## Issue 1 − BVolume 4 (2016)

ISSUE 1 − A ISSUE 1 − B ISSUE 1 − C ISSUE 1 − D
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 Article Type : Research Article Title : $M$*-open Sets in Topological Spaces Country : India Authors : A.Devika || A.Thilagavathi

Abstract: The aim of this paper is to introduce a new class of open sets called $M$*-Open sets and investigate some properties of these sets in topological spaces.

Keywords: Open sets, $M$*-open sets, $M$*-closed sets.

A.Devika
Department of Mathematics, PSG College of Arts and Science, Coimbatore, Tamilnadu, India.
E-mail: devirakavi@gmail.com

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 Article Type : Research Article Title : Slightly $(b, \mu)$-Continuous Functions Country : India Authors : O.Ravi || N.Navaneethakrishnan || P.Jeyalakshmi

Abstract: We study the concepts related to $\lambda$-b-open sets, $\lambda$-b-closed sets and $(b, \mu)$-continuity. Also some basic properties of slightly $(b, \mu)$-continuous functions and connectedness and covering properties of slightly $(b, \mu)$-continuous functions are investigated.

Keywords: $\mu$-clopen set, $\lambda$-closed set, $\lambda$-b-closed set, $(b, \mu)$-continuity, $(\lambda, \mu)$-continuity, slightly $(b, \mu)$-continuity.

O.Ravi
Department of Mathematics, P.M.Thevar College, Usilampatti, Madurai Dt, Tamil Nadu, India.
E-mail: siingam@yahoo.com

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 Article Type : Research Article Title : Some Class of Sasakian Manifolds with Respect to the Quarter-Symmetric Metric Connection Country : India Authors : D.G.Prakasha || B.S.Hadimani

Abstract: We consider $\mathcal{M}$-Projective curvature tensor on a Sasakian manifolds with respect to the quarter-symmetric metric connection. Here, we obtain the condition for the Sasakian manifold to be quasi-$\mathcal{M}$-Projectively flat and $\phi$-$\mathcal{M}$-projectively flat with respect to the quarter-symmetric metric connection.

Keywords: Sasakian manifold, $\mathcal{M}$-projective curvature tensor, quarter-symmetric metric connection, quasi-$\mathcal{M}$-projectively flat, $\phi$-$\mathcal{M}$-projectively flat.

D.G.Prakasha
Department of Mathematics, Karnatak University, Dharwad, India.
E-mail: prakashadg@mail.com

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 Article Type : Research Article Title : A Note on Matrix Representations of Finite Cyclic Groups Country : India Authors : S.K.Pandey

Abstract: In this article we provide a general technique to construct matrix representations of additive cyclic group of any finite order and multiplicative cyclic group of order $p-1$ (p is a positive prime).

Keywords: Group, finite group, matrix group, order of a group, cyclic group.

S.K.Pandey
Department of Mathematics, Sardar Patel University of Police, Security and Criminal Justice, Daijar, Jodhpur, Rajasthan, India.
E-mail: skpandey12@gmail.com

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 Article Type : Research Article Title : Weaker Form of $\delta$-open Sets via Ideals Country : India Authors : A.Anis Fathima || V.Inthumathi || M.Maheswari

Abstract: In this paper, the notions of $\delta_{\mathcal{I}}$-semi-open sets and $\delta_{\mathcal{I}}$-semi-closed sets are introduced and investigated in ideal topological spaces.

Keywords: $\delta_{\mathcal{I}}$-semi-open sets and $\delta_{\mathcal{I}}$-semi-closed sets.

A.Anis Fathima
Department of Mathematics(CA), Sri GVG Visalakshi College for Women, Udumalpet, Tamil Nadu, India.
E-mail: anisnazer2009@gmail.com

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 Article Type : Research Article Title : The Minimum Boundary Dominating Energy of a Graph Country : India Authors : Mohammed Alatif || Puttaswamy

Abstract: For a graph G, a subset $B$ of $V(G)$ is called a boundary dominating set if every vertex of $V(G)- S$ is vertex boundary dominated by some vertex of $S$. The boundary domination number $\gamma_{b}(G)$ of G is the minimum cardinality of minimum boundary dominating set in G. In this paper we introduce the minimum boundary dominating energy $E_{B}(G)$ of a graph G and computed minimum boundary dominating energies of some standard graphs. Upper and lower bounds for $E_{B}(G)$ are established.

