Mathematics and Computer Science, Volume 1 E-Book
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- Herausgeber: John Wiley & Sons
- Kategorie: Wissenschaft und neue Technologien
- Sprache: Englisch
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.
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Seitenzahl: 604
Veröffentlichungsjahr: 2023
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Contents
Cover
Series Page
Title Page
Copyright Page
Preface
1 Error Estimation of the Function by Using Product Means of the Conjugate Fourier Series
1.1 Introduction
1.2 Theorems
1.3 Lemmas
1.4 Proof of the Theorems
1.5 Corollaries
1.6 Example
1.7 Conclusion
References
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
References
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
References
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) <
d
4.4 Conclusion
References
5 Developments in Post-Quantum Cryptography
5.1 Introduction
5.2 Modern-Day Cryptography
5.3 Quantum Computing
5.4 Algorithms Proposed for Post-Quantum 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
5.8 Challenges on the Way of Post-Quantum Cryptography
5.9 Post-Quantum Cryptography Versus Quantum Cryptography
5.10 Future Prospects of Post-Quantum Cryptography
References
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
6.4 Analysis and Findings
6.5 Conclusion and Implications
References
Appendix
7 Some Fixed Point and Coincidence Point Results Involving
G
α
-Type Weakly Commuting Mappings
7.1 Introduction
7.2 Definitions and Mathematical Preliminaries
7.3 Main Results
7.4 Conclusion
7.5 Open Question
References
8 Grobner Basis and Its Application in Motion of Robot Arm
8.1 Introduction
8.2 Hilbert Basis Theorem and Grobner Basis
8.3 Properties of Grobner Basis
8.4 Applications of Grobner Basis
8.5 Application of Grobner Basis in Motion of Robot Arm
8.6 Conclusion
References
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
9.3 Computing the Number of Primitive Triples
9.4 Representation of Integers as Difference of Two Perfect Squares
9.5 Conclusion
References
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
10.5 Numerical Example
10.6 Conclusion
References
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
11.4 EDAS Method for
q
-ROF MADM Problem
11.5 Numerical Example
11.6 Comparative Analysis
11.7 Conclusions
Acknowledgments
References
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
References
13 Data Representation and Performance in a Prediction Model
13.1 Introduction
13.2 Data Description and Representations
13.3 Experiment and Result
13.4 Error Analysis
13.5 Conclusion
References
14 Video Watermarking Technique Based on Motion Frames by Using Encryption Method
14.1 Introduction
14.2 Methodology Used
14.3 Literature Review
14.4 Watermark Encryption
14.5 Proposed Watermarking Scheme
14.6 Experimental Results
14.7 Conclusion
References
15 Feature Extraction and Selection for Classification of Brain Tumors
15.1 Introduction
15.2 Related Work
15.3 Methodology
15.4 Results
15.5 Future Scope
15.6 Conclusion
References
16 Student’s Self-Esteem on the Self-Learning Module in Mathematics 1
16.1 Introduction
16.2 Methodology
16.3 Results and Discussion
16.4 Conclusion
16.5 Recommendation
References
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
References
18 Numerical Solution of Partial Differential Equations: Finite Difference Method
18.1 Introduction
18.2 Finite Difference Method
18.3 Multilevel Explicit Difference Schemes
18.4 Two-Level Implicit Scheme
18.5 Conclusion
References
19 Godel Code Enciphering for QKD Protocol Using DNA Mapping
19.1 Introduction
19.2 Related Work
19.3 The DNA Code Set
19.4 Godel Code
19.5 Key Exchange Protocol
