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Vol.10 No.2
Abstract
The purpose of this paper is to study the geometry of null curves in a 6-dimensional semi-Riemannian manifold <TEX>$M_q$</TEX> of index q, since the general n-dimensional cases are too complicated. We show that it is possible to construct three types of Frenet equations of null curves in <TEX>$M_q$</TEX>, supported by one example. We find each types of Frenet equations invariant under any causal change. And we discuss some properties of null curves in <TEX>$M_q$</TEX>.
Abstract
We estimate the stable rank of twisted crossed products of <TEX>$C^{*}-algebras$</TEX> by topological Abelian groups. As an application we estimate the stable rank of twisted crossed products of <TEX>$C^{*}-algebras$</TEX> by solvable Lie groups. In particular, we obtain the stable rank estimate of twisted group <TEX>$C^{*}-algebras$</TEX> of solvable Lie groups by the (reduced) dimension and (generalized) rank of groups.
Abstract
In this paper, when N is a compact Riemannian manifold, we considered the positive time solution to equation <TEX>$\Box_gu(t,x)-c_nu(t,x)+c_nu(t,x)^{(n+3)/(n-1)}$</TEX> on M ＝<TEX>$(-{\infty},+{\infty})\;{\times}_f\;N$</TEX>, where <TEX>$c_n$</TEX> ＝(n－1)/4n and <TEX>$\Box_{g}$</TEX> is the d'Alembertian for a Lorentzian warped manifold.
Abstract
The object of this paper is to extend and generalize the work of Brosowski ［Fixpunktsatze in der approximationstheorie. Mathematica Cluj 11 (1969), 195-200］, Hicks & Humphries ［A note on fixed point theorems. J. Approx. Theory 34 (1982), 221-225］, Khan & Khan ［An extension of Brosowski-Meinardus theorem on invariant approximation. Approx. Theory Appl. 11 (1995), 1-5］ and Singh ［An application of a fixed point theorem to approximation theory J. Approx. Theory 25 (1979), 89-90; Application of fixed point theorem in approximation theory. In: Applied nonlinear analysis (pp. 389-394). Academic Press, 1979］ in metric spaces having convex structure, and in metric linear spaces having strictly monotone metric.
Abstract
The aim of this paper is to prove some common fixed point theorems for the class of compatible maps to larger class of weakly compatible maps without appeal to continuity in Monger spaces and we also give a set of alternative conditions in place of completeness of the space. We improve and extend the results of Dedeic & Sarapa ［A common fixed point theorem for three mappings on Monger spaces. Math. Japon. 34 (1989), no. 6,919-923］ and Rashwan & Hedar ［On common fixed point theorems of compatible mappings in Monger spaces. Demonstratio Math. 31 (1998), no. 3, 537-546］.