Keywords: Boundary dominating set, Minimum Boundary Domination Matrix, Minimum Boundary Dominating Eigenvalues, Minimum Boundary Dominating Energy of a Graph.

Mohammed Alatif
Department of Mathematics, P.E.S.College of Engineering, Mandya, Karnataka State, India.
E-mail: aabuyasyn@gmail.com

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 Article Type : Research Article Title : Radiation effects of MHD Oscillatory Rotation Flow through a Porous Medium bounded by two Vertical Porous Plates in the Presence of Hall Current and Dufour effect with chemical reaction Country : India Authors : Dr.K.Balamurugan || Mr.R.Karthikeyan

Abstract: In this Article, Radiation Effects of Oscillatory flow through a porous medium bounded by two vertical porous plates in the presence of Hall Current and Dufour Effect with homogeneous First order chemical reaction under the influence of uniform magnetic field is studied. One plate is kept stationary and another plate is oscillating with uniform velocity. The Plates are subjected to the constant injection and suction velocities respectively. The basic governing equations of the problem are transformed into a system of non dimensional differential equations, which are solved analytically by using Perturbation techniques. The dimensionless Velocity, temperature and concentration profiles are displayed graphically showing the effects of fluid flow for the different values of the parameters involving in this problem like Hartmann Number M, Radiation Parameter F, Grashof Number Gr, chemical reaction parameter R, Dufour effects Du, It is observed that increase of Permeability parameter K, Hall Parameter m, shows the increase effects of Velocity profile. The increase of chemical reaction parameter R shows decrease effects of concentration.

Keywords: Hall Current, Dufour Effect, Chemical Reaction, MHD, Porous Medium, Oscillatory flow, Heat Source, Rotation effect.

Mr.R.Karthikeyan
Research Scholar, Department of Mathematics, Government Arts College, Tiruvannamalai, Tamilnadu, India.
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 Article Type : Research Article Title : New results on edge pair sum graphs Country : India Authors : P.Jeyanthi || T.Saratha Devi

