Mathematics and computer science. Volume 1. / edited by Sharmistha Ghosh [and four others].

Format:

Book

Author/Creator:

Ghosh, Sharmistha, Editor.

Contributor:

Ghosh, Sharmistha, editor.

Language:

English

Subjects (All):

Computer science--Mathematics.

Computer science.

Physical Description:

1 online resource (557 pages)

Edition:

1

Place of Publication:

Wiley 2023

Summary:

MATHEMATICS AND COMPUTER SCIENCE This first volume in a new multi-volume set gives readers the basic concepts and applications for diverse ideas and innovations in the field of computing together with its growing interactions with mathematics. This new edited volume from Wiley-Scrivener is the first of its kind to present scientific and technological innovations by leading academicians, eminent researchers, and experts around the world in the areas of mathematical sciences and computing. The chapters focus on recent advances in computer science, and mathematics, and where the two intersect to create value for end users through practical applications of the theory. The chapters herein cover scientific advancements across a diversified spectrum that includes differential as well as integral equations with applications, computational fluid dynamics, nanofluids, network theory and optimization, control theory, machine learning and artificial intelligence, big data analytics, Internet of Things, cryptography, fuzzy automata, statistics, and many more. Readers of this book will get access to diverse ideas and innovations in the field of computing together with its growing interactions in various fields of mathematics. Whether for the engineer, scientist, student, academic, or other industry professional, this is a must-have for any library.

Contents:

Cover

Title Page

Copyright Page

Contents

Preface

Chapter 1 Error Estimation of the Function by (Zrμ, r ≥1) Using Product Means (E,s)(N, pn,qn) of the Conjugate Fourier Series

1.1 Introduction

1.1.1 Definition 1

1.1.2 Definition 2

1.1.3 Definition 3

1.2 Theorems

1.2.1 Theorem 1

1.2.2 Theorem 2

1.3 Lemmas

1.3.1 Lemma 1

1.3.2 Lemma 2

1.3.3 Lemma 3

1.4 Proof of the Theorems

1.4.1 Proof of the Theorem 1

1.4.2 Proof of the Theorem 2

1.5 Corollaries

1.5.1 Corollary 1

1.5.2 Corollary 2

1.6 Example

1.7 Conclusion

References

Chapter 2 Blow Up and Decay of Solutions for a Klein-Gordon Equation With Delay and Variable Exponents

2.1 Introduction

2.2 Preliminaries

2.3 Blow Up of Solutions

2.4 Decay of Solutions

Acknowledgment

Chapter 3 Some New Inequalities Via Extended Generalized Fractional Integral Operator for Chebyshev Functional

3.1 Introduction

3.2 Preliminaries

3.3 Fractional Inequalities for the Chebyshev Functional

3.4 Fractional Inequalities in the Case of Extended Chebyshev Functional

3.5 Some Other Fracional Inequalities Related to the Extended Chebyshev Functional

3.6 Concluding Remark

Chapter 4 Blow Up of the Higher-Order Kirchhoff-Type System With Logarithmic Nonlinearities

