非光滑凸规划的割平面法及其在组合优化中的应用

本文利用次梯度构造了一种割平面 ,将非光滑凸规划松驰为光滑规划 ,给出了一种非光滑凸规划的割平面法 ,并证明了其收敛性 ,通过在组合优化中的应用说明该算法是有效的 .     

就“数轴”一节谈新教材的使用

新教材在编写上有很大改进已众所周知,但如何有效使用新教材却是急需探讨的问题。本文仅以“数轴”的第一课时为例,从两个方面谈谈笔者的看法。 1 新教材的特点和新旧教材的区别 1.1 “数轴”所处的地位和作用 “数轴”在有理数一章所处的地位很关键。从数形结合的角度出发,在理解有理数的概念、相反数和绝对值的概念,以及掌握比较有理效的大小方法,学习有理数的运算时,显得直观、方便,能使学生较顺     

基于可接受集的多维风险度量北大核心

在多维框架下提出了基于可接受集的两种风险度量概念,讨论了一些相应的性质,给出了这两种风险度量在满足一定条件下的表示定理.最后给出了几个实例.     

Analysis of radiometer effect on proof mass in purely gravitational orbit

Spacecrafts with the pure gravity environment are of great significance in precision navigation,gravity field measurement for celestial bodies,and basic physics experiments.The radiometer effect is one of the important interfering factors on the proof mass in a purely gravitational orbit.For the gravity field measurement system based on the inner-formation flying,the relationship between the radiometer effect on the innersatellite and the system parameters is studied by analytical and numerical methods.An approximate function of the radiometer effect suitable for the engineering computation and the correction factor are obtained.The analytic results show that the radiometer effect on the inner-satellite is proportional to the average pressure while inversely proportional to the average temperature in the outer-satellite cavity.The radiometer effect increases with the temperature difference in the cavity,and its minimum exists when the cavity radius increases.When the minimum of the radiometer effect arrives,the ratio of the cavity radius to the inner-satellite radius is 1.189 4.This constant is determined by the spherical cavity configuration and independent of the temperature and pressure distributions.When the ratio of the cavity radius to the inner-satellite radius is more than 10,it is believed that the cavity is large enough,the radiometer effect is approximately proportional to the square of the inner-satellite radius,and the influence of the outer-satellite cavity radius on the radiometer effect can be ignored.     

Cash subadditive risk measures for portfolio vectors

In this paper, from the viewpoint of the time value of money, we study the risk measures for portfolio vectors with discount factor. Cash subadditive risk measures for portfolio vectors are proposed. Representation results are given by two different methods which are convex analysis and enlarging space. Especially, the method of convex analysis make the line of reasoning and the representation result be simpler. Meanwhile, spot and forward risk measures for portfolio vectors are also introduced, and the relationships between them are investigated.     

中成药中马兜铃酸A的UPLC/MS研究

建立了中成药中马兜铃酸A的超高压液相色谱/质谱检测方法。测定结果表明,马兜铃酸A在超高压液相色谱/质谱的选择离子记录（SIR）中有较强的分子离子峰,检出限为0.1mg/kg,可以满足对中成药中马兜铃酸A测定要求。     

“席位分配问题的数学模型”的一个注解

对《数学的实践与认识》(2002年7月,第32卷,第四期)中的《席位分配问题的数学模型》一文作了注解,指出了一个错误之处.     

固相微萃取现场流动采样装置

为了满足固相微萃取（SPME）方法现场采样的要求，设计了一套流动采样装置，并采用直接萃取法来研究苯系物（BTEX）的萃取过程，以对该装置进行性能评估。结果表明：非平衡点流动采样方法的灵敏度与国家环保局规定的顶空法相当，BTEX的LOD值均在μg/L水平。该方法具有很好的精密度和准确度，BTEX的相对标准偏差均小于5％；加标回收率均在95．2％－100．9％之间。实际应用研究结果表明，这套流动采样装置可用于实际的现场采样测定。     

图的最大二等分问题的低秩可行方向算法

基于图的最大二等分问题的半定规划松弛模型,利用矩阵的低秩分解技巧,给出了该问题的半定规划松弛的一种低秩可行方向算法.在一定的条件下,证明了算法的收敛性.结合0.699随机扰动方法得到原问题的近似最优解.数值实验表明该方法能有效地求解图的最大二等分问题.     

最大割问题的二次规划方法

本文给出了最大割问题的二次规划算法。这种算法通过求解最大割问题的二次规划松弛给出了一种较好的界，然后用分支定界法得到了最大割问题的解。数值结果表明这种算法是非常有效的。