19.6 Encoding and Decoding of the Plain Text— The QKD Protocol
19.7 Experimental Setup
19.8 Detection Probability and Dark Counts
19.9 Security Analysis of Our Algorithm
19.10 Conclusion
References
20 Predictive Analysis of Stock Prices Through Scikit-Learn: Machine Learning in Python
20.1 Introduction
20.2 Study Area and Dataset
20.3 Methodology
20.4 Results
20.5 Conclusion
References
21 Pose Estimation Using Machine Learning and Feature Extraction
21.1 Introduction
21.2 Related Work
21.3 Proposed Work
21.4 Outcome and Discussion
21.5 Conclusion
References
22 E-Commerce Data Analytics Using Web Scraping
22.1 Introduction
22.2 Research Objective
22.3 Literature Review
22.4 Feasibility and Application
22.5 Proposed Methodology
22.6 Conclusion
References
23 A New Language-Generating Mechanism of SNPSSP
23.1 Introduction
23.2 Spiking Neural P Systems With Structural Plasticity (SNPSSP)
23.3 Labeled SNPSSP (LSNPSSP)
23.4 Main Results
23.5 Conclusion
References
24 Performance Analysis and Interpretation Using Data Visualization
24.1 Introduction
24.2 Selecting Data Set
24.3 Proposed Methodology
24.4 Results
24.5 Conclusion
References
25 Dealing with Missing Values in a Relation Dataset Using the DROPNA Function in Python
25.1 Introduction
25.2 Background
25.3 Study Area and Data Set
25.4 Methodology
25.5 Results
25.6 Conclusion
25.7 Acknowledgment
References
26 A Dynamic Review of the Literature on Blockchain-Based Logistics Management
26.1 Introduction
26.2 Blockchain Concepts and Framework
26.3 Study of the Literature
26.4 Challenges and Processes of Supply Chain Transparency
26.5 Challenges in Security
26.6 Discussion: In Terms of Supply Chain Dynamics, Blockchain Technology and Supply Chain Integration
26.7 Conclusion
Acknowledgment
References
27 Prediction of Seasonal Aliments Using Big Data: A Case Study
27.1 Introduction
27.2 Related Works
27.3 Conclusion
References
28 Implementation of Tokenization in Natural Language Processing Using NLTK Module of Python
28.1 Introduction
28.2 Background
28.3 Study Area and Data Set
28.4 Proposed Methodology
28.5 Result
28.6 Conclusion
28.7 Acknowledgment
Conflicts of Interest/Competing Interests
Availability of Data and Material
References
29 Application of Nanofluids in Heat Exchanger and its Computational Fluid Dynamics
29.1 Computational Fluid Dynamics
29.2 Nanofluids
29.3 Preparation of Nanofluids
29.4 Use of Computational Fluid Dynamics for Nanofluids
29.5 CFD Approach to Solve Heat Exchanger
29.6 Conclusion
References
About the Editors
Index
List of Tables
Chapter 6
Table 6.1 Kurtosis of cumulative returns.
Table 6.2 Month-wise return of each year over the period of 2009–2018 positive returns are in white while the negative returns are highlighted in grey.
Table 6.3 Result of t-test: Feb to June vs July to Jan.
Table 6.4 Result of t-test: Feb to Aug vs Sept to Jan.
Chapter 10
Table 10.1 Assigned SVNN corresponding to linguistic terms.
Table 10.2 Results for the pay-off matrix
Chapter 11
Table 11.1 Comparison among introduced score function and existing score functions.
Table 11.2
q
-ROF decision matrix.
Table 11.3 Decision maker’s opinion.
Table 11.4 Weighted sum and normalized weighted sum of
S
+
and
S
−
.
Table 11.5 Comparison table.
Chapter 12
Table 12.1
Table 12.2
Table 12.3
Table 12.4
Chapter 13
Table 13.1 Sample COVID-19 data of India in column format.
Table 13.2 Predicted and actual value.
Chapter 14
Table 14.1 Proposed algorithm robustness results (foreman.avi).
Table 14.2 Proposed algorithm robustness results (akiyo.avi).
Chapter 15
Table 15.1 List of open source datasets for MRI of brain.
Table 15.2 The classification accuracy for different classifiers with all features and with selected features.
