## Issue 3 − BVolume 3 (2015)

ISSUE 3 − A ISSUE 3 − B ISSUE 3 − C ISSUE 3 − D
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 Article Type : Research Article Title : Some Results on Odd Mean Graphs Country : India Authors : S. Suganthi || R. Vasuki || G. Pooranam

Abstract: Let $G=(V,E)$ be a graph with $p$ vertices and $q$ edges. A graph $G$ is said to have an odd mean labeling if there exists a function $f:V(G)\rightarrow\{0,1,2,\dots,2q-1\}$ satisfying $f$ is $1$-$1$ and the induced map $f^*:E(G)\rightarrow\{1,3,5,\dots,2q-1\}$ defined by $f^*(uv)=\left\{\begin{array}{ll}\frac{f(u)+f(v)}{2}&\quad\mbox{if f(u)+f(v) is even}\\ \frac{f(u)+f(v)+1}{2}&\quad\mbox{if f(u)+f(v) is odd.}\end{array}\right.$ is a bijection. A graph that admits an odd mean labeling is called an odd mean graph. In this paper, we prove that the graphs slanting ladder $SL_n$ for $n\geq 2,$ $Q_n\odot K_1$ for $n\geq 1,$ $TW(P_{2n})$ for $n\geq 2, H_n\odot mK_1$ for all $n\geq 1, m\geq 1$ and $mQ_3$ for $m\geq 1$ are odd mean graphs.

Keywords: Labeling, odd mean labeling, odd mean graph.

R. Vasuki
Department of Mathematics, Dr. Sivanthi Aditanar College of Engineering, Tiruchendur, Tamil Nadu, India.
E-mail: vasukisehar@gmail.com.

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 Article Type : Research Article Title : Counting Homomorphisms From Quasi-dihedral Group into Some Finite Groups Country : India Authors : R. Rajkumar || M. Gayathri || T. Anitha

Abstract: We derive general formulae for counting the number of homomorphisms from quasi-dihedral group into each of quasi-dihedral group, quaternion group, dihedral group, and modular group by using only elementary group theory.

Keywords: Finite groups, Homomorphisms.

R. Rajkumar
Department of Mathematics, The Gandhigram Rural Institute--Deemed University, Gandhigram, Tamil Nadu, India.
E-mail: rrajmaths@yahoo.co.in.

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 Article Type : Research Article Title : Enumeration of Homomorphisms From Modular Group into Some Finite Groups Country : India Authors : R. Rajkumar || M. Gayathri || T. Anitha

Abstract: We derive general formulae for counting the number of homomorphisms from modular group into each of modular group, dihedral group, quaternion group and quasi-dihedral group by using only elementary group theory.

Keywords: Finite groups, Homomorphisms.

R. Rajkumar
Department of Mathematics, The Gandhigram Rural Institute--Deemed University, Gandhigram, Tamil Nadu, India.
E-mail: rrajmaths@yahoo.co.in.

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 Article Type : Research Article Title : Higher Order Duality in Non−Differentiable Minimax Fractional Programming with Generalized ($F, \alpha, \rho, d$)−Type I Functions Country : India Authors : Gayatri Devi || Rashmita Mohanty

Abstract: Higher order dual for Minimax fractional programming problem is formulated. Weak duality strong duality and converse duality theorems are discussed involving generalized higher order ($F, \alpha, \rho, d$)−Type−I functions.

Keywords: Non differentiable fractional programming, Minimax programming, Higher order duality.

Gayatri Devi
Department of CSE, ABIT College, CDA-1, Cuttack, India.
E-mail: gayatridevi13@yahoo.com

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 Article Type : Research Article Title : Weak Continuity via Topological Grills Country : India Authors : N. Karthikeyan || N. Rajesh

Abstract: The aim of this paper is to introduce and characterize a new class of functions called weakly $\mathcal{G}$-precontinuous functions in ideal topological spaces by using $\mathcal{G}$-preopen sets.

