## Volume 5 (2017)Article in Press

ISSUE 2 − A ISSUE 2 − B ISSUE 2 − C
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 Article Type : Research Article Title : Electrons Drifting Effect on Dust Ion Acoustic Solitary Waves Using Relativistic Effect Country : India Authors : Riju Kumar

Abstract: In this paper we study dust ion acoustic solitary waves (DIASW) based on the dust charge $Z_{d} =\frac{n_{d_{0} } }{n_{i_{0} } } =\frac{equilibrium\, \, \, density\, \, \, of\, dust\, \, ions}{equilibrium\, \, density\, \, of\, \, ions}$. Compressive solitons are found to exist in presence of electron's drift velocity ($v'_{e}$). It is observed that compressive solitons exist for smaller values of dust charge $Z_{d}$ and greater values of$v'_{e}$.

Keywords: Dust ion acoustic solitary waves, electron's drift velocity, dust charge.

Riju Kumar
Department of Mathematics, Pandu College, Guwahati, Assam, India.
E-mail: kumarriju1@yahoo.com

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 Article Type : Research Article Title : Soft $g\zeta^{*}$-Closed Sets in Soft Topological Spaces Country : India Authors : V.Kokilavani and M.Myvizhi

Abstract: In this paper we consider a new class of soft set called soft generalized ${\zeta }^*$-closed sets in soft topological spaces. Also, we discuss some basic properties of soft $g{\zeta}^*$-closed sets.

Keywords: $g{\zeta}^*$-closed set, soft $g{\zeta}^*$-closed set, soft $g{\zeta}^*$-continuous function, soft $g{\zeta}^*$-irresolute function and soft $g{\zeta}^*$-spaces.

M.Myvizhi
Department of Mathematics, Asian College of Engineering and Technology, Coimbatore, India.
E-mail: myvizhimaths@gmail.com

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 Article Type : Research Article Title : On 0-Edge Magic Labeling of Some Graphs Country : Philippines Authors : Q.Laurejas and A.Pedrano

Abstract: A graph $G = (V,E)$ where $V = \left\{v_i, 1 \leq i \leq n \right\}$ and $E = \left\{v_iv_{i+1}, 1 \leq i \leq n \right\}$ is 0-edge magic if there exists a bijection $f: V(G) \rightarrow \left\{1,-1\right\}$ then the induced edge labeling $f : E\rightarrow \left\{ 0 \right\}$, such that for all $uv$ $\in$ $E(G)$, $f^*(uv)$ = $f(u) + f(v) = 0$. A graph $G$ is called \textit{0-edge magic} if there exists a 0-edge magic labeling of $G$. In this paper, we determine the 0-edge magic labeling of the cartesian graphs $P_m \times P_n$ and $C_m \times C_n$, and the generalized Petersen graph $P(m,n)$.

Keywords: Graph Labeling, 0-Edge Magic Labeling, Magic Labeling.

A.Pedrano
Department of Mathematics \& Statistics, College of Arts \& Sciences, University of Southeastern Philippines, Philippines.
E-mail: arielcpedrano@yahoo.com.ph

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 Article Type : Research Article Title : Cototal Domination Number of a Zero Divisor Graph Country : India Authors : K.Ananthi and N.Selvi

Abstract: Let R be a commutative ring and let Z(R) be its set of zero-divisors. We associate a graph $\Gamma(R)$ to R with vertices $Z(R)^{*}$ = $Z(R)-\{0\}$, the set of non-zero zero divisors of R and for distinct $u,v \in Z(R)^{*}$, the vertices $u$ and $v$ are adjacent if and only if $uv=0$. A dominating set D of G is a total dominating set if the induced subgraph of $\langle D \rangle$ contains no isolated vertices. The total domination number $\gamma_{t}(G)$ of G is the minimum cardinality of a total dominating set. A dominating set D of G is a cototal dominating set if every vertex $v \in V-D$ is not an isolated vertex in $\langle V-D \rangle$. The cototal domination number $\gamma_{ct}(G)$ of G is the minimum cardinality of a cototal dominating set. In this paper, we evaluate the cototal domination number of $\Gamma(Z_{n})$.

Keywords: Zero divisor graph, Domination number, Cototal domination number.

K.Ananthi
Department of Mathematics, Bharathidasan University, Tiruchirapalli, Tamilnadu, India.
E-mail: anakrish.maths@gmail.com

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 Article Type : Research Article Title : On Results of Common Fixed Points of Compatible maps in Generalized metric Space Country : India Authors : Latpate Vishnu and U.P.Dolhare

Abstract: In this paper we Prove some Common Fixed point theorems of compatible maps in G-metric Space.

