非线性向量微分方程初值问题的奇摄动

今研究一阶非线性向量微分方程初值问题:εy′=f(t,y,ε),(1)y(0,ε)=A(ε),(2)其可ε>0为小参数.y=(y_1,y_2,…,y_n)为 n 维向量函数.Howes 等人研究了一类高阶非线性标量微分方程的奇摄动问题.对于二阶非线性向量微分方程的奇摄动,也在许多文献中不同程度地研究过(例如[2],[3]).本文是研究更广泛的一类一阶非线性向量微分方程的奇摄动,提供了构造相应初值问题(1),(2)解的任意次精度的渐近展开     

弱粘弹性材料结构振动特性分析的摄动解法

本文提出了“弱粘弹性”概念,用以描述弱时变材料的动态性能,并构造了弱粘弹性模型进行结构振动分析。根据“弱”的特点,选择了小参数,给出弱粘弹性材料动态性能的描述形式。在此基础上,构造了两种摄动解法,第一种基于弹性解,第二种基于单粘弹性模量解。文中还特别讨论了松驰函数为指数形式时的情形。     

求数列通项的两个途径

<正>求数列的通项在数列中是一个最重要的课题,07年高考十九份试卷中,一半以上均有直接求数列通项的题目,求通项的解题方法和技巧很多,但总的思路有两种:其一是找出α_n与α_n-1的关系求通项,其二是找出S_n与S_n-1的关系求S_n,再由α_n=S_n—S_n-1得通项.     

Procreating tiles of double commutative-step digraphs

Double commutative-step digraph generalizes the double-loop digraph. A double commutative-step digraph can be represented by an L-shaped tile, which periodically tessellates the plane. Given an initial tile L（l, h, x, y）, Aguil5 et al. define a discrete iteration L（p） = L（l ＋ 2p, h ＋ 2p, x ＋ p, y ＋ p）, p = 0, 1, 2,..., over L-shapes （equivalently over double commutative-step digraphs）, and obtain an orbit generated by L（l, h, x,y）, which is said to be a procreating k-tight tile if L（p）（p = 0, 1, 2, ~ ~ ~ ） are all k-tight tiles. They classify the set of L-shaped tiles by its behavior under the above-mentioned discrete dynamics and obtain some procreating tiles of double commutative-step digraphs. In this work, with an approach proposed by Li and Xu et al., we define some new discrete iteration over L-shapes and classify the set of tiles by the procreating condition. We also propose some approaches to find infinite families of realizable k-tight tiles starting from any realizable k-tight L-shaped tile L（l, h, x, y）, 0 ≤ y - x ≤ 2k ＋ 2. As an example, we present an infinite family of 3-tight optimal double-loop networks to illustrate our approaches.     

STEADY-STATE SOLUTIONS FOR A ONE-DIMENSIONAL NONISENTROPIC HYDRODYNAMIC MODEL WITH NON-CONSTANT LATTICE TEMPERATURE

A one-dimensional stationary nonisentropic hydrodynamic model for semiconductor devices with non-constant lattice temperature is studied. This model consists of the equations for the electron density, the electron current density and electron temperature, coupled with the Poisson equation of the electrostatic potential in a bounded interval supplemented with proper boundary conditions. The existence and uniqueness of a strong subsonic steady-state solution with positive particle density and positive temperature is established. The proof is based on the fixed-point arguments, the Stampacchia truncation methods, and the basic energy estimates.     

抛物方程时间周期问题的有限元多格子动力学迭代

本文我们研究线性周期抛物方程的有限元多格子动力学迭代.多格子动力学迭代又称多重网格波形松弛,它是在函数空间中的一种迭代过程.对于由加速技术得到的多格子动力学迭代算子,我们通过计算周期函数的Fourier系数给出了新的谱表达式.从这些有用的表达式出发,我们推导了时间连续和离散格式的迭代收敛条件.数值实验进一步验证了本文的理论结果.     

计算最小奇异组的一个精化调和 Lanczos双对角化方法

在很多实际应用中需要计算大规模矩阵的若干个最小奇异组.调和投影方法是计算内部特征对的常用方法,其原理可用于求解大规模奇异值分解问题.本文证明了,当投影空间足够好时,该方法得到的近似奇异值收敛,但近似奇异向量可能收敛很慢甚至不收敛.根据第二作者近年来提出的精化投影方法的原理,本文提出一种精化的调和Lanczos双对角化方法,证明了它的收敛性.然后将该方法与Sorensen提出的隐式重新启动技术相结合,开发出隐式重新启动的调和Lanczos双对角化算法(IRHLB)和隐式重新启动的精化调和Lanczos双对角化算法(IRRHLB).位移的合理选取是算法成功的关键之一,本文对精化算法提出了一种新的位移策略,称之为"精化调和位移".理论分析表明,精化调和位移比IRHLB中所用的调和位移要好,且可以廉价可靠地计算出来.数值实验表明,IRRHLB比IRHLB要显著优越,而且比目前常用的隐式重新启动的Lanczos双对角化方法(IRLB)和精化算法IRRLB更有效.     

不需加人工变量的两阶段法

A method is provided to achieve an initial basic feasible solution of a linear programming in this paper. This method dose not need introducing any artificial variable, but needs only solving an auxiliary linear programming. Compared with the traditional two-phase method, it has advantages of saving the memories and reducing the computational efforts.     

伴有边界条件摄动的向量二阶半线性奇摄动问题解的估计

本文利用微分不等式的不变域理论,研究当ε→0~ 时向量二阶半线性边值问题εy″=g(x,y,ε)=y,(0,ε),A(ε),y(1,ε)=B(ε)解的存在和渐近性质,得到了包括边界层在内的任意阶近似的一致有效的渐近解。