Keywords: Grill topological spaces, $\mathcal{G}$-preopen sets, weakly $\mathcal{G}$-precontinuous functions.

N. Karthikeyan
Department of Mathematics, Jeppiaar Engineering College, Chennai, Tamilnadu, India.
E-mail: karthiratnam.natrajan@gmail.com

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 Article Type : Research Article Title : The Univarite and Multivariate Generalized Slash Student Distribution Country : Egypt Authors : A.H.El-Bassiouny || M.El-Morshedy

Abstract: In this paper, a new family of univariate and multivariate generalized slash student distribution is presented as the scale mixture of the student and the beta distributions. We called it generalized slash student distribution. It is shown that the new family of distributions can have heavier tails than the slash student distribution and slash normal distribution. Furthermore, moments and the invariant property under linear transformations are addressed. A simulation study is performed to investigate asymptotically the bias properties of the estimators.

Keywords: Slash distribution, slash student distribution, moments, heavy-tailed distribution.

M.El-Morshedy
Department of Mathematics, College of Science, Mansoura University, Mansoura, Egypt.
E-mail: mah_elmorshedy@yahoo.com

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 Article Type : Research Article Title : Soft Characteristic Interior Ideals in Semigroups Country : Egypt Authors : E. H. Hamouda

Abstract: Based on the concept of soft int-semigroups and soft ideals, we introduce the concept of soft fuzzy interior ideals and soft characteristic ideals of a semigroup. Also we give characterizations of them by specific soft sets.

Keywords: semigroups, soft int-semigroups, soft characteristic interior ideals.

E. H. Hamouda
Department of Basic Sciences, Faculty of Industrial Education, Beni-Suef University, Egypt.
E-mail: ehamouda70@gmail.com

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 Article Type : Research Article Title : New Generalized Continuous Functions Country : India Authors : M. Murugalingam || O. Ravi || S. Nagarani

Abstract: We introduce some new generalized continuous functions and new generalized open sets like B-$\alpha$-open, B-semi-open, B-preopen, B-$\beta$-open sets on simply extended topological spaces. We investigate characterizations and relationships among such functions and sets.

Keywords: $(\tau(B),\sigma(B'))$-continuity, $(\alpha,\sigma(B'))$-continuity, $(\sigma,\sigma(B'))$-continuity, $(\pi,\sigma(B'))$-continuity, $(\beta,\sigma(B'))$-continuity.

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 : Symmetry Classifications and Reductions of (2+1)-dimensional Potential Burgers Equation Country : India Authors : R. Asokan || S. Padmasekaran || R. Bala Priya

Abstract: We discuss the symmetries and reductions of the two-dimensional Potential Burgers Equation. We classify the one- and two-dimensional subalgebras of the symmetry algebra which is infinite-dimensional into conjugacy classes under the adjoint action of the symmetry group. Invariance under one-dimensional subalgebras provides the reductions to lower-dimensional partial differential equations (PDEs). Further reductions of these PDEs to second order ordinary differential equations (ODEs) are obtained through invariance under two dimensional subalgebras.

Keywords: A (2+1)-dimensional Potential Burgers Equation, Symmetry algebra, Conjugacy class.

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

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Abstract: In this paper, the Differential Transformation Method (DTM) is used to solve nonlinear Riccatti differential equation of the form: $$\label{GrindEQ__1_} \left(\frac{dj}{dt} \right)^{\beta } =S(t)j+Q(t)j^{2} +R(t), 0\le t\le 1$$ Subject to initial condition $j(0)=A$, where $S(t), Q(t), R(t), A$ are constant variables and when $\beta =1$, the above equation \eqref{GrindEQ__1_} is called Classical Riccati differential equation. The principle of differential transformation method is briefly introduced and applied for the first derivation of the set of nonlinear Riccatti differential equations. Accuracy and efficiency of the proposed method is verified through numerical examples. The result obtained with the proposed method are in good agreement with exact solution of the problem considered. The method is simply and efficient as numerical tool for any other class of the differential equations.