya16.1 Introduction 26416.2 Mathematical Concepts in Machine Learning 26416.3 Conclusion 299Disclaimer 299References 29917 Nature-Inspired Algorithms to Optimize the Hyper-Parameters of Deep-Learning Networks for Diagnosing Brain Disorders – A Review 301Manoj Kumar Sharma, M. Shamim Kaiser and Kanad Ray17.1 Introduction 30217.2 Literature Review 30317.3 Applications 30717.4 Challenges and Future Directions 30917.5 Conclusions and Perspectives 312References 31218 YOLOv8 for Anomaly Detection in Surveillance Videos: Advanced Techniques for Identifying and Mitigating Abnormal Events 317Rejuwan Shamim, Badria Sulaiman Alfurhood, Trapty Agarwal and Biswadip Basu Mallik18.1 Introduction 31818.2 Overview of YOLOv8 and its Advantages in Object Detection 31918.3 Related Work 32118.4 YOLOv8 Architecture 32418.5 Dataset Preparation 32718.6 Training YOLOv8 for Anomaly Detection 33018.7 Evaluation Metrics 33218.8 Results and Discussion 33418.9 Conclusion 343References 34619 Linear Stability and Resonance of Oblate Infinitesimal in the Nearby Region of Triangular Equilibrium Points for Triaxial Primaries in the Elliptic Restricted Three Body Problem 351Shilpi Dewangan, A. Narayan and Poonam Duggad19.1 Introduction 35219.2 Equation of Motion 35319.3 Position of Triangular Equilibrium Points 35519.4 Normalization at Hamiltonian for Stability of First Order 35619.5 Resonance Cases 36619.6 Conclusion 368References 37020 Magnetic Nanofluid Flow with Micro‐Organisms and Viscous Dissipation 373Shweta Mishra, Sharmistha Ghosh and Hiranmoy MondalNomenclature 37420.1 Introduction 37520.2 Mathematical Exploration 37620.3 Similarity Transformation 37820.4 Heat-Mass Transferal 37920.5 Discussion of Results 38020.6 Conclusion 384References 38421 The Application of Deep Learning to the Localization of Brain Tumors 387Charanarur Panem, Srinivasa Rao Gundu, J. Vijaylaxmi and Biswadip Basu Mallik21.1 Introduction 38821.2 Proposed Method 38921.3 Conclusion 395Acknowledgement 395References 39522 Contextual Information Retrieval using Root Word Stemming in Indian Languages 397Chandamita Nath and Bhairab Sarma22.1 Introduction 39722.2 Literature Review 39922.3 Problem Statement 39922.4 Experimental Work 40022.5 Conclusion and Future Work 402Disclaimer 403References 40423 Recent Advances in Object Detection Based on YOLO-V 4 and Faster RCNN: A Review 405Anwesa Das, Atanu Nandi and Ishani Deb23.1 Introduction 40623.2 Literature Review 40723.3 Proposed Methodology 40923.4 Result and Discussion 41323.5 Conclusion 416References 41724 Detection of Leukemia Using Transfer Learning 419Biplab Kanti Das, Chanchal Ghosh, Joydeb Sheet and Himadri Sekhar Dutta24.1 Introduction 42024.2 Literature Survey 42124.3 Dataset 42324.4 Proposed Methodology 42424.5 Pre-Processing of Image 42524.6 Deep Learning Model Generation 42624.7 Classification 43024.8 Results and Analysis 43024.9 Conclusion and Future Direction 434References 43425 IoMT – An ML-Based Patient Monitoring System with Prediction of Health Condition 437Kakali Das, Sagnik Ghosh and Himadri Sekhar Dutta25.1 Introduction 43825.2 System Architecture 44025.3 Machine Learning Algorithm 44325.4 Results and Discussion 44425.5 Conclusion 449References 44926 Eulerian Soft Graphs 453Jinta Jose, Bobin George and Rajesh K. Thumbakara26.1 Introduction 45326.2 Soft Graphs 45426.3 Eulerian Soft Graphs 45426.4 Conclusion 460References 46127 An Algorithm to Solve an Exponential Diophantine Equation 463Subramani K. and Srinivasa Prasanna27.1 Introduction 46427.2 Example 46627.3 Conclusion 475Acknowledgements 475References 47528 Optimal Number of Emergency Facility and Its Positioning Using Nature-Based Algorithm: A Case of Mumbai City 477K.V. Ajaygopal and Rakesh Verma28.1 Introduction 47828.2 Literature Review 47928.3 Real-Life Application 48428.4 Results and Discussion 48728.5 Conclusion 489References 490Appendix 49229 Chicken Swarm Optimization Algorithm-Based Propagation Delay Estimation in Transmission Path of UWASN 501A. Kannappan and R.M. Bommi29.1 Introduction 50229.2 General Biology Behavior of Chicken Swarm 50329.3 Chicken Swarm Pseudocode 50629.4 Results and Discussion 50729.5 Conclusion 508References 50930 Frequency Analysis of Coreference Resolution 513Mridusmita Das and Apurbalal Senapati30.1 Introduction 51430.2 Existing Literature 51530.3 Resource Building for the English and Assamese Languages 51730.4 Description of the Data Sets 51730.5 Frequency Analysis of Coreference Relations 51830.6 Experiment and Result 52030.7 Conclusion 520References 52031 Hate Neologism in Election Context in India 523Sujit Das and Apurbalal Senapati31.1 Introduction 52431.2 Related Work 52531.3 Corpus Creation 52631.4 Methodology 52831.5 Result 52931.6 Conclusion 530References 530Index 533