凸集的广义Reuleaux三角形

常宽凸集的面积最小者为Reulaux三角形，而非常宽凸集的面积最小者为何呢？它就是本文将给出的广义Reuleaux三角形△R。     

矩阵方程（A^TXA，B^TXB=（C，D）的反对称解及其最佳逼近

本利用矩阵对的标准相关分解，得到了矩阵方程(A^TXB，B^TXB)=(C，D)反对称解存在的充分必要条件及通解表达式，同时给出了解关于已知矩阵的最佳逼近．     

Effects of barium on the nonlinear electrical characteristics and dielectric properties of SnO2-based varistors

The effects of barium on electrical and dielectric properties of the SnO_2·Co_2O_3·Ta_2O_5 varistor system sintered at 1250℃ for 60min were investigated. It is found that barium significantly improves the nonlinear properties. The breakdown electrical field increases from 378.0 to 2834.5V/mm, relative dielectric constant (at 1kHz) falls from 1206 to 161 and the resistivity (at 1kHz) rises from 60.3 to 1146.5kΩ·cm with an increase of BaCO_3 concentration from 0mol% to 1.00mol%. The sample with 1.00mol% barium has the best nonlinear electrical property and the highest nonlinear coefficient (α=29.2). A modified defect barrier model is introduced to illustrate the grain-boundary barrier formation of barium-doped SnO_{2}-based varistors.     

The influence of hard‐segments on two‐phase structure and shape memory properties of PCL‐based segmented polyurethanes

Poly(ε‐caprolactone)‐based segmented polyurethanes (PCLUs) were prepared from poly(ε‐caprolactone) diol, diisocyanates (DI), and 1,4‐butanediol. The DIs used were 4,4′‐diphenylmethane diisocyanate (MDI), 2,4‐toluenediisocyanate (TDI), isophorone diisocyanate (IPDI), and hexamethylene diisocyanate (HDI). Differential scanning calorimetry, small‐angle X‐ray scattering, and dynamic mechanical analysis were employed to characterize the two‐phase structures of all PCLUs. It was found that HDI‐ and MDI‐based PCLUs had higher degree of microphase separation than did IPDI‐ and TDI‐based PCLUs, which was primarily due to the crystallization of HDI‐ and MDI‐based hard‐segments. As a result, the HDI‐based PCLU exhibited the highest recovery force up to 6 MPa and slowest stress relaxation with increasing temperature. Besides, it was found that the partial damage in hard‐segment domains during the sample deformation was responsible for the incomplete shape‐recovery of PCLUs after the first deformation, but the damage did not develop during the subsequent deformation. © 2007 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 45: 557–570, 2007     

CreditRisk+模型下商业银行经济资本配置研究

对金融资产风险的度量与经济资本的分配应该体现分散化效应,传统的V aR方式不能保证分散化效应的次可加性.本文讨论了基于T a ilV aR这一新的风险度量与经济资本分配标准,并在违约率均值不变情况下,对C red itR isk+模型下的商业银行经济资本分配进行了实证分析.     

Experimental 511 W Composite Nd：YAG Ceramic Laser

We demonstrate a 511 W laser diode pumped composite Nd：YAG ceramic laser. The optical pumping system is consisted of five laser diode stacked arrays arranged in a pentagonal shape around the ceramic rod whose size is φ6.35×144mm. When the pumping power is 1600 W, the cw laser output up to 511 W at 1064nm can be obtained with a linear piano-piano cavity, and the optical-to-optical efficiency is 31.9%. To our knowledge, this is the highest value of laser output by using a newly invented composite Nd：YAG ceramic rod as the gain medium.     

Robust H∞ control for linear Markovian jump systems with unknown nonlinearities

This paper studies the problem of stochastic stability and disturbance attenuation for a class of linear continuous-time uncertain systems with Markovian jumping parameters. The uncertainties are assumed to be nonlinear and state, control and external disturbance dependent. A sufficient condition is provided to solve the above problem. An H_∞ controller is designed such that the resulting closed-loop system is stochastically stable and has a disturbance attenuation γ for all admissible uncertainties. It is shown that the control law is in terms of the solutions of a set of coupled Riccati inequalities. A numerical example is included to demonstrate the potential of the proposed technique.     

激光相干阵列探测中的二元全息光栅

从外差阵列探测出发，围绕木振光束整形问题，就计算全息位相光栅在激光相干雷达系统中的应用进行了理论及实施方面的研究，得出较好的结果。     

氢化丁苯共聚物结构的核磁共振波谱表征Ⅰ.13C谱带的归属

本文分别用JEOL FX-90Q和Bruker AM-300波谱仪测定了氢化聚丁二烯和氢化丁苯共聚物的¹H,¹³C-NMR谱,得到了分辨率较高的谱图和新的结构信息。借助DEPT技术确定了各谱带的CH或CH₂类型。利用Grant-Paul和Lindeman-Adams介绍的化学位移经验计算公式,考虑苯基对α、β和γ碳原子的影响,计算了各种三单元序列中有关碳原子的化学位移。对脂肪碳部分的28组谱带重新进行了归属。化学位移计算值与实测值基本相符,并得到了不同组成的模型聚合物¹³C-NMR谱的各谱带强度变化规律的验证。     

Mean Value on the Difference Between a Quadratic Residue and Its Inverse Modulo p

The main purpose of this paper is to use the generalized Bernoulli numbers, Gauss sums and the mean value theorems of Dirichlet L-functions between a quadratic residue and its inverse modulo p value formula. to study the asymptotic property of the difference （a prime）, and to give an interesting hybrid mean