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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 nding trends in data sets and developing algorithms to help ma ke 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 so ware development phrase used to mean a type of agile relationship between development and IT operations. e 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 e ectively extract useful information. e 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 speci c direction Machine learning engineering is the process of using so ware 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 eld of Data Engineering and Machine Learning Engineering.
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Library of Congress Cataloging-in-Publication Data
ISBN 9781119879671
Front cover images supplied by Wikimedia Commons
Cover design by Russell Richardson
Set in size of 11pt and Minion Pro by Manila Typesetting Company, Makati, Philippines Printed in the USA 10 9 8 7 6 5 4 3 2 1
3.5
5.5
5.6
5.7
5.4.2
5.7.3
5.8
5.9
6.3.2.1
6.3.2.2
6.4
7 Some Fixed Point and Coincidence Point Results Involving
Krishna Kanta Sarkar, Krishnapada Das and Abhijit Pramanink
7.2.1
7.2.2
7.2.3
7.2.4
7.2.12
7.2.13
7.3.7
7.3.8
7.3.9
8
8.1 Introduction
8.1.1 Define Orderings in K[y1, ..., yn]
8.1.2
8.2 Hilbert Basis Theorem and Grobner Basis
8.3 Properties of Grobner Basis
8.4
8.4.1
8.4.2
8.5
8.5.2
8.5.3
8.5.4
8.6
9 A Review on the Formation of Pythagorean Triplets and Expressing an Integer as a Difference of Two Perfect Squares
Souradip Roy, Tapabrata Bhattacharyya, Subhadip Roy, Souradeep Paul and Arpan Adhikary
9.1
9.2
9.3
9.2.1
9.2.2
9.2.3
9.2.4
9.3.1
9.3.2
9.3.3
9.3.4
9.4 Representation of Integers as Difference of Two Perfect Squares
9.4.1
9.4.5
12.3 gs-Posets and gs-Chains
12.6
12.7
12.8
12.9
Senapati, Soumen Maji and Arunendu Mondal
18
J. Palanimeera and K. Ponmozhi
Iyyappan, M., Muskan
26.4
26.5
26.6
26.3.1
26.4.1
27 Prediction of Seasonal Aliments Using Big Data: A
K. Indhumathi and K. Sathesh Kumar
Vikash Kumar Mishra, Abhimanyu Dhyani, Sushree Barik and Tanish Gupta
28.6
M. Appadurai, E. Fantin Irudaya Raj and M. Chithambara Thanu 29.1
29.1.3
29.2.3
29.3
29.3.2
29.3.3
29.4
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.
1
Error Estimation of the Function by ≥ () ,r 1 r u Using Product Means ()Ep q s (, ), , nn of the Conjugate Fourier Series
The purpose of the current chapter is to attain the best result on a new way and the best approximation of different classes of the work, which has been discussed by different mathematician under different summability means. Here, we are presenting the theorems established under (, ), Ep,q snn () means of the CFS of a signal, belongs to rr µ , ≥ () 1 . Some known and unknown results have been proven by many mathematicians. But this is a new and unique way of proving a new result.
Keywords: Generalized Zygmund class rr µ , ≥ () 1 , product means, Degree of Approximation (DoA), Conjugate Fourier Series (CFS)
1.1 Introduction
Let, us take ∑a n − an infinite series and s n − the sequence of partial sums. Also, {pn} and {qn} are the sequences of positive real numbers s.t.∑ = = Pp nk k n 0 and ∑ = = Qq kk k n 0 and let R n = poqn + p1 qn − 1 + ⋯ + pnqo ≠ 0, p−1 = q-1 = R−1
