Reversed-phase high-performance liquid chromatographic separation of epimeric alkaloid N-oxides from Thalictrum simplex L.

A simple and precise method was developed for the analytical and preparative reversed-phase HPLC separation of a mixture of epimeric pavine N-oxides containing 49.1% of (−)-thalimonine N-oxide A and 50.1% of (−)-thalimonine N-oxide B isolated from Thalictrum simplex L. (Ranunculaceae). A reversed-phase system with Nucleosil C₁₈ analytical and preparative columns and ethanol-1.5% aqueous orthophosphoric acid (15:85) as the mobile phase was used. The epimeric pavine N-oxides were completely separated within 50 min.     

A computational framework for the form-finding and design of tensegrity structures

A new computational framework is proposed for the form-finding and design of tensegrity structures with or without super-stability. The form-finding of tensegrities is formulated as two unconstrained minimisation problems where their objective functions are defined based on eigenvalues of a modified force density matrix. The Nelder–Mead simplex method is then used to solve the minimisation problems. Furthermore, another efficient method is suggested for the interactive form-finding and design of tensegrities with geometrical and force constraints. Examples of the form-finding of tensegrities are presented and the results obtained are compared and contrasted with those analytical results documented in the literature, to verify the accuracy and efficiency of the developed methods.     

Two Special Simply Connected Spaces of Nonpositive Curvature

We construct two examples of spaces homeomorphic to R ⁿ (n3) each of which has a closed geodesic and admits no isoperimetric inequality. The first is a complete polyhedral metric space of nonpositive curvature, and the second is an incomplete Riemannian space with nonpositive sectional curvatures.     

从极优基未必能迅达最优基：兼与文献[1]作者商榷

本对献[1]提出的“求解线性规划的快速换基迭代法”从多阶段决策的观点阐述并举证了从极优基未必能快速到达最优基的论断。旨在说明用此方法求解一般线性规划问题时不一定能实现快速换基迭代的概念。     

求线性规划问题可行基的一种方法

文章给出了一般情形下从线性规划问题的标准型求可行基的一种方法，并通过与大Ｍ法、两阶段法及文［１］方法进行对比分析，说明这是一种有效可行且有可能较简便的方法     

线性规划的σj迭代计算方法

本提出并证明了求解线性规划（LP）的单纯形法中检验数（σj）的迭代计算方法的定理，由此定理得到的迭代计算方法比传统的按定义式计算法的渐近时间复杂度降了一级，同时简化了计算过程并提高了计算效率。     

多维随机变量的线性相关性

本文研究了n维随机变量分量间的线性相关性,给出了衡量线性相关性程度的量以及具有(在概率1意义下)严格线性关系的充分必要条件.     

关于n维单形的两个轨迹定理

在n维欧氏空间En中,应用向量方法,给出了关于n维单形的两个优美的轨迹定理.