4.1 Introduction

4.2 Preliminaries

4.3 Blow Up for Problem for E (0) &lt

d

4.4 Conclusion

Chapter 5 Developments in Post-Quantum Cryptography

5.1 Introduction

5.2 Modern-Day Cryptography

5.2.1 Symmetric Cryptosystems

5.2.2 Asymmetric Cryptosystems

5.2.3 Attacks on Modern Cryptosystems

5.2.3.1 Known Attacks

5.2.3.2 Side-Channel Attacks

5.3 Quantum Computing

5.3.1 The Main Aspects of Quantum Computing

5.3.2 Shor's Algorithm

5.3.3 Grover's Algorithm.

5.3.4 The Need for Post-Quantum Cryptography

5.4 Algorithms Proposed for Post-Quantum Cryptography

5.4.1 Code-Based Cryptography

5.4.2 Lattice-Based Cryptography

5.4.3 Multivariate Cryptography

5.4.4 Hash-Based Cryptography

5.4.5 Supersingular Elliptic Curve Isogeny Cryptography

5.4.6 Quantum-Resistant Symmetric Key Cryptography

5.5 Launching of the Project Called "Open Quantum Safe"

5.6 Algorithms Proposed During the NIST Standardization Procedure for Post-Quantum Cryptography

5.7 Hardware Requirements of Post-Quantum Cryptographic Algorithms

5.7.1 NTRUEncrypt

5.7.1.1 Polynomial Multiplication

5.7.1.2 Hardware to Accelerate NTRUEncrypt

5.7.2 Hardware-Software Design to Implement PCQ Algorithms

5.7.3 Implementation of Cryptographic Algorithms Using HLS

5.8 Challenges on the Way of Post-Quantum Cryptography

5.9 Post-Quantum Cryptography Versus Quantum Cryptography

5.10 Future Prospects of Post-Quantum Cryptography

Chapter 6 A Statistical Characterization of MCX Crude Oil Price with Regard to Persistence Behavior and Seasonal Anomaly

6.1 Introduction

6.2 Related Literature

6.3 Data Description and Methodology

6.3.1 Data

6.3.2 Methodology

6.3.2.1 Characterizing Persistence Behavior of Crude Oil Return Time Series Using Hurst Exponent

6.3.2.2 Zipf Plot

6.3.2.3 Seasonal Anomaly in Oil Returns

6.4 Analysis and Findings

6.4.1 Persistence Behavior of Daily Oil Stock Price

6.4.2 Detecting Seasonal Pattern in Oil Prices

6.5 Conclusion and Implications

Appendix

Chapter 7 Some Fixed Point and Coincidence Point Results Involving Gα-Type Weakly Commuting Mappings

7.1 Introduction

7.2 Definitions and Mathematical Preliminaries

7.2.1 Definition: G-metric Space (G-ms)

7.2.2 Definition: t-norm.

7.2.3 Definition: t-norm of Hadžić type (H-type)

7.2.4 Definition: G-fuzzy metric space (G-fms)

7.2.5 Definition

7.2.6 Lemma

7.2.7 Lemma

7.2.8 Definition

7.2.9 Definition

7.2.10 Definition: Φ-Function

7.2.11 Definition: Ψ-Function

7.2.12 Lemma

7.2.13 Definition

7.2.14 Definition

7.2.15 Definition

7.2.16 Definition

7.2.17 Definition

7.2.18 Remarks

7.2.19 Lemma

7.3 Main Results

7.3.1 Theorem

7.3.2 Theorem

7.3.3 Definition Ψ-Function

7.3.4 Theorem

7.3.5 Theorem

7.3.6 Corollary

7.3.7 Corollary

7.3.8 Example

7.3.9 Example

7.3.10 Example

7.3.11 Example

7.4 Conclusion

7.5 Open Question

Chapter 8 Grobner Basis and Its Application in Motion of Robot Arm

8.1 Introduction

8.1.1 Define Orderings in K[y1, ..., yn]

8.1.2 Introducing Division Rule in K[y1, ..., yn]

8.2 Hilbert Basis Theorem and Grobner Basis

8.3 Properties of Grobner Basis

8.4 Applications of Grobner Basis

8.4.1 Ideal Membership Problem

8.4.2 Solving Polynomial Equations

8.5 Application of Grobner Basis in Motion of Robot Arm

8.5.1 Geometric Elucidation of Robots

8.5.2 Mathematical Representation

8.5.3 Forward Kinematic Problem

8.5.4 Inverse Kinematic Problem

8.6 Conclusion

Chapter 9 A Review on the Formation of Pythagorean Triplets and Expressing an Integer as a Difference of Two Perfect Squares

9.1 Introduction

9.2 Calculation of Triples

9.2.1 Calculation for Odd Numbers

9.2.2 Calculation for Even Numbers

9.2.3 Code Snippet

9.2.4 Observation

9.3 Computing the Number of Primitive Triples

9.3.1 Calculation for Odd Numbers

9.3.2 Calculation for Even Numbers

9.3.3 Code Snippet

9.3.4 Observation

9.4 Representation of Integers as Difference of Two Perfect Squares

9.4.1 Calculation for Odd Numbers.

9.4.2 Calculation for Even Numbers

9.4.3 Corollaries

9.4.4 Code Snippet

9.4.5 Output

9.5 Conclusion

Chapter 10 Solution of Matrix Games With Pay.Offs of Single-Valued Neutrosophic Numbers and Its Application to Market Share Problem

