## Volume 4 (2016)Article in Press

ISSUE 1 − A ISSUE 1 − B ISSUE 1 − C ISSUE 1 − D
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 Article Type : Research Article Title : Complementary Tree Domination in Unicyclic Graphs Country : India Authors : S.Muthammai || P.Vidhya

Abstract: A set $D$ of a graph $G = (V, E)$ is a dominating set of every vertex in $V-D$ is adjacent to some vertex in $D$. The domination number $\gamma(G)$ of $G$ is the minimum cardinality of a dominating set. A dominating set $D$ is called a complementary tree dominating set if the induced subgraph  is a tree. The minimum cardinality of a complementary tree dominating set is called the complementary tree domination number of $G$ and is denoted by $\gamma_{ctd}(G)$. In this paper, connected unicyclic graphs for which $\gamma_{ctd}(G) = \gamma(G)$ nad $\gamma_{ctd}(G) = \gamma(G) + 1$ are characterized.

Keywords: Domination number, complementary tree domination number, unicyclic graphs.

P.Vidhya
S.D.N.B.Vaishnav College for Women (Autonomous), Chennai, India.
E-mail: vidhya_lec@yahoo.co.in

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 Article Type : Research Article Title : Changing and Unchanging of Complementary Tree Domination Number in Graphs Country : India Authors : S.Muthammai || P.Vidhya

Abstract: A set $D$ of a graph $G = (V, E)$ is a dominating set if every vertex in $V-D$ is adjacent to some vertex in $D$. The domination number $\gamma(G)$ of $G$ is the minimum cardinality of a dominating set. A dominating set $D$ is called a complementary tree dominating set if the induced subgraph  is a tree. The minimum cardinality of a complementary tree dominating set is called the complementary tree domination number of $G$ and is denoted by $\gamma_{ctd}(G)$. The concept of complementary tree domination number in graphs is studied in \cite{a}. In this paper, we have studied the changing and unchanging of complementary tree domination number in graphs.

Keywords: Domination number, complementary tree dominating set, complementary tree domination number.

P.Vidhya
S.D.N.B.Vaishnav College for Women (Autonomous), Chennai, India.
E-mail: vidhya_lec@yahoo.co.in

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 Article Type : Research Article Title : More Results on Complementary Tree Domination Number of Graphs Country : India Authors : S.Muthammai and P.Vidhya

Abstract: A set $D$ of a graph $G = (V, E)$ is a dominating set if every vertex in $V-D$ is adjacent to some vertex in $D$. The domination number $\gamma(G)$ is the minimum cardinality of a dominating set. A dominating set $D$ is called a complementary tree dominating set if the induced subgraph  is a tree. The minimum cardinality of a complementary tree dominating set is called the complementary tree domination number of $G$ and is denoted by $\gamma_{ctd}(G)$. In this paper, some results on complementary tree domination established.

Keywords: Domination number, graph.

P.Vidhya
S.D.N.B. Vaishnav College for Women (Autonomous), Chennai, Tamilnadu, India.
E-mail: vidhya_lec@yahoo.co.in

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 Article Type : Research Article Title : Cordial Labeling of Generalized Jahangir Graph Country : India Authors : S.J.Gajjar and A.K.Desai

Abstract: In this paper we have proved that the Generalized Jahangir graph $J_{m,n}$ is cordial for all $m\geqslant 1$ and $n\geqslant 3$, except $J_{1,4n-1}$ for all $n\geqslant 1$.

Keywords: Graph Labeling, Cordial Labeling, Generalized Jahangir graph.

S.J.Gajjar
General Department, Government Polytechnic, Himmatnagar, India.
E-mail: gjr.sachin@gmail.com

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 Article Type : Research Article Title : Some Observations of $t^*$ on Mortality Curve at Very Old Age Country : India Authors : E.S.Lakshminarayanan and C.Selvadeepa

Abstract: In the absence of age specific mortality data, we give some observations of the point $t^*$ at which starts to decline in a mortality curve by the extended Weibull model (Weon model).

Keywords: Survival function, Mortality function, Age-dependent stretched exponent (Shape parameter), Characteristic life and Vertex point.

