Banach空间上一类由算子导出的局部凸拓扑

本文我们研究了由半范簇｛ＰＴ｜Ｔ∈ψ（Ｅ，Ｅ１）｝在Ｅ上导出的局部凸拓扑σＥ（Ｅ１），其中ＰＴ（ｘ）＝Ｔｘ的范数，ｘ∈Ｅ。首先我们给出了拓扑σＥ（Ｅ１）＝ω和σＥ（Ｅ１）＝Ｅ上的范数的等价条件，接着讨论了在σＥ（Ｅ１）下的紧性与完备性，最后利用空间稠密特征和关于无穷基数幂等的Ｈｅｓｓｅｎｂｅｒｇ定理进一步研究了σＥ（Ｅ１）与Ｅ上的范数的关系，证明了当Ｅ的稠密特征足够大时在ω和Ｅ上的范数间有无穷多个     

Compactly bounded convolutions of measures

In this paper we extend classical results concerning generalized convolution structures on measure spaces. Given a locally compact Hausdorff space , we show that a compactly bounded convolution of point masses that is continuous in the topology of weak convergence with respect to can be extended to a general convolution of measures which is separately continuous in the topology of weak convergence with respect to .

     

An Intrinsic Homotopy Theory for Simplicial Complexes, with Applications to Image Analysis

A simplicial complex is a set equipped with a down-closed family of distinguished finite subsets. This structure, usually viewed as codifying a triangulated space, is used here directly, to describe spaces whose geometric realisation can be misleading. An intrinsic homotopy theory, not based on such realisation but agreeing with it, is introduced.The applications developed here are aimed at image analysis in metric spaces and have connections with digital topology and mathematical morphology. A metric space X has a structure t X of simplicial complex at each resolution >0; the resulting homotopy group _n (X) detects those singularities which can be captured by an n-dimensional grid, with edges bound by this works equally well for continuous or discrete regions of Euclidean spaces. Its computation is based on direct, intrinsic methods.     

Approaches for the coating of capillary columns with highly phenylated stationary phases for high-temperature GC

Two highly phenylated tetramethyl-p-silphenylene-diphenylsiloxane copolymers were coated on fused silica capillary columns and used as stationary phases in GC. The copolymers offered new insights into the coating process and column preparation due to their physicochemical properties. The fused silica capillary surface had to be pretreated in various ways to achieve a homogeneous film and a well deactivated surface: etching with ammonium bifluoride; leaching with sodium hydroxide and hydrochloric acid; silylation with tetraphenyldimethyldisilazane and triphenylsilylamine. Droplet formation was observed on tetraphenyldimethyldisilazane silylated surfaces leading to capillary columns with low separation efficiency. The topology of inhomogeneous films was investigated by light microscopy, scanning electron microscopy, and Auger electron spectroscopy. It became apparent that the stationary phase did not form droplets but islands, which are connected by a wetting layer according to the Stranski-Krastanov growth mode. Both copolymers are potential stationary phases for high-temperature GC with promising properties. They offer a higher overall polarity than 75% phenyl, 25% methyl-polysiloxanes in combination with increased thermal stability and reduced bleed levels.     

Characterization of Normal Traces on Von Neumann Algebras by Inequalities for the Modulus

It is proved that if a normal semifinite weight on a von Neumann algebra satisfies the inequality for any selfadjoint operators in , then this weight is a trace. Several similar characterizations of traces among the normal semifinite weights are proved. In particular, Gardner's result on the characterization of traces by the inequality is refined and reinforced.     

Critical level topology of energy hypersurfaces

Topologies are introduced into the nuclear configuration space R of molecular systems, based upon equipotential contour hypersurfaces on the otential energy hypersurface E. Critical level topologies T _fc and T _fc, based upon the number and distribution of various critical points of E, are of particular importance, since they represent convenient yet rigorous mathematical models for relations between elementary reaction mechanisms, and for relations between open sets of nuclear geometries which are classically accessible at a given total energy.     

Testing the relative positions of several points on a circle

This note introduces a programming technique that serves to facilitate the examination of the relative positions of several points on a circle, or—more generally—the relative positions of several entities that belong to a cyclic structure. The basic idea is to employ a function of the numerical representations of the individual positions which is invariant under rotation with regard to sign. The nature of the numerical representation makes it natural to introduce the term: cut-point-independent test procedure.     

The trousers problem revisited

Anderson and DeWitt considered the quantization of a massless scalar field in a spacetime whose spacelike hypersurfaces change topology and concluded that the topology change gives rise to infinite particle and energy production. We show here that their calculations are insufficient and that their propagation rule is unphysical. However, our results using a more general propagation rule support their conclusion.     

Tietze's extension theorem in fuzzy topological spaces

This paper discusses the conceptual difficulties of generalizing standard topological terms of L-fuzzy topological terms. In particular, a theory of relative topologies and relative functions for L-fuzzy topological spaces is developed. The extension of a relative L-fuzzy continuous function into the fuzzy unit interval is defined. The equivalence of L-fuzzy continuous functions and monotone families of open sets is proved, and this equivalence is exploited to establish a fuzzy version of Tietze's Extension Theorem. Finally, a partial converse to the theorem is proved.