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UNIQUE PRIMITIVE PYTHAGOREAN TRIPLES FOR EVERY
INTEGER
AND FOR EVERY SET OF TWO INTEGERS
Harry Z. Davis
Abstract:
The study of Pythagorean triples is very old, and may possibly
predate Pythagoras. One of the numerous related concepts that is
studied are formulae to generate primitive Pythagorean triples. A
formula given by Euclid requires an input of two parameters, herein
called M and N. Euclid’s formula has the ―advantages‖ of (1) being
unique, meaning any change in either M or N will change the triple
that results and (2) being exhaustive, meaning all primitive
Pythagorean triples may be generated by Euclid’s formula. However,
it has the ―disadvantage‖ that there is a dependency between M and
N, and they cannot be chosen independently. In this paper we
present two alternate formulae to generate primitive Pythagorean
triples that do not have this disadvantage. The first only requires one
parameter which may be any positive integer, and the second requires
an input of two parameters that are totally independent, and may be
any positive integers. These two formulae are also unique, but they
are not exhaustive—there exist primitive Pythagorean triples that are
not generated by either the first or second of these formulae.
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1-8
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PLANNING, SCHEDULING AND EARNED VALUE MANAGEMENT
ANALYSIS OF GREEN CONSTRUCTION
Mohammad Abdul Muqeet
Abstract:
Indian construction industry is the second largest sector after
agriculture. Construction Industry these days are going under
reformation, where paradigm is shifting towards Green
Construction. This type construction is eco-friendly and
sustainable. In light to any type of construction, the heart and
soul of any project is it proper planning and project
management, where we can keep record of duration, resources,
cost and other parameters.In the current paper, an existing
conventional building is transformed into green building by
replacement of some of its element with green ones, so as to
call it as Green project. Detail Estimate and BOQ is extracted
so as to plan and schedule the building in Primavera P6. EVM
analysis is performed on it to get EVM indicators such as EV,
PV, SPI, SV, CV and CPI.Apart from the green project,
existing/conventional project is also scheduled in Primavera P6
and EVM analysis is performed on it. So that results of both
Projects can be compared and concluded
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9-17
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INTERVAL GRAPH WITH CONSECUTIVE CLIQUES OF SIZE 3 -
SIGNED ROMAN DOMINATION
M. REDDAPPA
Abstract:
The theory of Graphs is an important branch of Mathematics that was developed
exponentially.Domination in graphs is rapidly growing area of research in graph theory
today. It has been studied extensively and finds applications to various branches of Science
& Technology.
Interval graphs have drawn the attention of many researchers for over 40 years.
They form a special class of graphs with many interesting properties and revealed their
practical relevance for modeling problems arising in the real world.
In this paper a study of signed Roman domination in an interval graph with
consecutive cliques of size 3 is carried out
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18-27
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ACO APPROACH ON CUTTING PARAMETERS IN AWJM PROCESS
FOR ALUMINIUM BASED ALLOY
DR.Y. BRUCELY
Abstract:
For as far back as years we have watched a fast development in the
improvement of harder, troublesome and multifaceted nature to
machine metals and alloys. AWJM is one of the as of late created
half and half, non traditional machining procedure in preparing
different sorts of hard-to-cut materials these days. It is a practical
technique for warmth touchy materials that can't be machined by
procedures that produce heat while machining. Machining parameters
assume the lead job in deciding the machine financial aspects and
nature of machining It is an affordable strategy for warmth touchy
materials that can't be machined by procedures that produce heat
while machining. Machining parameters assume the lead job in
characterizing the machine financial aspects and nature of machining
.In this examination the result of Pressure, Abrasive stream rate,
Orifice breadth, Focusing spout measurement and Standoff
separation AWJM process parameters on MRR and SR of Aluminum
6061 composite which is machined by AWJM was tentatively
performed and investigated. As per Response Surface Methodology
structure, different examinations were led with the blend of info
parameters on this compound.This paper presents the Prediction and
Optimization of MRR and SR on Aluminium 6061 alloy using Single
Objective Ant Colony Optimization.
