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Category: Issue 7

Quotient Hyper BCK-algebra and its Zero Divisor Graph

JIMBOY R. ALBARACIN (jimboy.albaracin@g.msuiit.edu.ph)
Department of Mathematics and Statistics College of Science and Mathematics MSU-Iligan Institute of Technology Tibanga, Iligan City, Philippines
JOCELYN P. VILELA (jocelyn.vilela@g.msuiit.edu.ph)
Department of Mathematics and Statistics College of Science and Mathematics MSU-Iligan Institute of Technology Tibanga, Iligan City, Philippines

ABSTRACT:

This study investigates some properties of regular congruence relations on a hyper BCK-algebra. Furthermore, the concept of zero divisor graph of quotient hyper BCK-algebra is introduced and some of its properties are investigated.

KEYWORDS: zero divisor graph, hyper BCK-algebra, quotient hyper BCK-algebra, AMS Subject Classification (2010): 05C25, 06F35, 03G25


This study investigates some properties of regular congruence relations on a hyper BCK-algebra. Furthermore, the concept of zero divisor graph of quotient hyper BCK-algebra is introduced and some of...

Optimization of Welded Beam with Imprecise Load and Stress by Parameterized Neutrosophic Optimization Technique

MRIDULA SARKAR (msarkar.rs2014@math.iiests.ac.in)
Department of Mathematics, Indian Institute of Engineering Science and Technology, Shibpur. P.O.-Botanic Garden, Howrah-711103, West Bengal, India
TAPAN KUMAR ROY
Department of Mathematics, Indian Institute of Engineering Science and Technology, Shibpur. P.O.-Botanic Garden, Howrah-711103, West Bengal, India

ABSTRACT:

This paper develops a solution procedure of Neutrosophic Optimization (NSO) to solve optimum welded beam design with inexact co-efficient and resources. Interval approximation method is used here to convert the imprecise co-efficient which is a triangular neutrosophic number to an interval number. We transform this interval number to a parametric interval valued functional form and then solve this parametric problem by NSO technique. Usually interval valued optimization consist of two level mathematical programs, but a parametric interval valued optimization in neutrosophic environment is direct approach to find the objective function, this is the main advantage. In this paper we have considered a welded beam design with cost of welding as objective and the maximum shear stress in the weld group, maximum bending stress in the beam, buckling load of the beam and deflection at the tip of a welded steel beam as constraints .Numerical example is given here to illustrate this structural model through this approximation method.

KEYWORDS: Single valued Neutrosophic set, Generalized Neutrosophic Number, Nearest Interval Approximation, Interval Valued Function, Neutrosophic Optimization, Welded Beam Optimization, Subject classification code:90C30, 90C70, 90C90


This paper develops a solution procedure of Neutrosophic Optimization (NSO) to solve optimum welded beam design with inexact co-efficient and resources. Interval approximation method is used here to convert...

Multi-Objective Welded Beam Optimization using Neutrosophic Optimization Technique: A Comparative Study

MRIDULA SARKAR (mridula.sarkar86@rediffmail.com)
Department of Mathematics, Indian Institute of Engineering Science and Technology, Shibpur. P.O.-Botanic Garden, Howrah-711103, West Bengal (India)
SWARUP GHOSH
Department of Civil Engineering, Indian Institute of Engineering Science and Technology, Shibpur. P.O.-Botanic Garden, Howrah-711103, West Bengal, India
TAPAN KUMAR ROY
Department of Mathematics, Indian Institute of Engineering Science and Technology, Shibpur. P.O.-Botanic Garden, Howrah-711103, West Bengal (India)

ABSTRACT:

This paper investigates multi–objective Neutrosophic Optimization (NSO) approach to optimize the cost of welding and deflection at the tip of a welded steel beam, while the maximum shear stress in the weld group, maximum bending stress in the beam, and buckling load of the beam have been considered as constraints. The problem of designing an optimal welded beam consists of dimensioning a welded steel beam and the welding length so as to minimize its cost, subject to the constraints as stated above. The purpose of the present study firstly to investigate the effect of truth, indeterminacy and falsity membership function in neutrosophic optimization in perspective of welded beam design and secondly is to analyse the results obtained by different optimization methods like fuzzy, intuitionistic fuzzy so that the welding cost of the welded steel beam become most cost effective with minimum deflection. Specifically based on truth, indeterminacy and falsity membership function, a multi objective NSO algorithm has been developed to optimize the welding cost, subjected to a set of constraints. It has been shown that NSO is an efficient method in finding out the optimum value in comparison to other iterative methods for nonlinear welded beam design in imprecise environment till investigated. Numerical example is also given to demonstrate the efficiency of the proposed NSO approach.

KEYWORDS: Neutrosophic Set, Single Valued Neutrosophic Set, Neutrosophic Optimization, Multi- Objective welded, beam optimization, Subject classification code:90C30, 90C70, 90C90


This paper investigates multi–objective Neutrosophic Optimization (NSO) approach to optimize the cost of welding and deflection at the tip of a welded steel beam, while the maximum shear stress...

