球面空间中的Pedoe不等式与张-杨不等式及应用

本文应用距离几何的理论与方法,研究了n维球面空间中n维单形与有限点集的几何不等式问题,建立了球面空间中n维单形一种形式的Pedoe不等式与有限点集一种形式的张-杨不等式,并应用它获得n维球面空间中Veljan-Korchmaros型不等式与Finsler-Hadwinger型不等式.     

Solving a multiobjective traveling salesman problem by dynamic programming

In this paper Klötzler's method of multiobjective dynamic programming is applied to the solution of a two-dimensional traveling salesman problem. In this way Bellman's and Held/Karp's dynamic programming approach to one-dimensional traveling salesman problems is extended to the multiobjective case.     

Improved asymptotic analysis of the average number of steps performed by the self-dual simplex algorithm

In this paper we analyze the average number of steps performed by the self-dual simplex algorithm for linear programming, under the probabilistic model of spherical symmetry. The model was proposed by Smale. Consider a problem ofn variables withm constraints. Smale established that for every number of constraintsm, there is a constantc(m) such that the number of pivot steps of the self-dual algorithm,(m, n), is less thanc(m)(lnn) ^m(m+1) . We improve upon this estimate by showing that(m, n) is bounded by a function ofm only. The symmetry of the function inm andn implies that(m, n) is in fact bounded by a function of the smaller ofm andn. Parts of this research were done while the author was visiting Stanford University, XEROX- PARC, Carnegie-Mellon University and Northwestern University and was supported in part by the National Science Foundation under Grants MCS-8300984, ECS-8218181 and ECS-8121741.     

基于数字非线性锁相环的相干态相位估计

基于量子理论获取相位参数的导航机制,理论上可以突破经典物理极限对导航精度的限制.利用量子零拍探测对相干态光场相位进行测量时,通常需要相位与之正交的本振光才能使测量精度达到量子标准极限.由于导航信号相位的高非线性特点,想要利用传统的线性锁相环获取完全满足条件的本振光具有一定的难度.为此,本文设计了一种基于容积准则的非线性锁相环,实现了在非正交本振光的条件下对相干态相位进行精确测量的功能.首先,利用相干态的Wigner函数推导了其相位在量子零拍探测的输出结果,设计了量子相位估计的非线性数字锁相环框架.然后基于正交单纯形容积准则设计了非线性滤波算法实现锁相环功能,该锁相环通过对本振相位进行多次状态更新,最终实现非线性迭代估计.实验结果表明,本文方法突破了本振光相位需与相干态相位正交的局限性,避免了传统量子锁相环方法引入的线性化误差,实现了对相干态相位的准确、稳定估计.     

线性规划问题的规范型算法

提出了线性规划问题的两种规范标准形式;证明了任意一个线性规划问题都可化为这两种形式之一;给出了不需引入人工变量的线性规划问题的求解算法。     

可变误差多面体法同时测定复方新诺明中二组分的含量

以可变误差多面体法处理多波长吸光光度数据同时测定了复方新诺明制剂模样和五个批号实际样品中磺胺甲恶唑（ＳＭＺ）,甲氧苯氨嘧啶（ＴＭＰ）的含量,１１份模拟样中ＳＭＺ、ＴＭＰ的回收率分别为９９．８％和１００．３％,复方新诺明片和注射液的测定结果与药典方法一致。     

En 中n维单形二面角的角平分面的性质

利用距离几何的理论与方法研究了En中n维单形内二面角与外二面角的角平分面的性质,获得了n维单形内二面角与外二面角平分面的2个定理.     

单纯形算法动态优化毛细管胶束电动色谱分离体系

采用控制加权可变步长单纯形算法对ＰＴＣ氨基酸的毛细管胶束电动色谱分离体系进行动态优化。寻优过程中同时考虑背景电解质的ｐＨ值、十二烷基硫酸钠浓度和有机添加剂浓度对体系分离效果的影响。分别使用Ｌｏｎｇ系数法和均匀设计表法确定初始单纯形顶点对分离体系进行动态优化。优化结果使１７种ＰＴＣ氨基酸获得了比较满意的分离。     

Inequalities for Edge Lengths and Volumes of Two Simplexes

In this paper, a class of geometric inequalities for the edge lengths and volumes of two n-dimensional simplexes are established. As a corollary, a generalization to several dimensions of the Neuberg–Pedoe inequality is given.