等截面连续受压直杆临界荷载的求解

利用材料力学、常微分方程及行列式知识,求解了连续受压杆率曲微分方程,计算了不同长度组合受压杆的整体临界荷载及计算长度系数,与钢结构设计中所采用的计算长度系数进行了对比分析。     

论组合数行列式

组合数是基础数的概念,被普遍的使用.由组合数构成的行列式具有特色.本文研究了组合数行列式的独特、奇妙的性质,并给出了严密的证明。     

油井管特殊扣产品拧接的自动判定法

在油井管特殊扣产品的加工过程中,拧接是一个重要工序,而拧接设备是否具有自动判定的功能,自动判定方法合适与否,都会对生产节奏和质量控制产生影响。本文介绍了一种自动判定的方法,通过对拐点的扭矩数值、圈数的判断,再加上一些防错手段,实现对特殊扣拧接曲线的自动判定。     

我国商业保险需求决定因素分析

本文结合我国商业保险市场的发展情况,在1985~1999年的数据基础上,借助于多元回归方法,对我国商业保险需求的决定因素进行了尝试性的分析, 并讨论了影响我国商业保险需求的其他因素。     

Formation control using range-only measurements

This paper proposes algorithms to coordinate a formation of mobile agents when the agents are not able to measure the relative positions of their neighbors, but only the distances to their respective neighbors. In this sense, less information is available to agents than is normally assumed in formation stabilization or station keeping problems. To control the shape of the formation, the solution advanced in the paper involves subsets of non-neighbor agents cyclically localizing the relative positions of their respective neighbor agents while these are held stationary, and then moving to reduce the value of a cost function which is nonnegative and assumes the zero value precisely when the formation has correct distances. The movement schedule is obtained by a novel vertex-coloring algorithm whose computation time is linear in the number of agents when implemented on the graphs of minimally rigid formations. Since in some formations, it may be that an agent is never allowed to be stationary (e.g. it is a fixed-wing aircraft), or because formations may be required to move as a whole in a certain direction, the results are extended to allow for cyclic localization of agents in this case. The tool used is the Cayley–Menger determinant.     

Eigenvectors of tridiagonal matrices of Sylvester type

Eigenvectors of the tridiagonal matrices of Sylvester type are explicitly determined. These are closely related to orthogonal polynomials named after Krawtchouk, (dual) Hahn and Racah as well as to q-Racah polynomials.      

一类n阶实方阵行列式的几何意义探究

在对一类n阶实方阵行列式D(n)的几何意义 ,进行由三维到n维欧氏空间En 上n维向量的推广 ,建立了D(n)与n - 1阶实方阵行列式 |An -1|之间的关系 ,提供了二者相互转化的方法 ,并对二者作了对比 ,最后给出了若干结论     

Euler 公式的新证明

数学家Euler创立了许多著名的数学公式，不少后人用不同的工具来证明这些公式．本文利用二重积分公式，幂级数在收敛区问内的收敛性质、一致收敛性质及可逐项积分的性质来证明Euler公式。     

On the methods to derive frequency equations of beams carrying multiple masses

Two commonly used methods to generate the eigenfrequency equation of a beam carrying multiple concentrated masses at an arbitrary location are of main concern in this paper. Both the methods of frequency determinant and the method of Laplace transform are considered and compared here for the effectiveness of each derivation for the frequency equation of the same system. The dimensionless frequency equation for a clamped–clamped beam carrying two different masses is obtained for comparison. The computational times to generate the same expression by using the two methods are noted. It is found that the processing and computational time by using the Laplace transform is longer although the resultant system equations are often claimed to be more compact than those by the method of frequency determinant.