GENERAL MATHEMATICS NOTES

Vol. 5, No. 1, July 2011

 Contents

Title: Dependance of Solution of Difference Equation on Initial Conditions and Parameters

Author: K.L. Bondar

Abstract: In this paper we consider the problem of continuity of solutions x(t, t₀, x₀) of system

Δ x(t)= f(t, x(t)), x(t₀)= x₀, t₀ >= 0,

with respect to the initial values (t₀, x₀).

PP. 1-6

Title: Free Actions on Semiprime Gamma Rings

Authors: Kalyan Kumar Dey and Akhil Chandra Paul

Abstract: Let M be a semiprime Г-ring. We study on some mappings related to left centralizers, centralizers, derivations, (σ, τ)-derivations and generalized (σ, τ)-derivations which are free actions on semiprime Г-rings. If φ(x) = T(x)αx – xαT(x) for all x in M, α in Г is a mapping from M into M. Then we show that it is a free action. If F : M →M is a generalized (σ,τ)-derivation with associate (σ, τ)-derivation d, and a in F is a dependent element, then we also show that it is a dependent element of (σ+d). Furthermore, we prove that for centralizer f and a derivation d of a semiprime Г-ring M, φ = d◦f is a free action.

PP. 7-14

Title: Certain Properties of Mixed Super Quasi Einstein Manifolds

Authors: Ram Nivas and Anmita Bajpai

Abstract: In this paper we have defined mixed super quasi-Einstein manifold  MS(QE)_n which is more generalized form of  Einstein manifold, quasi-Einstein manifold, generalized quasi-Einstein manifold and super quasi-Einstein manifold . In this paper it has been shown that MS(QE)_n(n>3) is a MS(QC)_n  if it is conformally flat. Moreover, it is shown that MS(QC)_n(n>3) is a conformally  flat MS(QE)_n and an example of  mixed super quasi Einstein manifold  is also given . Properties of the curvature tensor of in a conformally flat, projectively flat  and conharmonically flat manifold have been discussed. It has also been shown that a totally umbilical hypersurface of a conharmonically flat MS(QE)_n (n>3) is a manifold  of mixed super quasi-constant curvature.

PP. 15-26

Title: On Generalized Solutions of Boundary Value Problems for Some Class of Fourth Order Operator-Differential Equations on the Segment

Author: R.Z. Humbataliyev

Abstract: In the paper we give definition of a generalized solution of boundary value problems for some fourth order operator-differential equations, and prove the existence of generalized solution of this problem by the coeffcients of the equations on the segment.

PP. 27-33

Title: Composite Implicit Random Iterations for Approximating Common Random Fixed Point for a Finite Family of Strictly Pseudocontractive Random Operators

Authors: Shrabani Banerjee and Binayak S.Choudhury

Abstract: In the present work we construct a composite implicit random iterative process for a finite family of strictly pseudocontractive random operators and study the necessary and sufficient condition for the convergence of this process to a common random fixed point of a finite family strictly pseudocontractive random operators.

PP. 34-45

Title: Intuitionistic Fuzzy Sets in Ordered Г-Semigroups

Author: S. Lekkoksung

Abstract: We consider the intuitionistic fuzzification of the concept of several ideal in an ordered Г-semigroup, and investigate some properties of such ideals.

PP. 46-56