On an Inverse Free Steffensen-Type Method for the Approximation of Stiff Differential Equations

In this article, an inverse free Steffensen-type method is introduced. The method is applied to approximate the systems of equations associated to implicit schemes approximating a stiff differential equation. The method has quadratic convergence without evaluating neither any derivative nor inverse operator. Finally, hypotheses ensuring the semilocal convergence and the R-order of convergence are presented.     

关于Bernoulli数的同余性质

本文的主要目的是利用Ｂｅｒｎｏｕｌｉ数的递推公式，研究Ｂｅｒｎｏｕｌｉ数的同余性质，给出几个有趣的同余公式     

线性递推序列的幂

本文对a1,…,am∈c,am≠0和满足递推关系un=a1un-1 … a mun-m, n≥m,的序列{un}∞n=0给出递推关系ukn=b1uk/n-1 … bmuk/m-m, n≥m的系数b1,…bm的递推公式,其中k∈z,m=[m k-1/k].     

矩阵乘幂的一种显式公式

本文给出用线性Ｄｉｏｐｈａｎｔｕｓ方程的解计算矩阵乘幂的显式公式，并给出常系数联立线性递推关系组的解的显式表达式。     

一类红灯环境下随机游动的保守集和正常返性

设随机环境→ξ={ξn,n=…,-1,0,1,…}为某类平稳遍历,具有红灯的Markov-链,就该双无限环境下的随机游动{Xn}n∈z ,给出相应Markov-双链{ηn}n∈z ={(Xn,T→ξ)}n∈z 的保守集,并讨论在该平稳遍历环境→ξ下,{Xn}n∈z 的常返和正常返性.     

Recurrence of the integral of an odd conditionally periodic function

We prove that the integral of a sufficiently smooth odd conditionally periodic function with zero mean and incommensurable frequencies recurs. Furthermore, we obtain the lower and upper bounds for smoothness guaranteeing the recurrence of the integral. Translated fromMatematicheskie Zametki, Vol. 61, No. 4, pp. 570–577, April, 1997. Translated by N. K. Kulman     

Some explicit formulas for the polynomial decomposition of the matrix exponential and applications

This paper is devoted to the study of some formulas for polynomial decomposition of the exponential of a square matrix A. More precisely, we suppose that the minimal polynomial M_A(X) of A is known and has degree m. Therefore, e^tA is given in terms of P₀(A),…,P_m−1(A), where the P_j(A) are polynomials in A of degree less than m, and some explicit analytic functions. Examples and applications are given. In particular, the two cases m=5 and m=6 are considered.     

舰船运动预报模型算法及软件

本文根据仿真模型的现代建模理论与方法 ,采用 AR(p )模型参数法 ,用模型参数的递推算法 ,对舰船运动状态的四个指标进行估计、预报和修正 ,并给出程序流程图和部分结果