On n-relator 3-manifolds Which Are Handlebodies

Let H be a handlebody, y = |∫1,……,∫n| a collection of 2-sided pairwise disjoint simple closed curves on eH. The 3-manifold obtained from H by attaching 2-handles to H .along the curves in y is called an n-relator 3-manifold, and is denoted as Hy. In tiffs paper, a sufficient and necessary condition for Hy to be a handlebody is described.     

n-李代数的结构

主要研究特征为2的代数闭域上(n+1)维n-李代数的结构,给出了(n+1)维n-李代数的分类,描述了其可解性与幂零性,刻画了(n+1)维n-李代数的导子代数与内导子代数的结构.     

概率n-度量空间中的不动点定理

本文引进了概率 n-度量空间 ,并将 [1 ]、[2 ]的某些主要结果拓广至 Menger概率 n-度量空间     

微生物酶催化的不对称还原反应合成(S)-(+)-4-苯基-2-丁醇

以LB培养基培养Pseudomonas monteilii TA-5,将其整细胞作为生物催化剂（Cat）,催化4-苯基-2-丁酮(1)的不对称还原反应,对映选择性地合成了(S)-(+)-4-苯基-2-丁醇。在最佳反应条件［1 10 mmol·L^-1, c（Cat） 30 g cdw·L^-1, 10%丙三醇,pH 8.0, 300 r·min^-1,于30 ℃反应24 h］下,转化率82%, ee值91%。     

Relative syzygies and grade of modules

Recently, Takahashi established a new approximation theory for finitely generated modules over commutative Noetherian rings, which unifies the spherical approximation theorem due to Auslander and Bridger and the Cohen-Macaulay approximation theorem due to Auslander and Buchweitz. In this paper we generalize these results to much more general case over non-commutative rings. As an application, we establish a relation between the injective dimension of a generalized tilting module ω and the finitistic dimension with respect to ω.     

Multi-weight, Weighted Weak Type Estimates for the Multilinear Calderón-Zygmund Operators

Let m be an integer and T be an m-linear Calderón-Zygmund operator, u, v1,..., vm be weights. In this paper, the authors give some sufficient conditions on the weights (u, vk) with 1 ≤ k ≤ m, such that T is bounded from Lp1(Rn, v1) × ··· × Lpm(Rn, vm) to Lp,∞(Rn, u).     

一类特征单的n-李代数

利用结合代数与n-李代数的张量积构造了一类无限维特征单的n-李代数,且证明了除n=3的情形以外,这类特征单n-李代数的内导子代数是特征单李代数.     

具NCVD核和B核的周期卷积函数类的相对n-宽度

本文考虑具NCVD核和B核的周期卷积函数的相关宽度问题,并得到量Kn（Kp（K）,Kp（K））q和Kn（Bp（G）,Bp（G））q在情形p=1,∞,1≤q≤∞的渐近估计．     

传递系统中的不变攀援集

推广了攀援集的概念.研究了传递系统中的不变攀援集.证明了在相当广泛的条件下,一个传递系统有一个不变的稠密的σ-Cantor子集是完全攀援集.