An Equivalence of Two Categories of sl(n,C)-Modules

We prove that the following two categories of sl(n,C)-modules are equivalent: (1) the category of modules with integral support filtered by submodules of Verma modules and complete with respect to Enright's completion functor; (2) the category of all subquotients of modules FM, where F is a finite-dimensional module and M is a fixed simple generic Gelfand–Zetlin module with integral central character. Our proof is based on an explicit construction of an equivalence which, additionally, commutes with translation functors. Finally, we describe some applications of this both to certain generalizations of the category O and to Gelfand–Zetlin modules.     

小扰动下奇异闭轨附近后继函数的光滑性

扰动系统在奇异闭轨附近的后继函数对于判断奇异闭轨分支出极限环的个数、极限环的稳定性和相对位置具有极其重要的作用。通过对Dulac映射及正则映射的光滑性的研究得到结论:具有奇异闭轨的Ck系统在小扰动下奇异闭轨附近的的后继函数为Ck-1的。所得结果简洁,可为以后相关研究工     

关于模上赋值的拓展

旨在研究交换环上模的赋值的拓展问题。通过构造反例表明,一个模的赋值在该模的扩张上不一定总存在拓展。基于一些有关模上赋值的拓展的事实,模上赋值在扩模上存在拓展的两个充分必要条件被获得。     

三值序列的特征检测及其产生

本文重新定义了三值序列的表述及其规范,根据三值序列特征检测及其产生电路含有模3乘2运算,本文提出了具有Q,2Q双轨输出的三值D型触发器,以简化相关电路的逻辑结构并减少延迟,本文还讨论了三值线性模和特征序列及相应的电路设计。     

Complete Distributivity of Lattice Ordered Groups and of Vector Lattices

In this paper we investigate the possibility of a regular embedding of a lattice ordered group into a completely distributive vector lattice.     

A description of Kac-systems of multiplicative unitary operators

Let V be a multiplicative unitary operator on a separable Hilbert spaceH, then there are two subalgebras ofB( H) denoted byA( V) and ?( V), respectively, which correspond to V. If V satisfiesV ² =I, then we will obtain the necessary and sufficient condition of Baaj and Skandalis’ main theorem, i.e.V has a Kac-system if and only if the linear closed space of the product of the above two algebras is the compact operator space; with this condition the above algebras are also quantum groups.     

有限秩算子的表示（I）

定义了子空间格代数的（弱闭双边）模,对有限维Hilbert空间的强自反子空间格代数的模及原子Boolean格代数的模中的有限秩算子进行了讨论,得到了有限秩算子一定可以表示为秩1算子的和。     

Extremal Forex Returns in Extremely Large Data Sets

Exciting information for risk and investment analysis is obtained from an exceptionally large and automatically filtered high frequency data set containing all the forex quote prices on Reuters during a ten-year period. It is shown how the high frequency data improve the efficiency of the tail risk cum loss estimates. We demonstrate theoretically and empirically that the heavy tail feature of foreign exchange rate returns implies that position limits for traders calculated under the industry standard normal model are either not prudent enough, or are overly conservative depending on the time horizon.     

Generalized Rank Estimates For An Autoregressive Time Series: A U-Statistic Approach

A class of weighted rank-based estimates for estimating the parameter vector of an autoregressive time series is considered. This class of estimates is similar to, and contains, the class proposed by Terpstra et al. [54]. Asymptotic linearity properties are derived for the so called GR-estimates. Based on these properties, the GR-estimates are shown to be asymptotically normal at rate n ^1/2. The theory of U-statistics along with a characterization of weak dependence that is inherent in stationary AR(p) models are the primary tools used to obtain the results. The so called pair-wise slopes estimator, which is a special case of this class of estimates, is discussed in an AR(1) context. This revised version was published online in June 2006 with corrections to the Cover Date.     

The Graded Algebra Generated by Two Eulerian Derivatives

We study the algebra R _p,q generated by the Eulerian derivatives for two parameters p and q. Subject to certain conditions on the parameters, we show that R _p,q is a finitely presented N-graded algebra of Gelfand–Kirillov dimension 3. We establish a criterion for the cyclic module R _p,q /R _p,q f to be Noetherian, where f is homogeneous of degree 1. For some choices of the parameters, this criterion always holds and we know of no situation where it fails. It is not known whether R _p,q is Noetherian. We classify the point modules for R _p,q and determine the normal elements and graded automorphisms for R _p,q .