Chapter 16
Table 16.1 Academic performance of the students before and after the use of self-learning module.
Table 16.2 Significant relationship between the academic performance of the students before and after the use of self-learning module.
Table 16.3 The response on the statements of the student’s self-esteem on the self-learning module in Mathematics 6.
Table 16.4 Significant relationship on the academic performance of grade 6 students in mathematics on the utilization of the self-learning module and the response on the statements of the student’s self-esteem on the self-learning module in mathematics 6.
Table 16.5 Self-study matrix on the utilization of the self-learning module in Mathematics 6.
Chapter 17
Table 17.1 Comparison of Nusselt number for various values of
Pr.
Chapter 18
Table 18.1 List of solutions for different methods.
Chapter 19
Table 19.1 DNA to binary to decimal conversion code set.
Table 19.2 DNA conversion table.
Table 19.3 Encryption using Godel code.
Table 19.4 Decryption using Godel code.
Chapter 21
Table 21.1 Tagging human joints.
Chapter 24
Table 24.1 Dataset of term 1 and term 2 marks of the student.
Table 24.2 Dataset of the student’s activity in a day.
Chapter 25
Table 25.1 DataFrame.
Table 25.2 Use of Isnull() function on the DataFrame.
Table 25.3 Use of Notnull() function on the DataFrame.
Table 25.4 Use of DropNa() function on the DataFrame to find the rows and columns with missing values.
Chapter 26
Table 26.1 BCT properties.
Chapter 27
Table 27.1 Comparison of various disease prediction algorithms.
Guide
Cover
Table of Contents
Series Page
Title Page
Copyright Page
Preface
Begin Reading
Index
End User License Agreement
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Scrivener Publishing
100 Cummings Center, Suite 541JBeverly, MA 01915-6106
Advances in Data Engineering and Machine Learning
Series Editors: Niranjanamurthy M, PhD, Juanying XIE, PhD, and Ramiz Aliguliyev, PhD
Scope: Data engineering is the aspect of data science that focuses on practical applications of data collection and analysis. For all the work that data scientists do to answer questions using large sets of information, there have to be mechanisms for collecting and validating that information. Data engineers are responsible for finding trends in data sets and developing algorithms to help make raw data more useful to the enterprise.
It is important to have business goals in line when working with data, especially for companies that handle large and complex datasets and databases. Data Engineering Contains DevOps, Data Science, and Machine Learning Engineering. DevOps (development and operations) is an enterprise software development phrase used to mean a type of agile relationship between development and IT operations. The goal of DevOps is to change and improve the relationship by advocating better communication and collaboration between these two business units. Data science is the study of data. It involves developing methods of recording, storing, and analyzing data to effectively extract useful information. The goal of data science is to gain insights and knowledge from any type of data — both structured and unstructured.
Machine learning engineers are sophisticated programmers who develop machines and systems that can learn and apply knowledge without specific direction. Machine learning engineering is the process of using software engineering principles, and analytical and data science knowledge, and combining both of those in order to take an ML model that’s created and making it available for use by the product or the consumers. “Advances in Data Engineering and Machine Learning Engineering” will reach a wide audience including data scientists, engineers, industry, researchers and students working in the field of Data Engineering and Machine Learning Engineering.
Publishers at ScrivenerMartin Scrivener ([email protected])Phillip Carmical ([email protected])
Mathematics and Computer Science Volume 1
Edited by
Sharmistha Ghosh
M. Niranjanamurthy
Krishanu Deyasi
Biswadip Basu Mallik
and
Santanu Das
This edition first published 2023 by John Wiley & Sons, Inc., 111 River Street, Hoboken, NJ 07030, USA and Scrivener Publishing LLC, 100 Cummings Center, Suite 541J, Beverly, MA 01915, USA© 2023 Scrivener Publishing LLCFor more information about Scrivener publications please visit www.scrivenerpublishing.com.
