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Scrivener Publishing
100 Cummings Center, Suite 541J Beverly, 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 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.
Publishers at Scrivener
Martin Scrivener (martin@scrivenerpublishing.com)
Phillip Carmical (pcarmical@scrivenerpublishing.com)
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 LLC
For more information about Scrivener publications please visit www.scrivenerpublishing.com.
All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording, or otherwise, except as permitted by law. Advice on how to obtain permission to reuse material from this title is available at http://www.wiley.com/go/permissions.
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While the publisher and authors have used their best efforts in preparing this work, they make no representations or warranties with respect to the accuracy or completeness of the contents of this work and specifically disclaim all warranties, including without limitation any implied warranties of merchantability or fitness for a particular purpose. No warranty may be created or extended by sales representatives, written sales materials, or promotional statements for this work. The fact that an organization, website, or product is referred to in this work as a citation and/or potential source of further information does not mean that the publisher and authors endorse the information or services the organization, website, or product may provide or recommendations it may make. This work is sold with the understanding that the publisher is not engaged in rendering professional services. The advice and strategies contained herein may not be suitable for your situation. You should consult with a specialist where appropriate. Neither the publisher nor authors shall be liable for any loss of profit or any other commercial damages, including but not limited to special, incidental, consequential, or other damages. Further, readers should be aware that websites listed in this work may have changed or disappeared between when this work was written and when it is read.
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
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
J. Palanimeera and K. Ponmozhi
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
1.1.1 Definition 1
Sequence-to-sequence of the transformation: E s n nss s n n n = +
defines, EEs ,( ,) n s mean of {s n}.
If ∞ →→Esasn n s the ∑a n is summable to s by (E,s) method regular ([12] Hardy, 1949).
1.1.2 Definition 2
Sequence-to-sequence transformation:
where, R n = poqn + p1 qn − 1 + ⋯ + pnqo (≠), p−1 = q-1 = R−1 then the series ∑a n is () pq,,nn summable to s. Regularity conditions [12]-
1. ∞ →∀ ≥→ pq R kasn 0, 0, kk n 2. ∑ < = pqsMR|| kkk k n n 0 , where M > 0 and independent of n.
1.1.3 Definition 3
The transform (E,s) over () pq,,nn summability and is given by [7]-
(1.3) and ∑a n is said to summable to s by the product means ()Espq(, ), , nn .
Remark. If we put qn = 1 in equation (1.3) then () pq,,nn summability mean reduces to () p , n mean and for pn = 1 it becomes to , qn () mean.
Now we take Fourier and its CFS (Conjugate Fourier series) as-
The partial sum is given by,
2 known as space function which is 2π - periodic and also integrable. Norm ||.||r is defined as,
Lggxdx [0 2] [0 2] , : , : |( )| ,1 z
also,
=+ +− ≤∈ wghsupgxtgxt (, )| () () |. hx0, again, C2π- The Banach space of 2π- periodic functions, defined on [0, 2π] under the sup. norm. Where, 0 < α ≤ 1, {} () =+ +− = απ α gCgxtgxtOt :| () ()|| () | () 2 the function space [11]. =+
For g ∈ Lr [0, 2π], r ≥ 1,
