Mathematics and Computer Science, Volume 1

1. Auflage 2023
ISBN: 978-1-119-87967-1
Verlag: Wiley

Buch, Englisch, 560 Seiten, Format (B × H): 155 mm x 229 mm, Gewicht: 885 g

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.

Autoren/Hrsg.

Ghosh, Sharmistha

Niranjanamurthy, M.

Deyasi, Krishanu

Mallik, Biswadip Basu

Das, Santanu

Inhaltsverzeichnis

Preface xix

1 Error Estimation of the Function by (Z ru ,r = 1) Using Product Means (E,s)( N, pn ,qn) n of) the Conjugate Fourier Series 1
Aradhana Dutt Jauhari and Pankaj Tiwar

1.1 Introduction 1

1.1.1 Definition 1 2

1.1.2 Definition 2 2

1.1.3 Definition 3 2

1.2 Theorems 5

1.2.1 Theorem 1 5

1.2.2 Theorem 2 5

1.3 Lemmas 6

1.3.1 Lemma 1 6

1.3.2 Lemma 2 6

1.3.3 Lemma 3 9

1.4 Proof of the Theorems 9

1.4.1 Proof of the Theorem 1 9

1.4.2 Proof of the Theorem 2 15

1.5 Corollaries 16

1.5.1 Corollary 1 16

1.5.2 Corollary 2 16

1.6 Example 16

1.7 Conclusion 18

References 18

2 Blow Up and Decay of Solutions for a Klein-Gordon Equation With Delay and Variable Exponents 21
Hazal Yüksekkaya and Erhan Piskin

2.1 Introduction 21

2.2 Preliminaries 23

2.3 Blow Up of Solutions 26

2.4 Decay of Solutions 36

Acknowledgment 43

References 43

3 Some New Inequalities Via Extended Generalized Fractional Integral Operator for Chebyshev Functional 45
Bhagwat R. Yewale and Deepak B. Pachpatte

3.1 Introduction 45

3.2 Preliminaries 46

3.3 Fractional Inequalities for the Chebyshev Functional 47

3.4 Fractional Inequalities in the Case of Extended Chebyshev Functional 53

3.5 Some Other Fracional Inequalities Related to the Extended Chebyshev Functional 57

3.6 Concluding Remark 63

References 64

4 Blow Up of the Higher-Order Kirchhoff-Type System With Logarithmic Nonlinearities 67
Nazli Irkil and Erhan Piskin

4.1 Introduction 67

4.2 Preliminaries 69

4.3 Blow Up for Problem for E (0) 5 Developments in Post-Quantum Cryptography 89
Srijita Sarkar, Saranya Kumar, Anaranya Bose and Tiyash Mukherjee

5.1 Introduction 90

5.2 Modern-Day Cryptography 90

5.2.1 Symmetric Cryptosystems 91

5.2.2 Asymmetric Cryptosystems 91

5.2.3 Attacks on Modern Cryptosystems 92

5.2.3.1 Known Attacks 93

5.2.3.2 Side-Channel Attacks 93

5.3 Quantum Computing 93

5.3.1 The Main Aspects of Quantum Computing 94

5.3.2 Shor’s Algorithm 95

5.3.3 Grover’s Algorithm 96

5.3.4 The Need for Post-Quantum Cryptography 96

5.4 Algorithms Proposed for Post-Quantum Cryptography 97

5.4.1 Code-Based Cryptography 97

5.4.2 Lattice-Based Cryptography 98

5.4.3 Multivariate Cryptography 99

5.4.4 Hash-Based Cryptography 99

5.4.5 Supersingular Elliptic Curve Isogeny Cryptography 100

5.4.6 Quantum-Resistant Symmetric Key Cryptography 100

5.5 Launching of the Project Called “Open Quantum Safe” 100

5.6 Algorithms Proposed During the NIST Standardization Procedure for Post-Quantum Cryptography 101

5.7 Hardware Requirements of Post-Quantum Cryptographic Algorithms 101

5.7.1 NTRUEncrypt 101

5.7.1.1 Polynomial Multiplication 102

5.7.1.2 Hardware to Accelerate NTRUEncrypt 103

5.7.2 Hardware-Software Design to Implement PCQ Algorithms 103

5.7.3 Implementation of Cryptographic Algorithms Using HLS 103

5.8 Challenges on the Way of Post-Quantum Cryptography 104

5.9 Post-Quantum Cryptography Versus Quantum Cryptography 105

5.10 Future Prospects of Post-Quantum Cryptography 106

References 107

6 A Statistical Characterization of MCX Crude Oil Price with Regard to Persistence Behavior and Seasonal Anomaly 111
Anindita Bhattacharjee, Jaya Mamta Prosad and M.K. Das

6.1 Introduction 111

6.2 Related Literature 113

6.3 Data Description and Methodology 114

6.3.1 Data 114

6.3.2 Methodology 115

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

Über Autor(innen)

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 a reviewer of journals as well as doctoral theses in India as well abroad.

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.

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.

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 books 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.

Santanu Das is an assistant professor in the Department of Basic Sciences and Humanities at the Institute of Engineering and Management, India. He completed his undergraduate degree, and is pursuing his doctorate, from Jadavpur University.