关于圈的完全正矩阵实现

本文给出了一个关联图为圈的非负、半正定矩阵A为完全正的一个充要条件.我们还证明了这样的矩阵A（当A为完全正时）的分解指数即为A的阶数.     

中国证券市场股指波动的条件异方差特性分析

股指的波动具有持续性、集聚性 ,如何进行判别 ?本文用 Garch模型理论探讨沪深股指的这种条件异方差特征 ,进一步分析波动是否影响股指未来变化 ,以及股市对利好、利空的消息是否存在不对称的反映。同时 ,比较不同类型的股指的共性及差异 ,并对上述现象作了解释和说明。     

信用担保风险的模糊综合评审研究

信用担保机构是连接银行和企业的桥梁，对于改善企业融资环境和拓展银行业务具有重要意义，信用担保风险的评审是担保机构能否生存及有效运行的关键。信用风险的评审机制主观性强，对担保项目进行客观，公正的评审比较困难。本采用模糊数学中的综合判别方法，全面考虑风险评审所涵盖的各种风险指标及其重要度，建立了定性分析与定量分析方法相结合的信用担保风险综合评审模型，为担保机构提供了一种相对科学、客观的评审方法。     

宽带膜厚实时监控过程中膜层折射率的确定方法

为了准确计算出镀膜过程中每层膜的折射率，介绍了实时监控过程中确定膜层折射率的2种方法：一种是由实测的透射比光谱直接反算出膜层的折射率；另一种是用最小二乘法的优化算法实时拟合折射率。试验结果表明：在线反算适合单点监控，所得折射率误差小于2%。然而在实际镀膜过程中,由于宽带内膜层参数误差较大,一般大于25%。为此，采用最小二乘法拟合，即在整个宽光谱范围内采集每个波长点的信息，所得结果误差很小，一般都在2％～5%之间,有时可达到10%,在很大程度上提高了实际镀膜时膜厚监控的精度。     

相变光盘介电薄膜ZnS-SiO2 的微结构和光学特性

采用射频磁控溅射法制备了ZnS-SiO₂ 介电薄膜,利用透射电镜和椭偏仪研究了溅射条件对ZnS-SiO₂薄膜微结构和折射率n的影响.研究表明,ZnS-SiO₂薄膜中存在微小晶粒,大小为2～10 nm的ZnS颗粒分布在SiO₂基体中,当溅射功率和溅射气压变化时,ZnS-SiO₂薄膜的微结构和折射率n发生显著变化,微结构的变化是导致折射率n变化的主要原因,通过优化溅射条件可以制备适用于相变光盘的高质量ZnS-SiO₂介电薄膜.     

Extremes of deterministic sub‐sampled moving averages with heavy‐tailed innovations

Let {X_k}_k?1 be a strictly stationary time series. For a strictly increasing sampling function g:?→? define Y_k=X_g(k) as the deterministic sub‐sampled time series. In this paper, the extreme value theory of {Y_k} is studied when X_k has representation as a moving average driven by heavy‐tailed innovations. Under mild conditions, convergence results for a sequence of point processes based on {Y_k} are proved and extremal properties of the deterministic sub‐sampled time series are derived. In particular, we obtain the limiting distribution of the maximum and the corresponding extremal index. Copyright © 2003 John Wiley & Sons, Ltd.     

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.     

对求解非线性方程方法的探索

BaiCL在2001年提出了双曲函数法，并把解设成具体的双曲函数，即sinhw和coshw的线性组合．本文把解设成是由2个函数f(ξ)和g(ξ)组成的线性组合，它们可以有多种取法，从而使方程更直接、更有效．借助数学软件Maple，用改进后的方法和吴文俊消元法，求解Bai C L文中的一个例子，获得了包含Bai文结果在内的更为丰富、精确的行波解．     

A novel tridentate nitrogen donor as ligand in copper catalyzed ATRP of methyl methacrylate

A tridentate ligand, BPIEP: 2,6‐bis[1‐(2,6‐diisopropyl phenylimino) ethyl] pyridine, having central pyridine unit and two peripheral imine coordination sites was effectively employed in controlled/“living” radical polymerization of MMA at 90°C in toluene as solvent, Cu^IBr as catalyst, and ethyl‐2‐bromoisobutyrate (EBiB) as initiator resulting in well‐defined polymers with polydispersities M_w/M_n ≤ 1.23. The rate of polymerization follows first‐order kinetics, k_app = 3.4 × 10^?5 s^?1, indicating the presence of low radical concentration ([P*] ≤ 10^?8) throughout the reaction. The polymerization rate attains a maximum at a ligand‐to‐metal ratio of 2:1 in toluene at 90°C. The solvent concentration (v/v, with respect to monomer) has a significant effect on the polymerization kinetics. The polymerization is faster in polar solvents like, diphenylether, and anisole, as compared to toluene. Increasing the monomer concentration in toluene resulted in a better control of polymerization. The molecular weights (M_n,SEC) increased linearly with conversion and were found to be higher than predicted molecular (M_n,Cal). However, the polydispersity remained narrow, i.e., ≤1.23. The initiator efficiency at lower monomer concentration approaches a value of 0.7 in 110 min as compared to 0.5 in 330 min at higher monomer concentration. The aging of the copper salt complexed with BPIEP had a beneficial effect and resulted in polymers with narrow polydispersitities and higher conversion. PMMA obtained at room temperature in toluene (33%, v/v) gave PDI of 1.22 (M_n = 8500) in 48 h whereas, at 50°C the PDI is 1.18 (M_n = 10,300), which is achieved in 23 h. The plot of lnk_app versus 1/T gave an apparent activation energy of polymerization as (ΔE^≠_app) 58.29 KJ/mol and enthalpy of equilibrium (ΔH⁰_eq) to 28.8 KJ/mol. Reverse ATRP of MMA was successfully performed using AIBN in bulk as well as solution. The controlled nature of the polymerization reaction was established through kinetic studies and chain extension experiments. © 2005 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 43: 4996–5008, 2005     

试探方程法及其在非线性发展方程中的应用

提出了一种比较系统的求解非线性发展方程精确解的新方法, 即试探方程法. 以一个带5阶 导数项的非线性发展方程为例, 利用试探方程法化成初等积分形式，再利用三阶多项式的完 全判别系统求解，由此求得的精确解包括有理函数型解, 孤波解, 三角函数型周期解, 多项 式型Jacobi椭圆函数周期解和分式型Jacobi椭圆函数周期解 关键词： 试探方程法 非线性发展方程 孤波解 Jacobi椭圆函数 周期解