On gspsg-homeomorphisms and sggsp-homeomorphisms in topological spaces

MANOJ GARG (garg_manoj1972@yahoo.co.in)
P. G. Department and Research Centre of Mathematics, Nehru Degree College, Chhibramau, Kannauj, U.P., (India)

ABSTRACT:

In the present paper we introduce two new types of mappings called gspsg-homeomorphism and sggsp-homeomorphism and then shown that one of these mapping has a group structure. Further we investigate some properties of these two homeomorphisms.

KEYWORDS: Homeomorphism, gspsg-homeomorphism, sggsp-homeomorphism


In the present paper we introduce two new types of mappings called gspsg-homeomorphism and sggsp-homeomorphism and then shown that one of these mapping has a group structure. Further we...

On **gs- Homeomorphism In Topological Spaces

MANOJ GARG (garg_manoj1972@yahoo.co.in)
P. G. Department and Research Centre of Mathematics, Nehru Degree College, Chhibramau, Kannauj, U.P. (India)

ABSTRACT:

In this paper we introduce a new class of closed maps namely **gs-closed maps which settled in between the class of *gs-closed maps18 and the class of gs-closed maps8. We also introduce and study new class of homeomorphisms called **gs-homeomorphisms and **gs*-homeomorphisms. Further we show that the set of all **gs*-homeomorphisms form a group under the operation composition of maps.

KEYWORDS: **gs-closed maps, *gs-homeomorphisms, **gs*-homeomorphisms, 2000 Mathematics Subject Classification: Primary 54a05, Secondary 54c08


In this paper we introduce a new class of closed maps namely **gs-closed maps which settled in between the class of *gs-closed maps18 and the class of gs-closed maps8....

New Class of Continuity in Nano Product Topology

M. LELLIS THIVAGAR (mlthivagar@yahoo.co.in)
School of Mathematics, Madurai Kamaraj University, Madurai- 625 021. Tamilnadu, India
I. GEETHA ANTOINETTE (geetharegis@yahoo.co.in)
Jayaraj Annapackiam College for Women,Periyakulam, Theni – 625 601. Tamilnadu, India

ABSTRACT:

The purpose of the study is to introduce a new class of continuous function among the nano product topology and study the behaviour of these functions. We characterise the properties of the new function.The impact of nano projection mapping between nano product topology is also considered.

KEYWORDS: Nano product topology, nano continuous function, nano projection mapping, nano quotient topology, 2010 Mathematics Subject classification code: 54C05


The purpose of the study is to introduce a new class of continuous function among the nano product topology and study the behaviour of these functions. We characterise the...

A Study of Magnetohydrodynamic Flow of Conducting Walter’s Visco-Elastic Fluid in a Long Uniform Rectangular Channel

ANIL TRIPATHI (atkkdc@gmail.com)
Department of Mathematics, K.K. (P.G.) College, Etawah (U.P.), (India)

ABSTRACT:

The aim of the present paper is to study the magneto hydrodynamic flow of conducting Walter’s visco-elastic fluid in a long uniform straight channel of rectangular cross-section under the influence of time varying pressure gradient and uniform magnetic field applied perpendicularly to the flow of fluid. The exact solution for the velocity of fluid has been obtained by using integral transform technique. Some particular cases of pressure gradient have been discussed in detail. Also we have discussed the case when magnetic field is withdrawn. Besides, the corresponding viscous flow problem has been derived as a limiting case when the relaxation time parameter tends to become zero.

KEYWORDS: Magnetohydrodynamic, visco-elastic, pressure gradient, Magnetic field, 2010 MSC u2013 76W05


The aim of the present paper is to study the magneto hydrodynamic flow of conducting Walter’s visco-elastic fluid in a long uniform straight channel of rectangular cross-section under the...

Accurate Connected Edge Domination Number in Graphs

VENKANAGOUDA M. GOUDAR
Department of Mathematics, Gouthama Research Centre, (Affiliated to Kuvempu University), Sri Siddhartha Institute of Technology, Tumkur, karnataka, India
VENKATESH S.H (sh1.venkatesh@gmail.com)
Research Scholar, Gouthama Research Centre, (Affiliated to Kuvempu University), Sri Siddhartha Institute of Technology, Tumkur, Karnataka, India
VENKATESHA
Department of Mathematics, Kuvempu University Shankarghatta, Shimoga, Karnataka, India
TEJASWINI K.M.
Department of Mathematics, Sri Siddhartha Institute of Technology, Tumkur, karnataka, India

ABSTRACT:

An accurate edge dominating set D of a graph G = (V,E) is an accurate connected edge dominating set, if < D > is connected. The accurate connected edge domination number (G) cae  is the minimum cardinality of an accurate connected edge dominating set. In this paper, we initiate a study of (G) cae  in terms of vertices, edges, cut vertices and different parameters of G . Further we characterize the accurate connected edge domination number in cartesian product and corona of graphs.

KEYWORDS: Edge dominating set, Accurate edge dominating set, Accurate connected edge dominating set, Mathematics Subject Classification: 05C, 5C05, 05C70


An accurate edge dominating set D of a graph G = (V,E) is an accurate connected edge dominating set, if < D > is connected. The accurate connected edge...