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Issue 3 − B
Volume 3 (2015)

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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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Article Type |
: | Research Article |

Title |
: | Solving Classical Nonlinear Riccati Differential Equations (RDEs) Using Differential Transformation Method (DTM) |

Country |
: | Nigeria |

Authors |
: | K.I.Falade || S.A.Raifu |

**Abstract: ** In this paper, the Differential Transformation Method (DTM) is used to solve nonlinear Riccatti differential equation of the form:
\begin{equation}\label{GrindEQ__1_}
\left(\frac{dj}{dt} \right)^{\beta } =S(t)j+Q(t)j^{2} +R(t), 0\le t\le 1
\end{equation}
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.

**Keywords:** Differential Transformation Method (DTM), Nonlinear, Classical Riccatti Equation and Variable constants.

K.I.Falade

Department of Computer Science \& Mathematics, Nigeria Police Academy (POLAC) Wudil, P.M.B 3474 Kano State, Nigeria.

E-mail: faladekazeem2013@gmail.com