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28-44
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WIRELESS NETWORK CODING ON IMAGE PROCESSING AND ITS MAJOR
APPLICATIONS: A STUDY
SheilyVerma
Abstract:
This research gives a general depiction of how researchers utilized the essential idea of network
coding in a few potential approaches to improve the performance of wireless networks. The
parameters of performance, delay, bundle conveyance report, jitter, and so forth. Wireless
networks are framed when gadgets associate with different gadgets through electromagnetic
energy noticeable all around and start their communication utilizing radio waves. These
networks can be grouped into networks dependent on infrastructures and specially appointed
networks. Infrastructure-put together networks depend with respect to an access point for every
one of their communications, while specially appointed networks are self-sorted out networks.A
wireless sensor network (WSN) incorporates base stations and some wireless sensors (nodes).
The WSNs are extraordinarily assigned networks (wireless nodes that self-sort out in an
infrastructure without a network). Wireless sensor networks are commonly relevant to numerous
cutting-edge military or mechanical applications, including normal checking, perception,
challenge observing or wellbeing checking.
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45-53
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FUZZY UNIFORMITIES ON FUNCTION SPACE
Dr.EKTA TRIPATHI
Abstract:
In this paper we study several uniformities on a function space and show that the fuzzy
topology associated with the fuzzy uniformity of uniform convergence is jointly fuzzy
continuous on 𝑐𝑓(𝑋, 𝑌), the collection of all fuzzy continuous function from a fuzzy topology
space X into a fuzzy inform space Y. We define fuzzy uniformity of uniform convergence on
starpluscompacta and show that its corresponding fuzzy topology is the starplus compact open
fuzzy topology. Moreover, we introduce the notion of fuzzy equicontinuity and fuzzy uniform
equicontinuity on fuzzy subset of a function space and study their properties. We also elaborate
on the pointwise fuzzy uniformity, fuzzy uniformity of uniform and fuzzy uniformity of uniform
convergence of starpluscompacta and their associated fuzzy topology on function space. The
fuzzy topology of uniform convergence on starpluscompacta is the starplus compact open fuzzy
topology.
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54-61
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Ancient Vedic Mathematics and its Application
DR. VINOD KUMAR YADAW
Abstract:
The „Vedas‟ are considered „divine‟ in origin and are assumed to be direct revelations from God.
Much of the hype about this topic is based on one single book authored by the Sankaracharya,
Jagadguru Swami Sri Bharati Krisna Tirthaji Maharaja titled Vedic Mathematics and published
in the year 1965 and reprinted several times since the 1990s. In this the authors probe into Vedic
Mathematics and explore whether it is really „Vedic‟ in origin or „Mathematics‟ in content. The
entire field of Vedic Mathematics is supposedly based on 16 one - to three - word sutras
(aphorisms) in Sanskrit, which can solve all modern mathematical problems. In this paper we
have gone through different literature on ancient Vedic mathematics and its application. In this
paper we discussed the Sutra: Nikhilam Navataścaramam Daśatah and its application.
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62-67
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A LITERARY REVIEW: MATLAB AS A TEACHING AND LEARNING TOOL FOR
MATHEMATICS
Pramod Joshi
Abstract:
This is research on “A Literary Review: Matlab as a Teaching and Learning Tool for
Mathematics”, and in this article, we discuss how to make use of computer technology in the
educational setting. The exposure that students have to the software MATLAB, which is used to
facilitate the teaching and learning of mathematical ideas, may have a significant influence on
the learning processes that they use. In this empirical research, we demonstrated the many
methods in which MATLAB was used as a teaching and learning aid for mathematics. MATLAB
is an acronym that stands for "computer algebra system." It has been used as a tool for the
visualization of the graphs of mathematical functions, calculation, problem-solving, encouraging
good attitudes toward mathematics, enhancing motivation and self-confidence, and so on.
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68-77
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