Abstract: Let $G$ be a (p,q) graph. An injective map $f:E(G)\rightarrow\left\{\pm1,\pm2,\cdots,\pm q \right\}$ is said to be an edge pair sum labeling if the induced vertex function $f^{*}:V(G)\rightarrow Z-\left\{0\right\}$ defined by $f^{*}(v)= \mathop\sum\limits_{e\epsilon E_{v}}f\left(e\right)$ is one- one where $E_{v}$ denotes the set of edges in $G$ that are incident with a vertex $v$ and $f^{*}(V(G))$ is either of the form $\left\{\pm k_{1},\pm k_{2},\cdots,\pm k_{\frac{p}{2}}\right\}$ or $\left\{\pm k_{1},\pm k_{2},\cdots,\pm k_{\frac{p-1}{2}}\right\}$ $\bigcup$$\left\{\pm k_{\frac{p+1}{2}}\right\} according as p is even or odd. A graph that admits an edge pair sum labeling is called an edge pair sum graph. In this paper we prove that the graphs jelly fish, Y-tree, theta, the subdivision of spokes in wheel SS(W_{n}), P_{m} + 2K_{1}, C_{4} \times P_{m}, P_{n}\odot K^{c}_{m} admit edge pair sum labeling. Keywords: Edge pair sum labeling, edge pair sum graph, jelly fish, Y-tree, theta graph, subdivision of spokes in wheel. T.Saratha Devi Department of Mathematics, G.Venkataswamy Naidu College, Kovilpatti, India. E-mail: rajanvino03@gmail.com • Citation • Abstract • Corresponding Author • Download  Article Type : Research Article Title : Fibonacci Sequence Generated From Two Dimensional q-difference Equation Country : India Authors : G.Britto Antony Xavier || T.G.Gerly Abstract: In this paper, we define generalized Fibona-sequence using two-dimensional q-difference operator and we derive some algebraic identities as it includes its relationship with Fibonacci numbers. Also we derive theorems using inverse two-dimensional q-difference operator. Keywords: Fibonacci numbers, Two-dimensional q-difference operator and Summation solution. G.Britto Antony Xavier Department of Mathematics, Sacred Heart College, Tirupattur, Vellore District, Tamil Nadu, India. E-mail: brittoshc@gmail.com • Citation • Abstract • Corresponding Author • Download  Article Type : Research Article Title : Some Finite Summations Involving Srivastava-Daoust Double Hypergeometric Functions Country : India Authors : M.I.Qureshi || K.A.Quraishi || Mohd.Sadiq Khan || Rahul Singh Abstract: The main object of the present paper is to obtain seven finite summation formulae (not recorded earlier) involving Srivastava-Daoust double hypergeometric functions using series rearrangement technique. Keywords: Pochhammer's symbol; Double hypergeometric functions of Exton and Srivastava-Daoust; Ordinary Gaussian hypergeometric function. K.A.Quraishi Department of Applied Sciences and Humanities, Mewat Engineering College (Waqf), Palla, Nuh, Mewat, Haryana, India. E-mail: kaleemspn@yahoo.co.in • Citation • Abstract • Corresponding Author • Download  Article Type : Research Article Title : Hyers-Ulam Stability of Quartic Functional Equation in Matrix Paranormed Spaces Country : India Authors : R.Murali || A.Antony Raj || M.Boobalan Abstract: In this paper, we prove the Hyers-Ulam stability of quartic functional equation$$f(3a+b)+f(a+3b)=24f(a+b)-6f(a+b)+64f(a)+64f(b)$$in matrix paranormed spaces. Keywords: Matrix paranormed spaces, Hyers-Ulam stability, quartic functional equation. R.Murali Department of Mathematics, Sacred Heart College, Tirupattur, TamilNadu, India. E-mail: shcrmurali@yahoo.co.in • Citation • Abstract • Corresponding Author • Download  Article Type : Research Article Title : A Hendecagonal Fuzzy Number and Its Vertex Method Country : India Authors : A.Victor Devadoss || A.D.Dhivya || A.Felix Abstract: The decision data of human judgements with preferences are often vague so that the usual ways of using crisp values are inadequate in many real life situation. Also using fuzzy numbers such as triangular, trapezoidal are not suitable in few cases where the uncertainties arises in eleven different points. Therefore, Hendecagonal Fuzzy Number$(H_DFN)$and its arithmetic operations based on$\alpha -$cut is introduced. Also, the linguistic terms can be expressed in hendecagonal fuzzy numbers and a vertex method is defined to calculate the distance between two hendecagonal fuzzy numbers. Keywords: Fuzzy Arithmetic, Linguistic values, Hendecagonal Fuzzy Number$(H_DFN)$,$\alpha-$cut. A.Felix School of Advanced Sciences, VIT University, Vellore, Tamil Nadu, India. E-mail: felix.a@vit.ac.in • Citation • Abstract • Corresponding Author • Download  Article Type : Research Article Title : Analysis of Results that the Class of Metric Spaces is a Proper Subclass of the Class of Fuzzy Metric Spaces Country : India Authors : Dipen Saikia || Tazid Ali Abstract: In this paper we will establish that every metric space induces a fuzzy metric space using some results and examples of fuzzy metric space from the reference of George and Veeramani [4] and Kramosil and Michalek [9]. Keywords: Metric space, Fuzzy metric space, Stationary fuzzy metric. Dipen Saikia Department of Mathematics, CMJ University, Meghalaya, India. E-mail: • Citation • Abstract • Corresponding Author • Download  Article Type : Research Article Title : Study of Non-Newtonian Herschel-Bulkley Model through Stenosed Arteries Country : India Authors : Vipin Kumar Verma Abstract: The present paper contains a study of blood flow in arteries from the heart keeping in view the nature of blood flow circulation in human body. Blood has been represented by a non-Newtonian fluid obeying Herschel-Bulkley equation. The usual blood flow in arteries is obstructed by abnormal tissue development on the walls of these vessels, called as stenosis in bio transport system.Integral method has been used to solve the unsteady non linear Navier- Stokes equations in cylindrical coordinates system governing flow assuming axial symmetry under laminar flow condition. The effect of the stenosis geometry is assumed to overshadow any influence of wall distensibilty. Keywords: Artery, stenosis, distensibility, laminar flow. Vipin Kumar Verma Department of Mathematics, SRM University, NCR Campus,Modinagar (India). E-mail: vipin2002om@yahoo.com • Citation • Abstract • Corresponding Author • Download  Article Type : Research Article Title : Some Bounds on Co-isolated Locating Domination Number Country : India Authors : S.Muthammai || N.Meenal Abstract: Let G (V, E) be a simple, finite and undirected connected graph. A non – empty set S Í V of a graph G is a dominating set, if every vertex in V – S is adjacent to atleast one vertex in S. A dominating set S Í V is called a locating dominating set, if for any two vertices v, w Î V – S, N(v)ÇS ¹ N(w)ÇS. A locating dominating set S Í V is called a co – isolated locating dominating set (cild – set), if there exists atleast one isolated vertex in . The co – isolated locating domination number gcild is the minimum cardinality of a co – isolated locating dominating set. In this paper, some bounds on co – isolated locating domination number are obtained. Also minimal cild – sets are characterized. Further the graphs for which gcild to be p – 2 are obtained. Keywords: Dominating set, locating dominating set, co – isolated locating dominating set, co – isolated locating domination number. N. Meenal J.J. College of Arts and Science, Pudukkottai, Tamilnadu, India. E-mail: meenal_thillai@rediffmail.com • Citation • Abstract • Corresponding Author • Download  Article Type : Research Article Title : Study of Anomalous Behavior of blood flow in Capillary Surrounded by tissue Country : India Authors : Rekha Bali || Swati Mishra || P.N.Tandon Abstract: A Mathematical model for the two phase flow of blood in a narrow capillary surrounded by the tissue has been presented in this paper. We have developed the earlier two phase models of blood flow in capillaries into a model of capillary-tissue fluid exchange system by including porous tissue enclosing the capillary. Blood is not a homogeneous fluid, It is a suspension. The suspended blood cells accumulate at the axis in response to flow, resulting in a blunting of the velocity profile near the axis in contrast to the parabolic profile observed in homogeneous fluids. Earlier models have not included the effect of fluid exchange in between the capillary and the tissue while microtubes or capillaries are surrounded by tissue. Therefore, our aim is to include effects of permeability of the tissue with two phase flow of blood in narrow tubes. The model consists of a core region of suspension of all erythrocytes and a peripheral layer of plasma surrounding the core. The governing partial differential equations have been solved by using mathematical and computational techniques. Analytical results, in the proposed model for apparent viscosity, Bluntness and ratio of capillary hematocrit with discharge hematocrit values have been presented and discussed through graphs for various values of parameters and with their axial variations. Keywords: Anomalous behavior, Apperant viscosity, Bluntness, Capillary-tissue fluid exchange. Swati Mishra Department of Mathematics, Harcourt Butler Technological Institute, Kanpur (India). E-mail: swatimishra1982@yahoo.co.in • Citation • Abstract • Corresponding Author • Download  Article Type : Research Article Title : Quotient of Ideals of a Vague Lattice Country : India Authors : I.Arockiarani || K.Reena Abstract: In this Paper we define the Ideal of a Vague Lattice and give some characterization of these Ideals in terms of operations on VS(L). Also we discuss the residual of ideals of a Vague Lattice and prove that the residual of ideals is again a Vague Ideal of the Vague Lattice. Moreover we establish that it is the largest ideal with respect to some property on the operations. Keywords: Ideal of a Vague Lattice, residual. K.Reena Department of Mathematics, Nirmala College for women, Coimbatore, India. E-mail: reenamaths1@gmail.com • Citation • Abstract • Corresponding Author • Download  Article Type : Research Article Title : Algorithmic Aspects of k-Geodetic Sets in Graphs Country : India Authors : Dr.A.Anto Kinsley || K.Karthika Abstract: Let \textit{G} be a connected graph of order \textit{p}$\mathrm{\ge}$2. We study about the geodetic sets and \textit{k}-geodetic sets of \textit{G}. We study link vectors and prove a theorem to develop an algorithm to find the \textit{k}-geodetic sets. Initially we study algorithms to find the closed interval between any two vertices of \textit{G} and to find it's link vectors. In this paper we present two algorithms to check whether a given set of vertices is a \textit{k}-geodetic set and to find the minimum \textit{k}-geodetic set of \textit{G}. Keywords: Graph, geodetic set, k-geodetic set, graph algorithms. Dr.A.Anto Kinsley Department of Mathematics, St. Xavier’s (Autonomous) College, Palayamkottai, India. E-mail: antokinsley@yahoo.com • Citation • Abstract • Corresponding Author • Download  Article Type : Research Article Title : Another Decomposition of Continuity via$g\mu$-closed Sets Country : India Authors : Selvaraj Ganesan || Sakkari Veeranan Chandrasekar Abstract: There are various types of generalization of continuous functions in the development of topology. Recently some decompositions of continuity are obtained by various authors with the help of generalized continuous functions in topological spaces. In this paper we obtain a decomposition of continuity using a generalized continuity called$g\mu$-continuity in topology. Keywords:$g\mu$-closed set,$g\mu$lc*-set,$g\mu$-continuous function,$g\mu$lc*-continuous function. Selvaraj Ganesan Assistant Professor, Department of Mathematics, Government Arts College(Autonomous), Salem-636007, Tamil Nadu, India. E-mail: sgsgsgsgsg77@yahoo.com • Citation • Abstract • Corresponding Author • Download  Article Type : Research Article Title : Nano Generalized Closed Sets in Nano Bitopological Space Country : India Authors : K.Bhuvaneswari || K.Karpagam Abstract: The basic objective of this paper is to introduce and investigate the properties of Nano (1,2)* generalized closed sets in Nano Bitopological Spaces which is the extension work of Nano closed sets introduced by K. Bhuvaneswari et.al [1] also further investigated the properties of Nano generalized closed set in Nano bi topological space. Keywords: Nano (1,2)* closed sets , Nano (1,2)*Interior , Nano (1,2)* closure , Nano(1,2)* generalized closed sets. K.Bhuvaneswari Associate Professor, Department of Mathematics, Mother Teresa Women’s University , Kodaikanal, India. E-mail: drkbmaths@gmail.com • Citation • Abstract • Corresponding Author • Download  Article Type : Research Article Title : Intuitionistic Fuzzy Sequences in Metric Spaces Country : India Authors : A.M.Ali || S.S.Kumar || T.Chandra Abstract: In this paper, the notion of intuitionistic fuzzy sequence in a metric space is introduced and define a convergence property of an intuitionistic fuzzy sequence. Also discussed the comparison between crisp sequence and intuitionistic fuzzy sequence in metric space. Theorems related to the convergence of crisp sequence and intuitionistic fuzzy sequence are derived. Keywords: Fuzzy set, Intuitionistic fuzzy sequence, Convergence, Metric Space A.M.Ali Department of Mathematics, K P National College of Arts and Science, Batlagundu, Dindigul, India. E-mail: mohamedali1128$@$gmail.com • Citation • Abstract • Corresponding Author • Download  Article Type : Research Article Title : Two Methods to Approach Collatz Conjecture Country : India Authors : T.Kannan || C.Ganesa Moorthy Abstract: Two methods are explained in this article which may lead to a positive solution to Collatz conjecture, if these methods stop at finite stage. Keywords: Asymptotic density, stopping time. T.Kannan Department of Mathematics, Sree Sevugan Annamalai college, Devakottai, TamilNadu, India. E-mail: hardykannan@gmail.com • Citation • Abstract • Corresponding Author • Download  Article Type : Research Article Title : Dual And Non-Dual Elemeents In Finite Fields (Rings) Country : India Authors : S.K.Pandey Abstract: Let$F$be a finite field (ring) and$a,b\in F$. We call$a$and$b$as dual elements if$a^{2} =b^{2} =-1$( where$1$is the identity element of$F$). The term dual elements refers to the dual properties of$a$and$b$as$a$and$b$are the additive as well as multiplicative inverse of each other. If$a^{2} =b^{2} =-c$, where$c$is any element of$F$then we call$a$and$b$as non-dual elements of$F$. We note that if$a\in F$such that$a^{2} =-a$then$a$is not necessarily the zero element of$F\$.

