Bi-Invariant Domains in Semisimple Groups: Nonprincipal Orbits and Boundaries

Let G be a complex semisimple group with real form G . For the action of G × G on G by left and right translation, we define and study an orbit-type stratification of G. In particular, we compute the dimension of an arbitrary stratum; we identify certain strata of low codimension in G, the union of whose closures contains every nonprincipal stratum; and we describe the boundaries and adjacency relations of the maximal connected domains in G that contain only principal orbits.     

Exponential Objects in Coreflective or Quotient Reflective Subconstructs: A Comparison

We prove that in the construct PRAP of pre-approach spaces the class of exponential objects completely determines the exponential objects in certain subconstructs. We show that Exp B Exp PRAP for every coreflective subconstruct B and from this inclusion we deduce the equality Exp B = B Exp PRAP for every subconstruct B that is coreflective and finitely productive. We prove that the same equality holds for non-trivial quotient reflective subconstructs. These results induce well known answers to similar questions on the construct of pretopological spaces and are compared to the topological situation.     

A continuous decomposition of the Menger curve into pseudo-arcs

It is proved that the Menger universal curve admits a continuous decomposition into pseudo-arcs with the quotient space homeomorphic to .

     

Representations of distributive semilattices in ideal lattices of various algebraic structures

We study the relationships among existing results about representations of distributive semilattices by ideals in dimension groups, von Neumann regular rings, C*-algebras, and complemented modular lattices. We prove additional representation results which exhibit further connections with the scattered literature on these different topics. Received March 2, 1998; accepted in final form November 9, 2000.     

几类非Abel群之增广商群的结构

记ZG为有限群G的整群环,△n(G)为增广理想△(G)的n次幂,Qn(G)=△"(G)/△n 1(G)为G的增广商群.本文考虑了二面体群D2tk(k 奇)和m次对称群Sm,证明了Qn(D2tk)为秩不超过2t 1的基本2-群以及Qn(Sm)≌Z2.     

The exactness of the projective limit functor on the category of quotients of Frechet spaces

We give conditions under which the functor projective limit is exact on the category of quotients of Fréchet spaces of L.Waelbroeck [18].     

Quantification of the push-pull character of azo dyes and a basis for their evaluation as potential nonlinear optical materials

The push-pull characters of a large series of donor-acceptor substituted azo dyes—71 structures in all—have been quantified by the NN double bond lengths, d_NN, the ¹⁵N NMR chemical shift differences, Δδ_15N, of the two nitrogen atoms and the quotient, π^∗/π, of the occupations of the antibonding π^∗, and bonding π orbitals of this partial NN double bond. The excellent correlation of the occupation quotients with the bond lengths strongly infers that both π^∗/π and d_NN are excellent parameters for quantifying charge alternation in the push-pull chromophore and the molecular hyperpolarizability, β₀, of these compounds. By this approach, selected compounds can be appropriately considered as viable candidates for nonlinear optical (NLO) applications.     

包含$l^{\beta}(0<\beta<1)$渐近等距翻版的有界线性算子空间

Assume X is a normed space,every x ＊ ∈ S（X＊） can reach its norm at some point in B（X）,and Y is a β-normed space.If there is a quotient space of Y which is asymptotically isometric to l β,then L（X,Y） contains an asymptotically isometric copy of l β.Some sufficient conditions are given under which L（X,Y） fails to have the fixed point property for nonexpansive mappings on closed bounded β-convex subsets of L（X,Y）.     

On Kaufmanʼs theorem

Kaufman?s theorem (Kaufman, 1978 [9]) on representing closed linear operators as quotients of bounded operators is given a new constructive proof, and is extended to operators between two Hilbert spaces. Two different definitions of operator quotients existing in the literature are compared.