The Novikov Conjecture for Low Degree Cohomology Classes

We outline a twisted analogue of the Mishchenko–Kasparov approach to prove the Novikov conjecture on the homotopy invariance of the higher signatures. Using our approach, we give a new and simple proof of the homotopy invariance of the higher signatures associated to all cohomology classes of the classifying space that belong to the subring of the cohomology ring of the classifying space that is generated by cohomology classes of degree less than or equal to 2, a result that was first established by Connes and Gromov and Moscovici using other methods. A key new ingredient is the construction of a tautological C* _r (, )-bundle and connection, which can be used to construct a C* _r (, )-index that lies in the Grothendieck group of C* _r (, ), where is a multiplier on the discrete group corresponding to a degree 2 cohomology class. We also utilise a main result of Hilsum and Skandalis to establish our theorem.     

Index Heuristics for Multiclass M/G/1 Systems with Nonpreemptive Service and Convex Holding Costs

We consider the optimal service control of a multiclass M/G/1 queueing system in which customers are served nonpreemptively and the system cost rate is additive across classes and increasing convex in the numbers present in each class. Following Whittle's approach to a class of restless bandit problems, we develop a Langrangian relaxation of the service control problem which serves to motivate the development of a class of index heuristics. The index for a particular customer class is characterised as a fair charge for service of that class. The paper develops these indices and reports an extensive numerical investigation which exhibits strong performance of the index heuristics for both discounted and average costs.     

One-armed bandit models with continuous and delayed responses

One-armed bandit processes with continuous delayed responses are formulated as controlled stochastic processes following the Bayesian approach. It is shown that under some regularity conditions, a Gittins-like index exists which is the limit of a monotonic sequence of break-even values characterizing optimal initial selections of arms for finite horizon bandit processes. Furthermore, there is an optimal stopping solution when all observations on the unknown arm are complete. Results are illustrated with a bandit model having exponentially distributed responses, in which case the controlled stochastic process becomes a Markov decision process, the Gittins-like index is the Gittins index and the Gittins index strategy is optimal. Acknowledgement.We thank an anonymous referee for constructive and insightful comments, especially those related to the notion of the Gittins index.Both authors are funded by the Natural Sciences and Engineering Research Council (NSERC) of Canada.     

The Structure of the (Outer) Automorphism Group of a Bieberbach Group

Referring to Tits alternative, we develop a necessary and sufficient condition to decide whether the normalizer of a finite group of integral matrices is polycyclic-by-finite or is containing a non-Abelian free group. This result is of fundamental importance to conclude whether the (outer) automorphism group of a Bieberbach group is polycyclic-by-finite or has a non-cyclic free subgroup.     

用形状指数研究苯酚类化合物对大型蚤的急性毒性

基于分子拓扑理论，计算了18种取代苯酚的Kier分子形状拓扑指数（^mK）．利用最小二乘法建立了不同pH值下11种取代苯酚对大型蚤急性毒性（pIC50）的QSAR模型，其相关系数（R^2）依次为：0．963（pH=6．0），0．966（pH=7．8），0.846（pH=9．0）．这些模型的计算值与其实验值基本吻合．通过留一法检验及对其余7种取代苯酚类化合物的pIC50值进行预测，结果表明该模型具有良好的稳健性和预测能力．     

非线性差分方程组多正解的存在性

本文应用不动点指数理论证明了一个非线性差分方程组多正解的存在性.     

基于小波分形理论的股价指数信息量测度研究

本把小波分析和分形理论引入到股价指数时间序列的分析中，给出了股价指数波动复杂性的信息量测度方法——信息熵和分形维方法。通过对上证综指和深证成指1994年1月3日至2002年3月4日期间的数据进行的实证分析显示，两种方法均能刻画股价指数波动的复杂程度，这对初步了解我国股市场的波动规律有一定的实际意义。     

区域技术创新系统评估体系的研究

技术创新对提升企业竞争力、提高综合国力、促进经济增长和国家持续发展非常重要。本在研究了区域经济发展和国家创新系统的相关献基础上，建立了系统、量化的区域技术创新系统评估指标体系，提出了决定区域创新系统技术创新能力的主要因素，并用TOPSIS方法对指标的量化进行了尝试。     

风险企业的委托-代理模型

传统的委托—代理理论在解释风险企业家的行为时遇到了困难。通过对传统的委托—代理理论进行重新构造和拓展，本提出逆反努力法则，验证了隐藏行动的道德风险的存在，并通过Newton迭代法和图形学方法对风险企业家的长期努力水平进行计算，发现努力水平对努力效应指数n表现出协同效应。     

树的稳定子集和稳定指标

一个实矩阵的符号稳定性问题在经济学、生态学等诸多领域中都有应用背景．本文利用[1]中给出的不可约矩阵的符号稳定性的有关结论，将一个实矩阵的符号稳定性判定问题转化为一个等价的图论问题，即判定无向树中一个点子集的稳定性问题．本文引入了树的稳定子集的概念并给出了稳定子集的递归判别方法．本文还提出井研究了树的稳定指标，即树中所有稳定子集的最小基数，证明了关于稳定指标的一个min—max型定理，井给出了n阶树的稳定指标的最好上界及达到上界的极树的完全刻划。