## Issue 3 − CVolume 3 (2015)

ISSUE 3 − A ISSUE 3 − B ISSUE 3 − C ISSUE 3 − D
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 Article Type : Research Article Title : Semi Smooth Graceful Labeling on Some Graphs Country : India Authors : V J Kaneria || Meera Meghpara

Abstract: This paper contains some results on semi smooth graceful graph. We proved that $B_{m,n}$, $S^{'}(B_{m,n})$ and $S^{'}(P_{n})$ are semi smooth graceful and a graph obtained by joining $G$ and $B^{2}_{m,n}$ with an arbitrary path $P_{r}$ is a graceful.

Keywords: Graceful graph, semi smooth graceful graph, bistar graph, square of bistar, path, splitting graph.

Meera Meghpara
E-mail: meera.meghpara@gmail.com

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 Article Type : Research Article Title : Some Relationship Between Matrix Completion Problems Country : India Authors : Kalyan Sinha

Abstract: In this paper relationship between the solutions of the matrix completion problems for certain class of matrices is studied. Specifically the similarities and dissimilarities among the class $P_0^{+}$ and its subclasses completion problem are discussed.

Keywords: Partial matrix; Matrix completion; $P_0^{+}$-matrix.

Kalyan Sinha
Department of Mathematics, PSTDS Vidyapith, Chinsurah, Hooghly, West Bengal, India.
E-mail: kalyansinha90@gmail.com

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 Article Type : Research Article Title : Some Generating Relations Involving Laguerre Polynomials of Several Variables Country : India Authors : M.I.Qureshi || Deepak Kumar Kabra || Naseem Ahmad Khan

Abstract: The present paper deals with $m$-variable polynomial sets generated by the functions in the form $e^t \phi_1 (x_1 t) \phi_2 (x_2 t)\phi_3(x_3 t)\ldots \phi_m(x_m t)$.Two generating relations are obtained as applications of general theorems associated with multiple series identities.

Keywords: Laguerre polynomials of several variables, Generating function and Generating relation, Multiple series identities, Multi-variable Humbert function.

Deepak Kumar Kabra
Department of Mathematics, Govt. College Kota, University of Kota, Kota, Rajasthan, India.
E-mail: dkabra20@gmail.com

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 Article Type : Research Article Title : New Weakly Generalized locally Closed Sets Country : India Authors : O. Ravi || L. Rajendran || J. Xavier Adaikalaraj || A. Pandi

Abstract: The aim of this paper is to introduce and study the classes of $g^\#$-locally closed sets, $g^\#$-lc$^\#$ sets and $g^\#$-lc$^{\# \#}$ sets which are weaker forms of the class of locally closed sets. Furthermore the relations with other notions connected with the forms of locally closed sets are investigated.

Keywords: Topological space, g-closed set, $g^\#$-closed set, $g^\#$-lc$^\#$ set, $g^\#$-lc$^{\# \#}$ set.

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

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 Article Type : Research Article Title : Common Fixed Point Theorems in Intuitionistic Generalized Fuzzy Metric Spaces Country : India Authors : R.Muthuraj || R.Pandiselvi

Abstract: In this paper, we prove Common fixed point theorems in intuitionistic generalized fuzzy metric spaces. We also, discuss result related to R-weakly commuting mappings.

Keywords: R-weakly commuting mappings and intuitionstic fuzzy metric spaces, R-weakly commuting mappings of type (P-1) and type (P-2).

R.Pandiselvi
E-mail: rpselvi@gmail.com

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 Article Type : Research Article Title : Some Generalized Results on $G_{\delta}$-diagonal Regular Spaces Country : India Authors : Pralahad Mahagaonkar

Abstract: In this paper we constructed a space X possessing a regular $G_{\delta}$-diagonal set of full measure, then the space X has a diagonal set if $\{(x,x):x\in X\}$ and is regular in $G_{\delta}-set$ for $X\times X$. We extend our result for some characterization of spaces with $G_{\delta }$-diagonal set. Such a kind obtained by Borges.C.J.R [1], Cinder.J.G [2] and Zenor.P [5].

Keywords: Regular spaces, $G_{\delta }$-diagonals,$w\Delta -$spaces.

Department of Mathematics, Ballari Institute of Technology and Management, Ballari, India.

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 Article Type : Research Article Title : Left-invertible Linear Transformations Country : Ethiopia Authors : Gezahagne Mulat Addis

Abstract: In this paper we consider a linear transformation $T$ of an $n$ -dimensional vector space V into an $m$-dimensional vectorspace W and we provide necessary and sufficient conditions for ${T}$ to have an inverse from the left side. Moreover, we characterize the class of all left inverses of ${T}$.

Keywords: Injective linear transformations, Left-invertible linear transformations, Left-Cancellable linear transformations, a basis for a vector space.

Department of Mathematics, Dilla University, Dilla, Ethiopia.
E-mail: buttu412@yahoo.com

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 Article Type : Research Article Title : Certain Formulas for Jacobi Polynomials of Several Variables Country : Yemen Authors : Ahmed Ali Atash || Salem Saleh Barahmah

Abstract: The aim of this research paper is to derive somegenerating functionsof Jacobi polynomials of several variables[4].Manyapplications of our main results lead us to obtain some hypergeometric formulasof Jacobi polynomials of two, three and several variables.Some generating functions (known or new)of Jacobi polynomialshave been obtained as special cases of our main results.

Keywords: Generating functions , Jacobi polynomials,generalizedLauricella function of several variables,hypergeometric functions.

Ahmed Ali Atash
E-mail: ah-a-atash@hotmail.com

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 Article Type : Research Article Title : Fundamental Relation on Intuitionistic Fuzzy $\Gamma$-hypermodule Country : India Authors : S. Abirami || S. Murugesan

Abstract: In this paper, we introduce and study the fundamental relation on intuitionistic fuzzy $\Gamma$-hypermodule as a generalization of the usual fuzzy $\Gamma$- hypermodule. Examples of fundamental relation on intuitionistic fuzzy $\Gamma$-hypermodule are constructed and some their proposition are proved.

Keywords: Intuitionistic Fuzzy Regular Relation, Intuitionistic Fuzzy Strongly Regular Relation, Fundamental Relation on Intuitionistic Fuzzy $\Gamma$- Hypermodule.

S. Murugesan
Department of Mathematics, Sri S.Ramasamy Naidu Memorial College, Sattur, Tamilnadu, India.
E-mail: satturmuruges@gmail.com

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Abstract: In this paper, we introduce (1,2)*-Fuzzy generalized continuous maps and (1,2)*-Fuzzy$\ddot{{g}}$ continuous maps and study their relations with existing generalized (1,2)*-Fuzzy continuous maps.
Keywords: Fuzzy bitopological space,(1,2)*-fuzzy g- continuous maps, (1,2)*-fuzzy$\ddot{{g}}$-continuous maps.