Invariants for normal completely positive maps on the hyperfinite II1 factor

We investigate certain classes of normal completely positive (CP) maps on the hyperfinite II₁ factorA. Using the representation theory of a suitable irrational rotation algebra, we propose some computable invariants for such CP maps. Dedicated to Professor K B Sinha     

B（X）上保点谱的可加映射和初等算子

记Ｘ为复数域上无限维Ｂａｎａｃｈ空间，Ｈ为无限维复可分Ｈｉｌｅｒｔ空间。本文给出Ｂ（Ｘ）上保持点谱的满射可加射具有的形式，以及Ｂ（Ｈ）上某些初等算子保点谱的充要条件。     

分段函数的分类及分离型分段函数与初等函数之间的关系

将分段函数划分为连结型分段函数 ,分离型分段函数和它们的组合形式三种类型 ,得到了分离型分段函数是初等函数的充分必要条件 ,完整地解决了分离型分段函数与初等函数之间的关系 ,并且给出了初等函数在其任一截取集上的限制函数 (截取函数 )仍然是初等函数的结果     

Noise-induced asymptotic periodicity in a piecewise linear map

We examine asymptotically periodic density evolution in one-dimensional maps perturbed by noise, associating the macroscopic state of these dynamical systems with a phase space density. For asymptotically periodic systems density evolution becomes periodic in time, as do some macroscopic properties calculated from them. The general formalism of asymptotic periodicity is examined and used to calculate time correlations along trajectories of these maps as well as their limiting conditional entropy. The time correlation is shown to naturally decouple into periodic and stochastic components. Finally, asymptotic periodicity is studied in a noise-perturbed piecewise linear map, focusing on how the variation of noise amplitude can cause a transition from asymptotic periodicity to asymptotic stability in the density evolution of this system.     

基于零点的函数K图和dj图的转换

介绍了函数的最大项展开式和CRM展开式及其图形表示，提出函数K图和dj图的零点的概念，并以此为基础讨论了基于零点的函数K图和dj图之间的转换方法。     

Convergence of Riemannian Manifolds and Laplace Operators, II

We study spectral convergence of compact Riemannian manifolds or more generally certain Dirichlet spaces, obtaining some compactness results on harmonic functions and harmonic maps. Mathematics Subject Classifications (2000) 53C21, 58D17, 58J50. Atsushi Kasue: Partly supported by the Grant-in-Aid for Scientific Research (B) No. 15340053 of the Japan Society for the Promotion of Science.     

Lemniscates and inequalities for the logarithmic capacities of continua

It is shown that if P(z) = z ⁿ + ? is a polynomial with connected lemniscate E(P) = {z: ¦P(z)¦ ≤ 1} and m critical points, then, for any n? m+1 points on the lemniscate E(P), there exists a continuum γ ? E(P) of logarithmic capacity cap γ ≤ 2^?1/n which contains these points and all zeros and critical points of the polynomial. As corollaries, estimates for continua of minimum capacity containing given points are obtained.     

Random walks generated by affine mappings

This article is concerned with Markov chains on ^m constructed by randomly choosing an affine map at each stage, and then making the transition from the current point to its image under this map. The distribution of the random affine map can depend on the current point (i.e., state of the chain). Sufficient conditions are given under which this chain is ergodic.     

Structural determinants of steroids for cytochrome P450 3A4-mediated metabolism

Cytochrome P450 3A4 (CYP3A4), a major member of cytochrome P450 isoenzymes, metabolizes the majority of steroids in 6β-position. For the purpose of determining requisite structural features of a series of structurally related steroids for CYP3A4-mediated metabolism, three-dimensional pharmacophore modeling as well as electrotopological state map were conducted for 15 steroids. Though prior studies speculated that the chemical reactivity of the allylic 6β-position might have a greater influence on CYP3A4 selective 6-hydroxylation than steric constraints in the enzyme, our results reveal that for CYP3A4 steroidal substrates, it is not the chemical reactivity of atoms at 6β-site, but the pharmacophoric features, i.e. the two hydrophobic rings together with two H-bond donors, that act as the key factors responsible for determining the CYP3A4 selective 6-hydroxylation of steroids.