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Issue 1 − B
Volume 4 (2016)

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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.

E-mail:

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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

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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

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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

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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

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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

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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:

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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

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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

**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

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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

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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

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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

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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

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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

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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

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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

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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.

E-mail:

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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