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 Article Type : Research Article Title : Stability of Quintic Functional Equation in 2-Banach Space Country : India Authors : R.Murali, M.Boobalan and A.Antony Raj

Abstract: In this paper, we investigate the Hyers-Ulam stability of the functional equation \begin {equation}\label{e0} 2g(2x+y)+2g(2x-y)+g(x+2y)+g(x-2y)=20\left[g(x+y)+g(x-y)\right]+90g(x) in 2-Banach space.

Keywords: Hyers-Ulam stability, 2-Banach space, Quintic functional equation.

R.Murali
Department of Mathematics, Sacred Heart College, Tirupattur, TamilNadu, India.
E-mail:

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 Article Type : Research Article Title : Intuitionistic Fuzzy $\ddot{g}$-Closed Sets Country : India Authors : N.Seenivasagan, O.Ravi, A.D.Ramesh Babu and M.Rajakalaivanan

Abstract: In this paper, we introduce the concepts of intuitionistic fuzzy $\ddot{g}$-closed sets and intuitionistic fuzzy $\ddot{g}$-open sets. Further, we study some of their properties.

Keywords: Intuitionistic fuzzy topology, Intuitionistic fuzzy $\ddot{g}$-closed set, Intuitionistic fuzzy $\ddot{g}$-open set.

O.Ravi
E-mail: siingam@yahoo.com

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 Article Type : Research Article Title : Invariant and Some Reductions of (2+1)- Dimensional Burger's Equation with Damping Country : India Authors : T.Siva Subramania Raja, S.Padmasekaran and R.Asokan

Abstract: We establish the invariant and reductions of (2+1)- Dimensional Burger's Equation with damping term, $u_t+u+uu_x+u u_y= u_{xx}+ u_{yy}$ is subjected to the Lie's classical method. Classification of its symmetry algebra into one- and two-dimensional subalgebras are carried out in order to facilitate its reduction systematically to (1+1)-dimensional PDEs and then to first or second-order ODEs.

Keywords: Burger's Equation, Symmetry algebra,Invariant.

T.Siva Subramania Raja
Department of Mathematics, Mary Matha College of Arts \& Science, Periyakulam East, Theni, Tamil Nadu, India.
E-mail: sivasumatrix@gmail.com

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 Article Type : Research Article Title : Further Study of $\omega$-closed Sets Country : India Authors : O.Ravi, M.Rajakalaivanan and I.Rajasekaran

Abstract: In 1982, the notions of $\omega$-closed sets and $\omega$-open sets were introduced and studied by Hdeib \cite{ho82}. In 2009, Noiri et al \cite{namnw09} introduced some generalizations of $\omega$-open sets and investigated some properties of the sets. Moreover, they used them to obtain decompositions of continuity. Quite Recently Ravi et al \cite{rsrpa} studied further generalizations of $\omega$-open sets in topological spaces. In this paper we introduce new classes of functions in topological spaces and study the characterizations of such functions in detail. Finally we obtain some decomposition theorems.

Keywords: $\omega$-open set, $\alpha$-$\omega$-open set, pre-$\omega$-open set, $\beta$-$\omega$- open set, $\omega$-t-set, $\delta$-$\omega$-open set, semi$^\star$-$\omega$-closed set.

O.Ravi
E- mail: siingam@yahoo.com

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 Article Type : Research Article Title : Optimization Strategies Applied to Discrete Epidemic Models with Specific Nonlinear Incidence Rate Country : Morocco Authors : Amine Bouaine, Mostafa Rachik and Khalid Hattaf

Abstract: The aim of this paper is to study discrete epidemic models with specific non linear incidence rate, and to investigate, in discrete time, optimal control strategies in which the controls are: vaccination and/or treatment. So, we make use of Pontryagin's maximum principle in order to compare and choose the best medical policy and economical strategy can be adopted and implemented. To end, numerical simulations are carried out to confirm the validity of the models and to prove the performance of the optimization strategies.

Keywords:Optimal control, Discrete epidemic model, Vaccination, Pontryagin's maximum principle.

