GENERAL MATHEMATICS NOTES
Vol. 3, No. 1, March 2011
Vol. 3, No. 1, March 2011
Contents
Title: D-Compact Sets in Random n-Normed Linear Spaces
Author: B. Surender Reddy
Abstract: The aim of this paper is to introduce the notion of D-bounded sets and D-compact sets in random n-normed linear space. Also we prove some results in relation between D-bounded and D-compact sets in random n-normed linear spaces.
PP. 1-13
Title: Fourier Transform in LP(R)Spaces, p ≥ 1
Authors: Devendra Kumar and Dimple Singh
Abstract: A method for restricting the Fourier transform of f belongs to LP(R),1≤p≤∞, spaces have been discussed by using the approximate identities.
PP. 14-25
Authors: Devendra Kumar and Abhishek Singh
Abstract: In this study we give recurrence relations of single and product moments of lower record values from modified-inverse Weibull distribution.
PP. 26-31
Title: Approach Merotopies and Near Filters Theory and Application
Authors: James F. Peters and Surabhi Tiwari
Abstract: This article considers the problem of how approach spaces can be used in the study of near filters, in general, and descriptively near filters, in particular. The solution to the problem stems from recent work on approach spaces, approach merotopies, near filters, descriptively near sets, and a specialized form of merotopy defined in terms of a variation of the Čech gap functional in measuring the distance between nonempty sets. A nonempty set equipped with a distance function satisfying certain properties is an approach space. This article investigates the theory and application of merotopies and near filters in terms of the nearness of digital images.
PP. 32-45
Authors: Lihui Yang, Jianguang Yang and Qianhong Zhong
Abstract: In this paper, the existence of periodic solutions of a predator-prey model with Beddington-DeAngelis type functional response is investigated by using the Gaines and Mawhin,s continuation theorem of coincidence degree theory on time scales. Some conditions are obtained for the existence of periodic solutions. The approach is unified to provide the existence of the desired solutions for the continuous differential equations and discrete difference equations.
PP. 46-54
Title: A Method for Orthogonal Grid Generation
Authors: Stephen Salako, Guojun Liao and Mehmet Ali Akinlar
Abstract: A grid is called orthogonal if all grid lines intersect at a right angle. An orthogonal grid offers significant advantages in the solution of systems of partial differential equations and in the simulations of computational fluid dynamics. In this paper we present a variational method which generates nearly orthogonal grids with suitable parameter values. We optimize a cost functional which consists of only area and orthogonality quantities. A significant contribution is that no volume functional needs to be added to the cost functional. We achieve to generate nearly orthogonal grids without changing the cell size distribution of the initial grids by well-achieved deformation based grid generation method.
PP. 55-72
Title: Topological Mappings via ğα-Sets
Authors: M. Lellis Thivagar and Nirmala Rebecca Paul
Abstract: The aim of this paper is to introduce the different notions of ğα-closed maps and study some of their basic properties.Strongly ğα-closed maps have been defined to find the relationship with ğα-closed maps and as an application ğα-regular spaces have been defined to study its properties in terms of ğα-closed maps.
PP. 73-85
Authors: Omar M. Saad and Mohamed S. Hafez
Abstract: This paper presents a fuzzy approach for solving the bi-level integer linear fractional programming problem (BILFPP). At the first phase of the solution algorithm and to avoid the complexity of non convexity of this problem, we begin by finding the convex hull of its original set of constraints using the cutting-plane algorithm, and then the Charnes and Cooper transformation is used to convert the BILFPP to an equivalent bi-level linear programming problem (BLPP). At the second phase, a membership function is constructed to develop a fuzzy model for obtaining the optimal solution of the BLPP. Finally, an illustrative numerical example is provided to clarify the proposed approach.
PP. 86-99
Title: Distance Two Labeling of Some Total Graphs
Authors: S. K. Vaidya and D.D. Bantva
Abstract: An L(2,1)-labeling (or distance two labeling) of a graph G is a function f from the vertex set V(G) to the set of all nonnegative integers such that |f(x) - f(y)| ≥ 2 if d(x,y) =1 and |f(x) - f(y)| ≥ 1 if d(x,y) = 2. The L(2,1)-labeling number λ(G) of G is the smallest number k such that G has an L(2,1) - labeling with max{f(v): v in V(G)} = k. In this paper we completely determine the λ-number for total graphs of path Pn, cycle Cn, star K1,n and friendship graph Fn.
PP. 100-107
Title: Connection Properties in FN-spaces
Authors: Suprabha D. Kulkarni and S. B. Nimse
Abstract: In this paper we have studied the connection properties in FN-spaces. We have defined the fuzzy uniform local uniform connectedness and fuzzy uniform local connectedness of fuzzy nearness spaces. We have shown that a FN-space is fuzzy uniformly locally uniformly connected iff its completion is. Also every topological fuzzy locally connected FN-space is fuzzy uniformly locally uniformly connected. We also establish the result for a fuzzy topological space X that X has a fuzzy locally connected regular T1- extension iff X is the underlying fuzzy topological space of a FN-space Y which is concrete, regular and fuzzy uniformly locally uniformly connected. Lastly we achieve the equivalence of the concepts of fuzzy uniform local uniform connectedness, fuzzy uniform local connectedness and fuzzy local connectedness.
PP. 108-115
Title: Some third-order Modifications of Newton’s Method
Authors: Bijan Rahimi, Behzad Ghanbari and Mehdi Gholami Porshokouhi
Abstract: In this paper a new family of methods, free from second derivative, is presented. This new family of methods is constructed such that convergence is of order three and requires two require two evaluations of the function and first derivative per iteration. To illustrate the efficiency and performance of the new family of methods, several numerical examples are presented. Further numerical comparisons are made with several other existing third-order methods to show the abilities of the presented family of methods.
PP. 116-123
Title: On the Generalized Solution for Composite Type Differential Equation
Author: Tarig. M. Elzaki
Abstract: In this paper, we study a boundary-value problem for a class of composite equation of a mixed–type problem in the space. The existence and uniqueness of the generalized solution is proved, the proof is based on an energy inequality and the density of the range of the operator generated by the problem.
PP. 124-129
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