N维欧氏空间曲线的曲率公式

给出了Ｎ维欧氏空间一般参数形式的曲线的曲率公式的一种简洁形式，同时给出了详细的推导和证明过程。     

RELIABILITY ASSESSMENT OF STRUCTURAL SYSTEMS BASED ON DIRECTIONAL VECTOR SIMULATION TECHNIQUE

The new improved directional vector simulation method for analyzing the reliability of structural systems failure probability is researched. This paper also points out the defects of general directional vector simulation, and gives rise to a new higher accuracy approximate integral formula of structural systems failure probability. A new geometric meaning of characteristic function is obtained. A new simple method of generating uniformly distributed random vector samples inn-dimensional unit hyper-spherical surface is put forward and strictly proved. This method is easy to put into practice. Numerical examples are given to show the applicability and effectiveness of the suggested approach to structural systems reliability problems. Supported by Chinese Postdoctor Fund([1998]6, 23).     

不动点集为∪from(i=1) to r(RP(1))~(m_i)×(CP(1))~(s_i)的对合

不动点集为∪ｒｉ＝１（ＲＰ（１））ｍｉ×（ＣＰ（１））ｓｉ的对合马凯刘宗泽（河北师范大学数学系，０５００１６，石家庄；第一作者２８岁，男，博士生）关键词协边；对合；吴公式分类号Ｏ１８９．２１９９３年，文献［１］作者讨论了对合的不动点集为（ＲＰ（１）...     

Holomorphic Lefschetz Fixed Point Formula for Non-compact K(a)hler Manifolds

The authors obtain a holomorphic Lefschetz fixed point formula for certain non-compact "hyperbolic" K(a)hler manifolds (e.g. K(a)hler hyperbolic manifolds, bounded domains of holomorphy) by using the Bergman kernel. This result generalizes the early work of Donnelly and Fefferman.     

带Markov调制的随机微分延迟方程的稳定性

本文采用了一例特定的Lyapunov函数,来研究带Markov调制的随机微分延迟方程的p阶指数稳定性,并对其几乎必然指数稳定性也进行了探讨.     

Convergence of the Magnus Series

The Magnus series is an infinite series which arises in the study of linear ordinary differential equations. If the series converges, then the matrix exponential of the sum equals the fundamental solution of the differential equation. The question considered in this paper is: When does the series converge? The main result establishes a sufficient condition for convergence, which improves on several earlier results.     

Hermite四点插指公式

文章利用Hermite插值基函数,将求解Hermite四点插指问题转换为求解8个派生出来的多项式插值问题,证明了Hermite四点插指公式的存在唯一性,并用两种方法构造出Hermite四点插指公式,最后给出了一个算例.     

Estimates of a certain sum involving coefficients of cusp forms in weight and level aspects

We consider the sum of coefficients which are in the Dirichlet series expansion of symmetric square L-functions. In this paper, we obtain two estimates of this sum in weight and level aspects. These imply two estimates of the sum of the n ²th Fourier coefficients of cusp forms.     

A novel method for nonlinear fractional partial differential equations: Combination of DTM and generalized Taylor's formula

In this article, a novel numerical method is proposed for nonlinear partial differential equations with space- and time-fractional derivatives. This method is based on the two-dimensional differential transform method (DTM) and generalized Taylor's formula. The fractional derivatives are considered in the Caputo sense. Several illustrative examples are given to demonstrate the effectiveness of the present method. Results obtained using the scheme presented here agree well with the analytical solutions and the numerical results presented elsewhere. Results also show that the numerical scheme is very effective and convenient for solving nonlinear partial differential equations of fractional order.     

A Fourier spectral-discontinuous Galerkin method for time-dependent 3-D Schrödinger–Poisson equations with discontinuous potentials

In this paper, we propose a high order Fourier spectral-discontinuous Galerkin method for time-dependent Schrödinger–Poisson equations in 3-D spaces. The Fourier spectral Galerkin method is used for the two periodic transverse directions and a high order discontinuous Galerkin method for the longitudinal propagation direction. Such a combination results in a diagonal form for the differential operators along the transverse directions and a flexible method to handle the discontinuous potentials present in quantum heterojunction and supperlattice structures. As the derivative matrices are required for various time integration schemes such as the exponential time differencing and Crank Nicholson methods, explicit derivative matrices of the discontinuous Galerkin method of various orders are derived. Numerical results, using the proposed method with various time integration schemes, are provided to validate the method.