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。     

基于超素数的托普利兹观测矩阵构造方法

观测矩阵在信号压缩感知中十分重要,直接决定信号的重构质量。为保证信号的重构精度,要求观测矩阵具有很强的随机性,但随机矩阵硬件实现非常困难;确定性观测矩阵易于实现,但其重构精度不足。针对观测矩阵对随机性与确定性的双重要求,提出利用超素数产生超长周期的伪随机序列,解决确定性观测矩阵对随机性的要求;结合托普利兹观测矩阵的确定性结构特征,得到一种改进的托普利兹观测矩阵。实验仿真表明:改进的托普利兹观测矩阵与高斯随机观测矩阵和常用托普利兹观测矩阵相比,其信号重构精度得到了很好的改善,且易于硬件实现。     

基于行列式随机循环的压缩感知测量矩阵研究

压缩感知理论,从信号的自身特性出发,通过变换作用域和线性投影实现对信号的采样和压缩。测量矩阵是该理论中获得最优测量,实现精确重构的关键。本文在介绍常用测量矩阵的基础上,重点研究了结构化测量矩阵。鉴于测量矩阵设计的最重要的原则是降低矩阵元素间的相干性,本文借鉴循环矩阵和广义轮换矩阵的优点,提出了采用均匀随机数对结构化测量矩阵进行随机循环的构造方法。仿真实验表明新矩阵在信号重建上具有更好的性能。     

A new version of Kovarik’s approximate orthogonalization algorithm without matrix inversion

In 1970 Kovarik proposed approximate orthogonalization algorithms. One of them (algorithm B) has quadratic convergence but requires at each iteration the inversion of a matrix of similar dimension to the initial one. An attempt to overcome this difficulty was made by replacing the inverse with a finite Neumann series expansion involving the original matrix and its adjoint. Unfortunately, this new algorithm loses the quadratic convergence and requires a large number of terms in the Neumann series which results in a dramatic increase in the computational effort per iteration. In this paper we propose a much simpler algorithm which, by using only the first two terms in a different series expansion, gives us the desired result with linear convergence. Systematic numerical experiments for collocation and Toeplitz matrices are also described.     

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.     

一类Toeplitz矩阵的平方根

给出了一类上三角Toeplitz矩阵的平方根的新的性质定理,还给出了求其平方根的迭代公式,数值例子验证了迭代公式的正确性.