Keywords: G-metric space, G-Cauchy sequence, G-Convergent sequence, Compatible maps.

Latpate Vishnu
Department of Mathematics, ACS college, Gangakhed, Maharashtra, India.
E-mail: vishnu.latpate@yahoo.com

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 Article Type : Research Article Title : Some Common Fixed Point Theorems in Dislocated Metric Spaces Country : India Authors : Vishnu Bairagi and V.H.Badshah

Abstract: In this paper, we discussed the existence and uniqueness of fixed point. The aim of this paper is to establish some new common fixed point theorems for two pairs of weakly compatible self-mappings in a dislocated metric space, which generalizes and improves similar fixed point theorems.

Keywords: Fixed point, common fixed point, dislocated metric space, weak compatible maps.

Vishnu Bairagi
Department of Mathematics, Government M.L.B.Girls P.G.college, Indore, (M.P), India.

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 Article Type : Research Article Title : Skew Semi-Heyting Almost Distributive Lattices Country : India Authors : Berhanu Assaye, Mihret Alamneh and Yeshiwas Mebrat

Abstract: In this paper the concept of skew semi-Heyting almost distributive lattice is introduced. We characterize skew semi-Heyting almost distributive lattice interms of a congruence relation and we show that the quotient ADL of a skew semi-Heyting almost distributive lattice modulo the congruence relation is the maximal lattice image of the ADL.

Keywords: Almost distributive lattice (ADL), semi-Heyting almost distributive lattice(SHADL), semi-Heyting algebra, skew semi-Heyting algebra and skew semi-Heyting almost distributive lattice(skew SHADL).

Yeshiwas Mebrat
Department of Mathematics, Faculty of Natural and Computational Science, Debre Tabor University, Debre Tabor, Ethiopia.
E-mail: yeshiwasmebrat@gmail.com

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 Article Type : Research Article Title : Quotient Heyting Algebras Via Fuzzy Congruence Relations Country : Ethiopia Authors : Berhanu Assaye Alaba and Derebew Nigussie Derso

Abstract: This paper aims to introduce fuzzy congruence relations over Heyting algebras (HA) and give constructions of quotient Heyting algebras induced by fuzzy congruence relations on HA. The Fuzzy First, Second and Third Isomorphism Theorems of HA are established.

Keywords: Heyting algebra, Fuzzy Heyting algebra, Fuzzy Congruence relation, Quotiont HA.

Derebew Nigussie Derso
Departement of Mathematics, Woldia University, Woldia, Ethiopia.
E-mail: nderebew@gmail.com

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Abstract: In this section we prove some elementary results on commutativity of non-associative rings. In an elementary commutativity theorem for rings, Johnsen, Outcalt and Yaqub [1] showed that a non-associative ring R with unity satisfying $\left(xy\right)^{2} =x^{2} y^{2}$ for all x, y in R is necessarily commutative. Boers [2] extended this to show that such a ring is also associative provided it is 2 and 3-torsion free. Without using that the ring is 2 and 3-torsion free, we prove that any assosymmetric ring in which $\left(xy\right)^{2} =x^{2} y^{2}$is commutative and associative. Further, if Z(R) denotes the center of the ring R, we prove the commutativity of a 2-torsion free non-associative ring R satisfying any one of the following identities:\\ (1). $\left(xy\right)^{2} \in Z\left(R\right)$\\ (2). $\left(xy\right)^{2} -xy\in Z\left(R\right)$\\ (3). $\left(\left(xy\right)z\right)^{2} -\left(xy\right)z\in Z\left(R\right)$\\ (4). $\left[\left(xy\right)^{2} -yx,x\right]=0$or $\left[\left(xy\right)^{2} -yx,y\right]=0$\\ (5). $\left[x^{2} y^{2} -xy,x\right]=0$ or $\left[x^{2} y^{2} -xy,y\right]=0$\\ (6). $\left[\left(xy\right)^{2} -x^{2} y-xy^{2} +xy,x\right]=0$ or $\left[\left(xy\right)^{2} -x^{2} y-xy^{2} +xy,y\right]=0$ for all x, y, z in R.\\ At the end of this section we also give some example which show that the existence of the unity and 2-torsion free are essential in some results. We know that an assosymmetric ring R is a non-associtative ring in which $(x, y, z) = (P(x), P(y), P(z))$, where P is any permutation of x, y, z in R.