Issue 4 Volume 6 (2018)

Authors : P. Maragatha Meenakshi and J. Sathya
Title : On $\beta^\star$-closed Spaces in Terms of Nets
Volume, Issue, Year : 6(4)(2018)
Pages : 1−4

Abstract: The purpose of this paper is to obtain various characterizations of $\beta^\star$-closed spaces interms nets.

Keywords: Topological spaces, $\beta^\star$-open sets, $\beta^\star$-closed spaces.

Authors : Fauzia Raza and A. K. Tiwari
Title : Radiation Effect on MHD Flow of Nanofluids Over an Exponentially Stretching Sheet
Volume, Issue, Year : 6(4)(2018)
Pages : 5−12

Abstract: The problem of MHD radiation flow over an exponentially sheet through a porous medium is considered. The consequences of various parameters will be analyzed in Copper $(Cu)$ and Silver $(Ag)$ nanofluid. The non-linear governing equations of flow of thermal fields are converted to ordinary differential equation using similarity transformations and their numerical solution is obtained using MATLAB software ``bvp4c'' under the related boundary conditions. The interesting outcomes for variant physical parameters are exhibited through plots and numerical tables.

Keywords: Boundary layer, exponentially stretching sheet, MHD, nanofluid, porous medium, thermal radiation.

Authors : Syama P. Bhattacharya and Asis Ghosh
Title : An Observation on the Interrelationship Between the Gravitational Weight and the Area of a Flat Sheet: A New Concept of Rapid Measurement of Areas Bended by Irregular Outlines
Volume, Issue, Year : 6(4)(2018)
Pages : 13−20

Abstract: An accurate measurement of a bended flat area with many bends and deflections is practically impossible to perform using any of the existing methods of mensuration. Therefore, an alternative method has been investigated which insists on the measurement of gravitational weight of the portion of paper occupied by the area of a map. However, the map should be drawn on a thin flat sheet having the quality of uniform gravitational weight. A simple method for the selection of an uniform thin sheet has also been discussed. A theorem, $I = W10^{2}$ has been proposed for the rapid determination of index of any flat surface irrespective of sizes and geometric forms.

Keywords: Uniform gravitational weight, Transparency, Index, Spot-Photograph, Asteroids.

Authors : A. Ibrahim and M. Indhumathi
Title : Fuzzy PWI-Ideals of Lattice Pseudo-Wajsberg Algebras
Volume, Issue, Year : 6(4)(2018)
Pages : 21−31

Abstract: In this paper, we introduce the notions of fuzzy pseudo-Wajsberg implicative ideal (fuzzy PWI-ideal) and fuzzy pseudo lattice ideal in lattice pseudo-Wajsberg algebra. Also, we obtain some of their related properties. Moreover, we investigate the properties of fuzzy PWI-ideal related to homomorphism and kernel.

Keywords: Wajsberg algebra, Pseudo-Wajsberg algebra, Lattice pseudo-Wajsberg algebra, Fuzzy PWI-Ideal, Fuzzy Pseudo lattice ideal, Homomorphism, Kernel.

Authors : A. Ibrahim and D. Saravanan
Title : Strong Implicative and Fuzzy Strong Implicative Filters of Lattice Wajsberg Algebras
Volume, Issue, Year : 6(4)(2018)
Pages : 33−41

Abstract: In this paper, we consider and discuss some properties of strong implicative filter of lattice Wajsberg algebra. Also, we introduce the notion of fuzzy strong implicative filter and investigate some properties with interesting illustrations. Moreover, we obtain the relation between a strong implicative filter and fuzzy strong implicative filter in lattice Wajsberg algebra.

Keywords: Wajsberg algebra, Lattice Wajsberg algebra, Implicative filter, Strong implicative filter, Fuzzy Strong implicative filter.

Authors : V. R. Kulli
Title : On Augmented Revan Index and its Polynomial of Certain Families of Benzenoid Systems
Volume, Issue, Year : 6(4)(2018)
Pages : 43−50

Abstract: Chemical Graph Theory is a branch of Mathematical Chemistry whose focus of interest is to finding topological indices of molecular graph which correlate well with chemical properties of the chemical molecules. In this paper, we propose the augmented Revan index and augmented Revan polynomial of a graph. Also we determine the augmented Revan index and its polynomial of triangular benzenoids, benzenoid rhombus, benzenoid hourglass and jagged rectangle benzenoid systems.

Keywords: Augmented Revan index, augmented Revan polynomial, benzenoid.

Authors : M. Amin Bahraoui
Title : Diagonal Bundle Methods for Convex Minimization : Theoritical Aspect
Volume, Issue, Year : 6(4)(2018)
Pages : 51−57

Abstract: The bundle method can be seen as an approximate form of the proximal method. We study in this paper the convergence of general bundle method and we give a diagonal version of it.

Keywords: Convex minimization, bundle method, proximal method, Mosco-convergence, diagonalization.

Authors : Stephanie A. Omega and Ina Marie P. Kintanar
Title : Strictly Locating Sets in a Graph
Volume, Issue, Year : 6(4)(2018)
Pages : 59−63

Abstract: Let $G$ be a connected graph. A subset $S$ of $V(G)$ is a locating set in $G$ if for all $u,v\in V(G)\backslash S$, $N_{G}(u)\cap S\neq N_{G}(v)\cap S$. A subset $S$ of $V(G)$ is a strictly locating set in $G$ if $S$ is a locating set in $G$ and $N_{G}(w)\cap S\neq S$ $\forall w\in V(G)\backslash S$. The minimum cardinality of a strictly locating set in $G$, denoted by $sln(G)$, is called the strictly locating number of $G$. In this paper, the concept of strictly locating set in a graph is investigated. Moreover, the strictly locating sets in the join and corona of graphs are characterized and the strictly locating numbers of these graphs are determined.

