iosr-Jm   Volume-11 ~ Issue-3 ~ May-June 2015

Abstract:Let G be a graph. The cardinalty of a minimum acyclic dominating set of G, is called the acyclic domination number of G and is denoted by γa(G). A subset E1 of E(G) is called an edge-vertex dominating set if for every vertex w in G, their exists an edge in E1 which dominates w. The minimum cardinality of an edge-vertex dominating set is called the edge-vertex domination number of G and is denoted by γev. An edge e = uv dominates a vertex w ∈ V (G) if w ∈ N[u] ∪ N[v].

[1]. A note on acyclic domination number in graphs of diameter two T.C. Edwin Chenga, , Yaojun Chena, b, C.T. Nga RECEIVED 11 December 2003, Revised 27 April 2005, Accepted 12 September 2005, Available on-line 28 November 2005
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[4]. T. W. Haynes, S.T.Hedetniemi and P. J. Slater, Fundamentals of Dom- ination in Graphs, Marcel Dekker, Inc, New York, 1998.
[5]. T. W. Haynes, S.T.Hedetniemi and P. J. Slater, Domination in Graphs:Advanced Topics, Marcel Dekker, Inc, New York, 1998.
[6]. O. Ore, Theory of Graphs, Amer. Math. Soc. Colloq. Publ, Vol.38, Amer- ican Mathematical Society, Providence RI,

Abstract: Let G = (V, E) be a simple graph of order p and size q. A subset S of V is said to be a Kr- dominating set of G if for every vertex v ∈ (V − S) is Kr- adjacent to atleast one vertex in S. Since v is always a Kr- dominating set, for every r, the existence of Kr-dominating set in G is guaranteed. A Kr- dominating set of minimum cardinality is called a minimum Kr- dominating set and its cardinality is denoted by γkr . Clearly γ = γK2 and γ ≤ γkr for every r > 2

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Abstract: The aim of this article is to introduce the concept of Conjugate EP(Con-𝐽-EP) matrices in the setting of indefinite inner product spaces with respect to the indefinite matrix product. Relation between Con-𝐽-EP and Con-EP matrices are discussed. Keywords: Indefinite matrix product, indefinite inner product space, EP matrices, Con-EP matrices, 𝐽-EP matrices.

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[3]. S. Jayaraman, EP matrices in Indefinite Inner Product Spaces, Funct. Anal. Approx. Comput., 4(2) (2012), 23-31.
[4]. K. Ramanathan, K. Kamaraj and K.C. Sivakumar, Inner product of matrices and applications to indefinite inner product spaces, J. Anal., 12 (2004) 135-142.
[5]. Ivana M. Radojevic , Nis , New Results For EP matrices in Indefinite Inner Product Spaces, Czechoslovak Mathematical Journal, 64 (134) (2014) , 91-103. www.apollotyres.com

Abstract: The purpose of this paper is to discuss the properties of regularity and strong regularity of fuzzy measure on metric spaces following the previous results. Some properties are defined with the help of null-additivity such as inner\outer regularity and the regularity of fuzzy measure. We define the strong regularity of fuzzy measures and show our result that the null-additive fuzzy measures possess a strong regularity on complete separable metric spaces.

Keywords: Fuzzy measure space, null-additivity, regularity, strong regularity.

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Abstract: The quality and reliability are fundamental criteria to accept or reject the manufactured products. Thus the Acceptance Sampling Plans are being introduced to accept or reject the lots of finished products in the present scenario. Such types of methods are involved in the inspection quality of product which is destructive where 100% inspection is not possible such as bullets, batteries, bulbs and so on. This paper study the CASP-CUSUM Schemes based on the assumption that the continuous variable under consideration follows a truncated Erlangian distribution. It is used the Lobatto Integration Method to solve the truncated integral equations. The Erlangian Distribution plays a vital role in Statistical Quality Control, particularly in estimating reliability by considering its distribution. Optimum CASP-CUSUM Schemes are suggested based on numerical results obtained.

Keywords: CASP-CUSUM Schemes, type-C OC Curve, ARL, Truncated Erlangian distribution

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Abstract:In this paper, a class of analytic functions associated with convolution is defined, and for this class we obtain Fekete-Szegö inequality, integral representation and structural formula for that class. 2000 Mathematics Subject Classification: 30A10, 30C45.
Keywords and phrases: Analytic function; Convolution; Starlike functions; subordination; Fekete-Szegö inequality

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order", East Asian Math J. 17 (2) (2001), 207-218.
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Abstract: In this paper, a food web model consisting of two predator-one stage structured prey involving Lotka-Voltera type of functional response and a prey refuge , is proposed and analyzed. It is assumed that the prey growth logistically in the absence of predator. The role of prey refuges in predator-prey model is investigated. The existence , uniqueness and boundedness of the solution are studied. The existence and the stability analysis of all possible equilibrium points are studied. Suitable Lyapunov functions are used to study the global dynamics of the proposed model. Numerical simulation for different sets of parameter value and for different sets of initial conditions are carried out to investigate the influence of parameters on the dynamical behavior of the model and to support the obtained analytical results of the model .

Keywords: food web , Lyapunov function , refuge , stability analysis , stage-structure .

[1]. T. K. Kar and Ashim Batabyal, Persistence and stability of a two prey one predator, International Jornal of Engineering, Science and Technology, Vol.2, No.2, 2010, pp.174-190.
[2]. Weiming Wang, Hailing Wan and Zhenqing Li, Chaotic behavior of a three-species beddington-type system with impulsive perturbations, Chaos, Solution and Fractals 37, 2008, 438-443.
[3]. Sunita Gakkar, Brahampal Singh and Raid Kamel Naji, Dynamical behavior of two predators competing over a single prey, BioSystems, 2007, 90.808-817.
[4]. Jawdat Alebraheem and YahYa Abu-Hasan, Presistence of predators in a two predators-one prey model with non-preiodic solution, App1.Math.Scie.,Vol.6, No.19, 2012, 943-956.
[5]. Madhusudanan V., Vijaya S. and Gunasekaran M, Impact of harvesting in three species food web model with two distinct functional response, International Journal of Innovative Research in Science Engineering and Technology,Vol.3, Issue 2,2014, p.9505-9513.

Abstract: In this paper, Rayleigh wave equation has been solved numerically for finding an approximate solution by Successive approximation method and Finite difference method. Example showed that Successive approximation method is much faster and effective for this kind of problems than Finite difference method. Keywords - Rayleigh wave equation, SAM, FDM.

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Abstract:Linear programming (LP) is one of the frequently applied tools in operations research, it plays a vital role for solving real-life problem because of its efficiency and simplicity. However, managers and decision makers may lack information about exact values of most of the parameters used in any of the optimization models, the flexible approach of fuzzy linear programming (FLP) comes up with a powerful tool to deal with such situations. In this paper, the simplex method for imprecise resources has been proposed to solve the parametrized LP. GAMS software can always be use to solve the FLP with fuzziness at the RHS in a simplest way.
Keyword Phrase: Fuzzy Linear Programming.

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Abstract:In this paper, we introduce a covering model on connected graph for modified lower and upper approximations operation on graph vertices with respect to connected sub graph. We obtain new classes induced by covering every sub graphs by lower and upper approximation operations using fuzzification set of vertices of main graph . Also, properties of these classes studied and illustrate that with examples.
Keywords: Graph theory, Rough set theory, Topology, Fuzzy set theory and Data mining.

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