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Vol.14 No.4
Abstract
The purpose of this paper is to study the geometry of null curves in a semi-Riemannian manifold (M, g) of index 2. We show that it is possible to construct new Frenet equations of two types of null curves in M.
Abstract
In this paper, we introduce the concepts of r-generalized fuzzy closed sets, r-generalized fuzzy continuous maps and several types of r-generalized compactness in fuzzy topological spaces and investigate some of their properties.
Abstract
Let R be a 2-torsion free semiprime ring. Suppose that there exists a 4-permuting 4-derivation <TEX>${\Delta}:R{\times}R{\times}R{\times}R{\rightarrow}R$</TEX> such that the trace is centralizing on R. Then the trace of <TEX>${\Delta}$</TEX> is commuting on R. In particular, if R is a 3!-torsion free prime ring and <TEX>${\Delta}$</TEX> is nonzero under the same condition, then R is commutative.
Abstract
Using the center instead of the Lipschitz condition we show how to provide weaker sufficient convergence conditions of the modified Newton Kantorovich method for the solution of nonlinear singular integral equations with Curleman shift (NLSIES). Finer error bounds on the distances involved and a more precise information on the location of the solution are also obtained and under the same computational cost than in [1].
Abstract
An extension of the contraction mapping theorem is provided in a Banach space setting to approximate fixed points of operator equations. Our approach is justified by numerical examples where our results apply whereas the classical contraction mapping principle cannot.
Abstract
We define and study a concept of <TEX>$H^f-space$</TEX> for a map, which is a generalized concept of an H-space, in terms of the Gottlieb set for a map. For a principal fibration <TEX>$E_{\kappa}{\rightarrow}X$</TEX> induced by <TEX>${\kappa}:X{\rightarrow}X'\;from\;{\epsilon}:\;PX'{\rightarrow}X'$</TEX>, we can obtain a sufficient condition to having an <TEX>$H^{\bar{f}}-structure\;on\;E_{\kappa}$</TEX>, which is a generalization of Stasheff's result [17]. Also, we define and study a concept of <TEX>$co-H^g-space$</TEX> for a map, which is a dual concept of <TEX>$H^f-space$</TEX> for a map. Also, we get a dual result which is a generalization of Hilton, Mislin and Roitberg's result [6].
Abstract
We study crossed products of the free group and semigroup <TEX>$C^*-algebras$</TEX> by actions of <TEX>${\mathbb{R}$</TEX>, i.e., flows, and estimate and compute their stable rank.
Abstract
In 2002, the author and professor Ryu introduced the concept of analogue of Wiener measure. In this paper, we prove the existence theorem of Fourier-Feynman transform on analogue of Wiener measure in <TEX>$L_2-norm$</TEX> sense.
Abstract
In this paper, we define an analogue of generalized Wiener measure and investigate its basic properties. We define (<TEX>${\hat}It{o}$</TEX> type) stochastic integrals with respect to the generalized Wiener process and prove the <TEX>${\hat}It{o}$</TEX> formula. The existence and uniqueness of the solution of stochastic differential equation associated with the generalized Wiener process is proved. Finally, we generalize the linear filtering theory of Kalman-Bucy to the case of a generalized Wiener process.