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Library of Congress Cataloging-in-Publication Data
ISBN 9781119879671
Front cover images supplied by Wikimedia CommonsCover design by Russell Richardson
Preface
The mathematical sciences are part of nearly all aspects of everyday life. The discipline has underpinned such beneficial modern capabilities as internet searching, medical imaging, computer animation, weather prediction, and all types of digital communications. Mathematics is an essential component of computer science. Without it, you would find it challenging to make sense of abstract language, algorithms, data structures, or differential equations, all of which are necessary to fully appreciate how computers work. In a sense, computer science is just another field of mathematics. It does incorporate various other fields of mathematics, but then focuses those other fields on their use in computer science. Mathematics matters for computer science because it teaches readers how to use abstract language, work with algorithms, self-analyze their computational thinking, and accurately model real-world solutions. Algebra is used in computer programming to develop algorithms and software for working with math functions. It is also involved in design programs for numerical programs. Statistics is a field of math that deploys quantified models, representations, and synopses to conclude from data sets.
This book focuses on mathematics, computer science, and where the two intersect, including heir concepts and applications. It also represents how to apply mathematical models in various areas with case studies. The contents include 29 peer-reviewed papers, selected by the editorial team.
3Some New Inequalities Via Extended Generalized Fractional Integral Operator for Chebyshev Functional
Bhagwat R. Yewale* and Deepak B. Pachpatte
Department of Mathematics, Dr. B. A. M. University, Aurangabad, Maharashtra, India
Abstract
In present article, we prove some integral inequalities for Chebyshev functional using extended generalized fractional operator. The result obtained in the case of differentiable as well as Lipschitz functions.
Keywords: Chebyshev functional, Integral inequalities, Extended generalized fractional integral operator
3.1 Introduction
In 1882, Chebyshev introduced the following inequality [13]:
Let be differentiable functions such that and
then
The constant is the best possible.
The functional (3.1) have large number of applications in the field of statistics and probability. Many researcher’s provided lot of integral inequalities related to this functional in their literature (see [9, 12, 14, 15]).
Integrals and derivatives of any positive order are allowed in fractional calculus. Due to its applications in a variety of domains, many authors have contributed to the development of fractional calculus. For more details, one may refer [11, 16, 20].
Integral inequalities in the sense of fractional operators (fractional integrals and fractional derivatives) have proved to be one of the most important and powerful tool for studying various problems in different branches of Mathematics. Dahmani [5–7] established certain Chebyshev type integral inequalities using the Riemann-Liouville fractional integral operator. In [21], Sarikaya et al. studied some integral inequalities by using (k, s)-Riemann Liouville fractional integral operator. Purohit and Raina used the Saigo fractional integral operator to study Chebyshev-like inequalities [17]. Using generalized Katugampola operator, Aljaaidi and Pachpatte established Gruss-type inequalities in [1]. Sousa et al. [25] derived Gruss-type inequalities by means of generalized fractional integrals. Since then many researchers have established large number of inequalities by employing various fractional integral operators, see [2, 4, 8, 10, 19, 22–24] and the references therein.
Inspired by aforementioned work, in this article, we obtain some new integral inequalities by employing extended generalized fractional integral operator. The remaining paper is organized as follows: In section 3.2, we give some preliminaries which will be useful in the sequel. In section 3.3, we establish some new inequalities involving extended generalized fractional integral operator related to the functional (3.1). Integral inequalities associated with the extended version of the functional (3.1) are derived in section 3.4 and in section 3.5.
3.2 Preliminaries
In this section, we mention some preliminary facts and definitions that are used to establish our main results:
Here, denotes the space of all Lebesgue measurable functions such that denotes the space of all bounded functions on [0, ∞)), with the norm defined by
Definition 3.2.1. [3] Let Then the extended generalized Mittag-Leffler function is denoted by and is defined as
where is an extension of the beta function
Definition 3.2.2 [3] Let Then the extended generalized fractional integral operator is denoted by and is defined as
For convenience, we use the following notation:
