AF-代数及其维数群的分类

<正> 一、引言 分类是算子代数的一个重要研究方向,Von Neumann代数的分类已有许多工作。近二十年来,随着算子K-理论的发展,C~*-代数的分类问题引起了人们的注意,但由于它的复杂性,没有取得大的进展。Cuntz和Pedersen仿照Von Neumann代数的情形引进了有限、半有限和纯无限的C~*-代数的概念。本文研究AF-代数的这种分类。我们在维数群中引进了一些新的概念,并利用这些概念完全刻划了AF-代数的分类。

GICAR代数的迹态空间

本文证明GICAR代数的迹态空间是—个Bauer单纯形,其端点集合同胚于[0,1]。

Stability of Mbuna Species Populations in Lake Malawi

The first comprehensive study of abundance, richness and distribution of Mbuna in Lake Malawi was carried out in the 1980s. The present study examined changes of species richness and abundance of Mbuna with time. Most sites demarcated during the 1980s survey were explored in order to determine changes in abundance and composition of Mbuna over a period of more than 20 years Chi-square analysis revealed significant difference （p 〈 0.05） in abundance of Mbuna between 1983 and 2005 with the exception of Chinyankhwazi and Chinyamwezi where the difference was not significant （p 〉 0.05）. Cluster analysis showed changes in species composition between 1983 and 2005 in various sites. Generally, there were more species lost in a given area than new species observed in 2005. Decline in Mbuna species richness might have been caused by siltation, harvesting of Mbuna for food and ornamental fish trade while new species were mostly introduced through translocation from one part of the lake to another.

Dragload and Downdrag Performances of Inclined Pile Group Embedded in Consolidating Soil

The performance of inclined pile group embedded in consolidating soil under surcharge load was investigated by experiment in comparison with vertical pile group and single pile under the same conditions; dragload, downdrag, and layered soil settlement were measured. A three-dimensional numerical model was built via FLAC3D software, and verified by the experimental results. Influence factors, such as consolidation time, pile spacing, and pile tilt angle were analyzed. The results show that dragload of inclined pile group increases with the increase of consolidation time and pile spacing or the decrease of pile tilt angle. Downdrag of inclined pile group increases with the increase of consolidation time, pile spacing and pile tilt angle.

CLASSIFICATION OF AF-ALGEBRAS AND THEIR DIMENSION GROUPS

This paper gives the intrinsic character of the classification for AF-algebras defined by J.Cuntz and G. K. Pedersen in terms of their dimension groups.

Some infinite dimensional representations of reductive groups with Frobenius maps

In this paper,we construct certain irreducible infinite dimensional representations of algebraic groups with Frobenius maps.In particular,a few classical results of Steinberg and Deligne&Lusztig on complex representations of finite groups of Lie type are extended to reductive algebraic groups with Frobenius maps.

Entire curves,integral sets and principal bundles

We compare the behaviour of entire curves and integral sets,in particular in relation to locally trivial fiber bundles,algebraic groups and finite ramified covers over semi-abelian varieties.

ON THE CLASSIFICATION OF AF-ALGEBRAS AND THEIR DIMENSION GROUPS(Ⅱ)

This paper is a continuation of [1]. It gives some applications of the results in [1], containing some examples of pure-infinite AF-algebras and the invariant properties of the types of the C-extensions by two AF-algebras of the same type.

Stably Calabi-Yau algebras and skew group algebras

Let G be a finite group and A be a finite-dimensional selfinjective algebra over an algebraically closed field. Suppose A is a left G-module algebra. Some suficient conditions for the skew group algebra AG to be stably Calabi-Yau are provided, and some new examples of stably Calabi-Yau algebras are given as well.

Hochschild cohomology of Beilinson algebra of exterior algebra

Let An be the Beilinson algebra of exterior algebra of an n-dimensional vector space, which is derived equivalent to the endomorphism algebra Endox （T） of a tilting complex T = II^ni=0^Ox （i） of coherent COx-modules over a projective scheme X = P^nk. In this paper we first construct a minimal projective bimodule resolution of An, and then apply it to calculate k-dimensions of the Hochsehild cohomology groups of An in terms of parallel paths. Finally, we give an explicit description of the cup product and obtain a Gabriel presentation of Hochschild cohomology ring of An. As a consequence, we provide a class of algebras of finite global dimension whose Hochschild cohomology rings have non-trivial multiplicative structures.

GENERALIZED SIMPLE NONCOMMUTATIVE TORI

The generalized noncommutative torus Tkp of rank n was defined in [4] by the crossed product Am/k ×a3 Z ×a4 … ×an Z, where the actions ai of Z on the fibre Mk(C) of a rational rotation algebra Am/k are trivial, and C*(kZ × kZ) ×a3 Z ×a4 ... ×an Z is a completely irrational noncommutative torus Ap of rank n. It is shown in this paper that Tkp is strongly Morita equivalent to Ap, and that Tkp (?) Mp∞ is isomorphic to Ap (?) Mk(C) (?) Mp∞ if and only if the set of prime factors of k is a subset of the set of prime factors of p.

Successful couplings for a class of stochastic differential equations driven by Lvy processes

By constructing proper coupling operators for the integro-differential type Markov generator, we establish the existence of a successful coupling for a class of stochastic differential equations driven by Levy processes. Our result implies a new Liouville theorem for space-time bounded harmonic functions with respect to the underlying Markov semigroups, and it is sharp for Ornstein-Uhlenbeck processes driven by s-stable Levy processes.

Study on implicit composite element method for seepage analysis in underground engineering

Based on the basic principle of the finite element method, the implicit composite element method for numerical simulation of seepage in underground engineering is proposed. In the simulation, the faults and drainage holes are set implicitly in the model elements without adding additional elements. Elements containing fault or drainage-hole data are termed composite elements. Then, their information data in model could be obtained. By determining the osmotic transmission matrix of the composite elements, the permeability coefficient matrix is then obtained. The method was applied to the numerical simulation of the seepage field around the underground powerhouse of the Ganhe Pumping Station in Yunnan, China, using a compiled three-dimensional finite element method calculation program. The rock mass around the site includes two faults. The seepage field in the rock mass was analyzed at different stages of the engineering project. The results show that, before the excavation of the underground caverns, the rock mass seepage is affected by the faults and the groundwater permeated down along the tangential fault plane. After the excavation of the caverns during the operation period, the groundwater is basically drained away and the underground caverns are mostly above the groundwater level. Thus, the calculation results of the engineering example verify the implicit composite method for the simulation of faults and drainage holes. This method can well meet the calculation demands of practical engineering.

Outlier Mining Based Abnormal Machine Detection in Intelligent Maintenance

Assessing machine's performance through comparing the same or similar machines is important to implement intelligent maintenance for swarm machine.In this paper,an outlier mining based abnormal machine detection algorithm is proposed for this purpose.Firstly,the outlier mining based on clustering is introduced and the definition of cluster-based global outlier factor(CBGOF) is presented.Then the modified swarm intelligence clustering(MSIC) algorithm is suggested and the outlier mining algorithm based on MSIC is proposed.The algorithm can not only cluster machines according to their performance but also detect possible abnormal machines.Finally,a comparison of mobile soccer robots' performance proves the algorithm is feasible and effective.