GENERAL MATHEMATICS NOTES
Vol. 3, No. 2, April 2011
Vol. 3, No. 2, April 2011
Contents
Title: On Fixed-point theorems in Intuitionistic Fuzzy Metric Space I
Authors: T.K. Samanta and Sumit Mohinta
Abstract: In this paper, first we have established two sets of sufficient conditions for a TS-IF contractive mapping to have unique fixed point in a intuitionistic fuzzy metric space. Then we have defined (ε, λ) IF-uniformly locally contractive mapping and η-chainable space, where it has been proved that the (ε, λ) IF-uniformly locally contractive mapping possesses a fixed point.
PP. 1-12
Author: D. Venu Gopala Rao
Abstract: In this work, series solutions are obtained for the two species Lotka –Volterra, prey-predator interaction species which are governed by a system of non linear differential equations. For this purpose, the Adomian decomposition method (ADM) and Homotopy Perturbation method (HPM) are employed and it is shown that the Homotopy Perturbation method is much easier and a more efficient method.
PP. 13-26
Authors: F. Nahayo, S. Khardi and M. Haddou
Abstract: This paper aims to reduce noise levels of two-aircraft landing simultaneously on approach. Constraints related to stability, performance and flight safety are taken into account. The problem of optimal control is described and solved by a Sequential Quadratic Programming numerical method 'SQP' when globalized by the trust region method. By using a merit function, a sequential quadratic programming method associated with global trust regions bypasses the non-convex problem. This method used a nonlinear interior point trust region optimization solver under AMPL. Among several possible solutions, it is shown that there is an optimal trajectory leading to a reduction of noise levels on approach.
PP. 27-49
Title: Analytical Solution of Differential Equation Associated with Simple Pendulum
Authors: M. I. Qureshi and Kaleem A. Quraishi
Abstract: In the present work, we provide the exact equation of motion of a simple pendulum of arbitrary amplitude. For first time, a new and exact expression is obtained for the time ``t" of swinging of a simple pendulum from the vertical position to an arbitrary angular position ``θ". The time period ``T" of such a pendulum is also exactly expressible in terms of hypergeometric functions.
PP. 50-58
Title: An Inequality of Subclasses of Univalent Functions Related to Complex Order by Convolution Method
Authors: Rajendra Kumar Sharma and Deepak Singh
Abstract: The purpose of this paper to introduce the class V (λ, μ, A, B, b) of analytic functions related to complex order b. We investigate various properties of functions belonging to this class and prove an inequality of the subclasses of univalent function by convolution method.
PP. 59-65
Title: Some Theorems on Fixed Point
Authors: Sampada Navshinde and J. Achari
Abstract: Fixed point theorems for a class of mappings using rational symmetric expression involving four points of the space under consideration have been studied.
PP. 66-72
Title: Weighted Composition Operators Induced by Operator Valued Maps on Spaces of Orlicz-Functions
Authors: Kuldip Raj, B.S. Komal and Vinay Khosla
Abstract: In this paper we characterize the weighted composition operators induced by operator valued maps on Orlicz function spaces and effort is made to characterize compactness, invertibility, dense range and closed range of these operators.
PP. 73-79
Title: Totally Transitive Maps-A Short Note
Authors: Indranil Bhaumik and Binayak S. Choudhury
Abstract: In this short note we discuss totally transitive maps. We show that all chaotic maps are not necessarily totally transitive, but there are chaotic maps with this property. Our discussion relates to symbol space ∑2 and real line.
PP. 80-83
Authors: Amelia Bucur and Marilena Blaj
Abstract: In this article we describe a mathematical model of the degree of acceptability specific to the participation conditions of human resources (particularly students, teachers, etc.) at planned actions. The idea of a probable forecasting model for this degree consists in the evaluation of the probable participation of human resource at a certain action. The model offers a qualitative superior forecasting of participation in various actions.
PP. 84-87
Authors: B. S. Mehrok, Deepak Gupta and Harjinder Singh
Abstract: Due to several mathematical symbols and expressions, abstract is with the paper only.
PP. 88-96
Title: The Longest Path Problem in Fuzzy Project Networks: A Case Study
Authors: Mohamed F. El-Santawy and Soha M. Abd-Allah
Abstract: In This article a real-life international construction and building project network problem is presented, the problem of identifying the critical path of the project within fuzzy parameters (the longest path) is formulated by applying a linear programming approach which incorporates the concept of α-cuts into two (primal and dual) models. In order to determine the solution a code was developed to solve 22 linear programming models that had been constructed at different α-cuts during formulation. Yager’s ranking method is applied to compare all paths, and determining the time of the longest one.
PP. 97-107
Title: About Dirichlet's Transformation and Theoretic-Arithmetic Functions
Author: N. Daili
Abstract: In this work, we are going to define a transformation from Dirichlet's series called discrete Dirichlet's transformation. We will obtain some classical results connected Riemann's zeta function and theoretic-arithmetic functions. Some probabilistic interpretations are maked explicit.
PP. 108-122
Authors: Y. Pragathi Kumar and B. Satyanarayana
Abstract: The object of this paper is to establish integrals involving the product of struve’s function, general class of polynomials and H-function of two variables. Some special cases have also derived.
PP. 123-129
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