Amine Bouaine
Department of Mathematics and computer Sciences, HassanII Mohammedia University, Sidi Othman, Casablanca, Morocco.
E-mail: amine.bouaine@gmail.com

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Abstract: In this paper, the authors investigate the general solution in vectors space and generalized Hyers-Ulam Stability of n-dimensional Cubic functional Equation \begin{align*} f\left(\sum^{n}_{i=1}{x_{i}}\right)+\sum^{n}_{j=1}f\left(-x_{j}+\sum_{i=1;i \neq j}{x_{i}}\right)&=\left(n-5\right)\sum_{ 1\leq i5$, and n is a positive integer using FNS,RNS,IFNS and FELBIN'S type spaces, using direct and fixed point methods. Keywords: Cubic functional equations, FNS, RNS, IFNS and FELBIN'S type spaces, fixed point, generalized Hyers-Ulam Stability. V.Govindan Department of Mathematics, Sri Vidya Mandir Arts and Science college, Uthangarai, Tamilnadu, India. E-mail: govindoviya@gmail.com • Citation • Abstract • Corresponding Author • Download  Article Type : Research Article Title : Relation Between Dominating and Total Dominating Color Transversal number of Graphs Country : India Authors : D.K.Thakkar and A.B.Kothiya Abstract: Total Dominating Color Transversal Set is the combination of three very well known concepts of graph theory,viz., Total Dominating Set, Transversal and Proper Coloring of vertices of a graph. It is defined as a Total Dominating Set which is also Transversal of Some$\chi$-Partition of vertices of G. Here$\chi$is the Chromatic number of the graph G. Total Dominating Color Transversal number of a graph is the cardinality of a Total Dominating Color Transversal Set which has minimum cardinality among all such Sets that the graph admits. Analogously, R.L.J.Manoharan defined Dominating Color Transversal number of a graph in \cite{2}. In this paper we investigate some relations between these two numbers. We give sufficient examples to justify our results. Keywords: Total Dominating Color Transversal number, Dominating Color Transversal number,$\chi$- Partition of a graph. A.B.Kothiya G.K.Bharad Institute of Engineering, Kasturbadham, Rajkot, India. E-mail: kothiyaamin@gmail.com • Citation • Abstract • Corresponding Author • Download  Article Type : Research Article Title : Common Fixed Point Theorems For A Pair Of Weakly Increasing/Decreasing Self Maps Under$\psi$-Weak Generalized Geraghty Contractions in Partially Ordered Partial b-Metric Spaces Country : India Authors : Vedula Perraju Abstract: In this paper we consider the concept of$\psi-$weak generalized Geraghty contractive pair of weakly increasing/decreasing self mappings in a complete partially ordered partial b-metric space. We study the existence of fixed points for such a pair of weakly increasing/decreasing self mappings in complete partially ordered partial b-metric spaces controlled by$\psi-$weak generalized Geraghty contractive type condition and obtain some fixed point results of G.V.R.Babu et.al [3] in complete partially ordered metric spaces as corollaries. Supporting example is also provided. An open problem is given at the end of the paper. Keywords: Fixed point theorems, weakly increasing/decreasing self mappings,$\psi-$contractive mappings, partial b-metric, ordered partial b-metric space, partially ordered partial b-metric space, Geraghty contraction. Vedula Perraju Principal, Mrs.A.V.N. College, Visakhapatnam, India. E-mail: perrajuvedula2004@gmail.com • Citation • Abstract • Corresponding Author • Download  Article Type : Research Article Title : A New Family of Exponentiated Weibull-Generated Distributions Country : Qassim(KSA) Authors : Amal S.Hassan and M. Elgarhy Abstract: Exponentiated Weibull distribution is a generalization of the most popular Weibull distribution which provides a more flexible model for analyzing observed data. We suggest an extended version of the Weibull-generated family of distributions which was previously defined in [1]. Properties of the exponentiated Weibull generated family are studied including; quantile function, order statistics, moments and mean deviation. Some special models in the exponentiated Weibull–generated distributions are provided. Further, the derived properties of the generated family apply to these selected models. Maximum likelihood method is applied to obtain parameter estimates of the exponentiated Weibull-generated family. The resilience and usefulness of the extended family is accomplished through an application to a real data set. Keywords: Weibull generated distributions, Order statistics, Quantiles. M. Elgarhy Burraydah colleges, Department of Mathematical Statistics, Qassim(KSA). E-mail: m_elgarhy85@yahoo.com • Citation • Abstract • Corresponding Author • Download  