一类求解奇异延迟微分方程的两步连续Runge-Kutta方法的收敛性

本文给出了一类求解延迟落在当前积分步内延迟微分方程的两步连续Runge-Kutta方法。在一定条件下我们证明了方法收敛性,数值试验表明方法是有效的。     

符号几何规划的一种分解方法

针对符号几何规划提出了一种直接的分解方法,将难于求解的符号几何规划问题等价地转化为一个非线性程度很低的可分离规划,为寻求困难度高且规模较大的符号几何规划问题的求解提供了一种方法,特别是经此方法分解后的每个子问题均易于求解,最后给出了数值实例,验证了此方法的有效性．     

基于界面跟踪方法的汽蚀模型和算法的有效性验证

针对两相附着汽蚀流动机理,基于界面跟踪方法发展了新的汽蚀模型和算法。所发展的汽蚀模型和算法不仅考虑了液相／气相界面处的压力差,而且考虑了耦合Reynolds-Averaged Navier-Stokes方程求解技术得到的流场压力梯度信息来迭代计算附着汽蚀形状。采用具有试验数据的半球形头部圆柱体汽蚀绕流作为算例来验证所提出的汽蚀模型和算法的有效性。采用不同的网格数和松弛因子数值验证了发展的汽蚀模型和算法的有效性。三种汽蚀数下的数值计算结果得到的压力系数分布与试验数据完全吻合。结果表明所提出的汽蚀模型和算法能够准确模拟出汽蚀发生点和汽蚀长度。     

关于正定可对称化线性代数方程组的预对称正则化算法

1引言考虑线性代数方程组A_x=b,A∈R~(n×n)非奇异,x,b∈R~n(1)的求解．当系数矩阵是大型稀疏的正定可对称化矩阵,文[1,2]讨论了一类预对称共轭梯度算法(LRSCG算法是其中之一),这类算法的实质是利用非对称的系数矩阵可对称化的性质,并结合共轭梯度法而构造的一种预处理的共轭梯度法[12,16,17]．但非对称的系数     

Hyperbolic-parabolic singular perturbation for quasilinear equations of Kirchhoff type

We consider a hyperbolic-parabolic singular perturbation problem for a quasilinear equation of Kirchhoff type, and obtain parameter-dependent time decay estimates of the difference between the solutions of a quasilinear dissipative hyperbolic equation of Kirchhoff type and the corresponding quasilinear parabolic equation. For this purpose we show time decay estimates for hyperbolic-parabolic singular perturbation problem for linear equations with a time-dependent coefficient.     

各向异性接合材料界面端部场数值分析

为了求解各向异性接合材料界面端部奇异性应力场,建立了一种新型杂交元模型.该模型的独特之处在于:基于有限元特征法得到的奇异性场数值特征解建立了一种新型界面端奇异单元.通过算例证明,新型杂交元模型能够利用较少的单元数获得较为精确的数值结果.当前模型应用范围广泛,能够用于复杂结构的界面端部场求解.     

A fiberwise analogue of the Borsuk-Ulam theorem for sphere bundles over a 2-cell complex II

We describe a finite complex B as I-trivial if there does not exist a Z₂-map from Si−1 to S(α) for any vector bundle α over B and any integer i with i>dimα. We prove that the m-fold suspension of projective plane FP² is I-trivial if and only if m≠0,2,4 for F=C, m≠0,4 for F=H. In the case where F is the Cayley algebra, the m-fold suspension is shown to be I-trivial for every m>0.     

Recent studies on phosphorus-bridging carbonyl derivatives: organophosphorus analogs of aldehydes and ketones

Reactions of disodium tetracarbonylferrate, Na₂Fe(CO)₄, with sterically hindered dialkylaminodichlorophosphines, R₂NPCl₂ (R₂N=diisopropylamino, dicyclohexylamino, and 2,2, 6, 6-tetramethylpiperidino) in diethyl ether lead to the air-stable phosphorus-bridging carbonyl derivatives (R₂NP)₂COFe₂(CO)₆ as the major products. The phosphorus-bridging carbonyl group in (i-Pr₂NP)₂COFe₂(CO)₆ has been found to undergo the following types of reactions: 1)Reduction, 2)Acylation, 3)Extrusion of the carbonyl group. The mechanisms of the reactions have been considered.This work was presented at the Workshop «The Modern Problems of Heteroorganic Chemistry» held on the ship «Nikolai Bauman» during the period May 8–13, 1993.Translated fromIzvestiya Akademii Nauk. Seriya Khimicheskaya, No. 11, pp. 1858–1867, November, 1993.