10.1 Introduction

10.2 Preliminaries

10.3 Matrix Games With SVNN Pay-Offs and Concept of Solution

10.4 Mathematical Model Construction for SVNNMG

10.4.1 Algorithm for Solving SVNNMG

10.5 Numerical Example

10.5.1 A Market Share Problem

10.5.2 The Solution Procedure and Result Discussion

10.5.3 Analysis and Comparison of Results With Li and Nanfs Approach

10.6 Conclusion

Chapter 11 A Novel Score Function-Based EDAS Method for the Selection of a Vacant Post of a Company with q-Rung Orthopair Fuzzy Data

11.1 Introduction

11.2 Preliminaries

11.3 A Novel Score Function of q-ROFNs

11.3.1 Some Existing q-ROF Score Functions

11.3.2 A Novel Score Function of q-ROFNs

11.4 EDAS Method for q-ROF MADM Problem

11.5 Numerical Example

11.6 Comparative Analysis

11.7 Conclusions

Acknowledgments

Chapter 12 Complete Generalized Soft Lattice

12.1 Introduction

12.2 Soft Sets and Soft Elements.Some Basic Concepts

12.3 gs-Posets and gs-Chains

12.4 Soft Isomorphism and Duality of gs-Posets

12.5 gs-Lattices and Complete gs-Lattices

12.6 s-Closure System and s-Moore Family

12.7 Complete gs-Lattices From s-Closure Systems

12.8 A Representation Theorem of a Complete gs-Lattice as an s-Closure System

12.9 gs-Lattices and Fixed Point Theorem

Chapter 13 Data Representation and Performance in a Prediction Model

13.1 Introduction

13.1.1 Various Methods for Predictive Modeling

13.1.2 Problem Definition

13.2 Data Description and Representations

13.3 Experiment and Result.

13.4 Error Analysis

13.5 Conclusion

Chapter 14 Video Watermarking Technique Based on Motion Frames by Using Encryption Method

14.1 Introduction

14.2 Methodology Used

14.2.1 Discrete Wavelet Transform

14.2.2 Singular-Value Decomposition

14.3 Literature Review

14.4 Watermark Encryption

14.5 Proposed Watermarking Scheme

14.5.1 Watermark Embedding

14.5.2 Watermark Extraction

14.6 Experimental Results

14.7 Conclusion

Chapter 15 Feature Extraction and Selection for Classification of Brain Tumors

15.1 Introduction

15.2 Related Work

15.3 Methodology

15.3.1 Contrast Enhancement

15.3.2 K-Means Clustering

15.3.3 Canny Edge Detection

15.3.4 Feature Extraction

15.3.5 Feature Selection

15.3.5.1 Genetic Algorithm for Feature Selection

15.3.5.2 Particle Swarm Optimization for Feature Selection

15.4 Results

15.5 Future Scope

15.6 Conclusion

Chapter 16 Student's Self-Esteem on the Self-Learning Module in Mathematics 6

16.1 Introduction

16.1.1 Research Questions

16.1.2 Scope and Limitation

16.1.3 Significance of the Study

16.2 Methodology

16.2.1 Research Design

16.2.2 Respondents of the Study

16.2.3 Sampling Procedure

16.2.4 Locale of the Study

16.2.5 Data Collection

16.2.6 Instrument of the Study

16.2.7 Validation of Instrument

16.3 Results and Discussion

16.4 Conclusion

16.5 Recommendation

Chapter 17 Effects on Porous Nanofluid due to Internal Heat Generation and Homogeneous Chemical Reaction

Nomenclature

17.1 Introduction

17.2 Mathematical Formulations

17.3 Method of Local Nonsimilarity

17.4 Results and Discussions

17.5 Concluding Remarks

Chapter 18 Numerical Solution of Partial Differential Equations: Finite Difference Method

18.1 Introduction.

18.2 Finite Difference Method.

Notes:

Chapter 6 A Statistical Characterization of MCX Crude Oil Price with Regard to Persistence Behavior and Seasonal Anomaly

Includes bibliographical references and index.

Description based on print version record.

ISBN:

9781119879831

1119879833

9781119879824

1119879825

OCLC:

1389609867