Keywords: Finite ring, finite field, Galois field, dual elements.

S.K.Pandey
Department of Mathematics, Sardar Patel University of Police, Security and Criminal Justice, Daijar, Jodhpur, Rajasthan, India.
E-mail: skpandey12@gmail.com

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 Article Type : Research Article Title : On Pre-Closure Sets in Topological Space Country : India Authors : Vaisakh Venu || Jomol T Joseph

Abstract: The aim this paper is to introduce pre-closure set and pre-closure topological spaces.

Keywords: Closure, pre closure, pre closure space.

Vaisakh Venu
Asst. professor, Dept. of Mathematics, Christ College of Engineerig, Irinjalakkuda, Kerala, India-680125.
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 Article Type : Research Article Title : Graphs with equal Total Domination and Inverse Total Domination Numbers Country : India Authors : V.R.Kulli

Abstract: Let D be a minimum total dominating set of G = (V, E). If V – D contains a total dominating set D' of G, then D' is called an inverse total dominating set with respect to D. The inverse total domination number t(G) of G is the minimum cardinality of an inverse total domination set of G. In this paper, we obtain some graphs for which . Also we find some graphs for which

Keywords: Total dominating set, inverse total dominating set, inverse total dominating number.

V.R.Kulli
Department of Mathematics, Gulbarga University, Gulbarga, 585106, India.
E-mail: vrkulli@gmail.com