Article Type : Research Article Title : Characteristic Properties for the Beta Exponentiated Weibull family Country : Saudi Arabia Authors : Fathy H.Eissa Abstract: The beta exponentiated Weibull family includes the beta Weibull, beta exponential, beta generalized exponential, beta Weibull and beta generalized Rayleigh distributions, among others. We provide a comprehensive treatment of new mathematical and statistical properties of the BEW distribution as a head member of this family of distributions. We derived an explicit mathematical formula for the mode. Impact of new parameters (a,b) on the corresponding first four moments are illustrated. Further, we discuss parametric characterizations for the failure-rate and associate mean residual life function. A general expression for the mean residual life function is derived. Simulation results are reported in several tables and graphs. The usefulness of some results is illustrated by applications to real data. Keywords: Beta Exponentiated Weibull; Mode, Unimodal, Failure rate, Mean Residual Life Function. Fathy H.Eissa Department of Mathematics, College of Science \& Arts-Rabigh, King Abdulaziz University, Saudi Arabia. E-mail: fathy_eissa@hotmail.com • Citation • Abstract • Corresponding Author • Download  Article Type : Research Article Title : The Hahn Sequence Space of Fuzzy Numbers Defined by a Modulus Function Country : India Authors : A.Pandiarani Abstract: In this article we introduce new sequence spaces$h(F,f)$,$h_{\infty}(F,f)$and$h_{p} (F,f,s)$of sequence of fuzzy numbers defined by a modulus function. Further some inclusion relations regarding these spaces are studied. Keywords: Fuzzy numbers, modulus function, hahn sequence space, completeness. A.Pandiarani Department of Mathematics, G.Venkataswamy Naidu College, Kovilpatti, Tamilnadu, India. E-mail: raniseelan_92@yahoo.co.in • Citation • Abstract • Corresponding Author • Download  Article Type : Research Article Title : Mathematical Expressions of Heat Transfer to MHD Oscillatory Flow and Homotopy Analysis Method Country : India Authors : V.Ananthaswamy and J.Soumyadevi Abstract: In this research paper we determine the combined effect of a transverse magnetic field and radiative heat transfer to unsteady flow of a conducting optically thin fluid through a channel filled with saturated porous medium and non-uniform walls temperature. The governing dimensionless equations are solved analytically and graphically. The approximate analytical expressions for the dimensionless axial velocity and temperature are obtained using the Homotopy analysis method. Also the analytical expressions for the shear stress function and the rate of heat transfer are also derived. The Homotopy analysis method has proven to be the best for solving complicated non-linear differential equations in MHD flow problems in engineering and applied sciences. Keywords: Oscillatory flow; Porous medium; Heat transfer; Magnetic field; Homotopy analysis method. V.Ananthaswamy Department of Mathematics, The Madura College, Madurai, Tamil Nadu, India. E-mail: ananthu9777@rediffmail.com • Citation • Abstract • Corresponding Author • Download  Article Type : Research Article Title : Existence and Sensitivity Analysis of Solutions for a System of Parametric General Nonlinear Variational Inequalities Country : China Authors : Yan Hao and Hongyan Guan Abstract: In this paper, we introduce and study a new class of system of parametric general nonlinear variational inequalities. Using the resolvent operator in Hilbert spaces, we establish the equivalence between the system of parametric general nonlinear variational inequalities and a fixed point problem. This equivalence is used to investigate the existence and uniqueness and sensitivity analysis of solutions for the system of parametric general nonlinear variational inequalities. Keywords: The system of parametric general nonlinear variational inequalities, existence, sensitivity analysis. Yan Hao School of Mathematics and System Science, Shenyang Normal University, Shenyang, Liaoning Province, People's Republic of China. E-mail: haoyan8012@163.com • Citation • Abstract • Corresponding Author • Download  Article Type : Research Article Title : Transformation Formulas of Lauricella's Function of the Fourth kind of Several Variables Country : Yemen Authors : Ahmed Ali Atash and Hussein Saleh Bellehaj Abstract: The aim of this research paper is to derive transformation formulas for Lauricella's function of the fourth kind of several variables with the help of generalized Kummer's theorem on the sum of the series${}_{2} F_{1} (-1)\$ obtained by Lavoie et al. [10]. Some special cases of these formulas are also deduced.