Keywords: Locating set, strictly locating set, join, corona.

Authors : S. Praveena and M. Kamaraj
Title : Some New Results on Bipolar-Valued Fuzzy d-Algebras
Volume, Issue, Year : 6(4)(2018)
Pages : 65−73

Abstract: In this paper we introduce definitions of generalized bipolar-valued fuzzy $d$-algebra and investigate some associate results.

Keywords: Fuzzy $d$-algebra, bipolar-valued fuzzy $d$-algebra, bipolar-valued fuzzy $d$-subalgebra and upper bipolar-valued fuzzy sets, $t$-level-cut of bipolar-valued fuzzy sets and some results.

Authors : Geetanjali Sharma, Akshay Sharma and Pankaj Tiwari
Title : Common Fixed Point Theorems in Menger Space
Volume, Issue, Year : 6(4)(2018)
Pages : 75−80

Abstract: In this paper, the concept of occasionally weakly compatible maps in Menger space has been introduced to prove common fixed point theorems. Which generalize the well known results.

Keywords: Common fixed points, Metric space, Menger space, Compatible maps, Occasionally weakly compatible mappings and weak compatible mappings.

Authors : S. N. Banasode and Y. M. Umathar
Title : Topological Energies of Some Standard Graphs
Volume, Issue, Year : 6(4)(2018)
Pages : 81−90

Abstract: Let $G$ be simple, finite, undirected graph (molecular graph) with vertex set $V=\{v_1,v_2,v_3,\dots,v_n\}$ and edge set $E=\{e_1,e_2,e_3,\dots ,e_n\}$. The energy concept originated in chemistry and was introduced by I Gutman in 1978. Similar to the energies like dominating energy, minimum dominating energy, minimum total dominating energy, Zagreb energy is having its own importance in the study of physic-chemical properties of chemical compound that are often modeled by means of topological indices. In this paper, we find, first Zagreb energy [1] (introduced by Gutman), second Zagreb energy and hyper Zagreb energy of some standard graphs like Complete graph, complete bipartite graph, star graph and crown graph.

Keywords: Graph, Topological Indices, Topological Energy, Zagreb matrix, Zagreb energy.

Authors : Premkumar T. Lalchandani
Title : Exact Zero-Divisor Graph of a Commutative Ring
Volume, Issue, Year : 6(4)(2018)
Pages : 91−98

Abstract: The aim of this article is to continue the study of exact zero-divisor graph of a commutative ring with nonzero identity. We discuss the properties and nature of exact zero-divisor graph and compare some of its properties with zero-divisor graph.

Keywords: Zero Divisor, Exact Zero Divisor, Exact Zero-Divisor Graph.

Authors : A. Albina and U. Mary
Title : A Study on Dominator Coloring of Friendship and Barbell Graphsg
Volume, Issue, Year : 6(4)(2018)
Pages : 99−105

Abstract: A dominator coloring of a graph $G$ is a proper coloring of $G$ in which every vertex should dominate every vertex of at least one color class. The dominator chromatic number $\chi_d(G)$ is the minimum number of color classes in a dominator coloring of $G$. In this paper we study the dominator chromatic number of the barbell graph $B_n$ and friendship graph $F_n$.

Keywords: Coloring, Domination, Dominator coloring.

Authors : K. Divya Joseph and P. A. Dinesh
Title : The Magnetic, Joule's and Ohmic Effect on Incompressible Viscous Flow Over a Hyperbolic Stretching Circular Cylinder
Volume, Issue, Year : 6(4)(2018)
Pages : 107−116

Abstract: In we study the heat transfer of boundary layer flow of an incompressible viscous fluid over hyperbolic stretching cylinder. The governing nonlinear partial differential equations are converted into ordinary differential equations by using suitable transformations, which are then tackled using the homotopy method. The homotopy method gives us solutions in the form of series. The influence of the Magnetic, Joule's and Ohmic effect on velocity as well as temperature profiles are investigated and results can be seen visually in graphs. The computational results without these effects agree excellently with the previous results by \cite{1}.

Keywords: Joule's effect, Ohmic effect, Magnetohydrodynamic, incompressible, boundary layer.

Authors : B. Basavanagoud and Chetana S. Gali
Title : On the General Product-connectivity Index of Generalized xyz-point-line Transformation Graphs
Volume, Issue, Year : 6(4)(2018)
Pages : 117−132

Abstract: The general product-connectivity index is a molecular descriptor defined as $R_{\alpha}(G)=\sum\limits_{uv\in E(G)}(d_{G}(u)d_{G}(v))^\alpha$, where $d_{G}(u)$ denotes the degree of vertex $u$ in a graph $G$ and $\alpha$ is a real number. In this paper, we compute the expressions for general product-connectivity index of generalized \textit{xyz}--point-line transformation graphs.

Keywords: Subdivision graph, Semitotal-point graph, Semitotal-line graph, General product-connectivity index, Generalized \textit{xyz}--point-line transformation graphs.

Authors : B. C. Dhage, N. S. Jadhav and S. D. Sarkate
Title : Differential Inequalities and Comparison Principles for Linearly Perturbed Differential Equations of First Type
Volume, Issue, Year : 6(4)(2018)
Pages : 133−141

Abstract: In this paper, some results concerning the global existence as well as comparison theorems for an initial value problem of first order hybrid differential equations with a linear perturbation of first type have been proved. The main results rely on the hybrid fixed point technique of Dhage involving the sum of two operators in a Banach space. Our results include several basic results for unperturbed nonlinear differential equations as special cases.

Keywords: First order hybrid differential equation, Hybrid fixed point principle, Existence theorem, Maximal and minimal solutions.