let  be a graded ring and  be a graded -module. we define a topology on graded prime spectrum  of the graded -module  which is analogous to that for , and investigate several properties of the topology.

in this paper, a pointwise pseudo-metric function on the l-realline is constructed. it is proved that the topology induced by this pointwisepseudo-metric is the usual topology.

Given any real-analytic CR manifold M, we provide general conditions on M guaranteeing that the group of all its global real-analytic CR automorphisms AutCR (M) is a Lie group (in an appropriate topology). In particular, we obtain a Lie group structure for AutCR (M) when M is an arbitrary compact real-analytic hypersurface embedded in some Stein manifold.

Pyridyl functionalized host molecules are oxidized to their N-oxide analogues and form a series of coordination polymers and discrete complexes with transition metal cations. Complex {[Ag(3)(NMP)(6)(L1)(2)]·3(ClO(4))}(∞) where L1 = tris(isonicotinoyl-N-oxide)cyclotriguaiacylene, NMP = N-methylpyrrolidone, is a three-dimensional (3-D) 3,6-connected coordination polymer of pyrite-like (pyr) topol...

Given an unknown attractor A in a continuous dy-namical system, how we can discover the topology and dynamics of A? As a practical matter, how can we do so from only a-nite amount of information? One way of doing so is to produce a semi-conjugacy from A onto a model system M whose topology and dynamics are known. The complexity of M then provides a lower bound for the complexity of A. In this p...

In this paper, closed ideals in Cc(X), the functionally countable subalgebra of C(X), with mc-topology, is studied. We show that ifX CUC-space, then C*c(X) uniform norm-topology a Banach algebra. Closed Cc(X) as modified analogue C(X) m-topology are characterized. For zero-dimensional space X, we proper ideal if and only it an intersection maximal Cc(X). It also shown every mc-topology X P-spac...

In coding theory, a channel coding algorithm is good if it achieves the Shannon capacity [1]. Similarly, we seek to derive a universal curve against which we can measure how good (or bad) a variable topology routing protocol (e.g. for ad-hoc networks) performs, in comparison with a theoretical minimum routing overhead, which is the amount of information needed to describe the changes in a dynam...