样条扇形单元

本文在样条分片插值及样条矩形单元的基础之上进而讨论极坐标中二次及三次样条分片插值及样条(圆环)扇形单元.以用于求解圆(环)域与(圆环)扇形域上的各类问题.圆环扇形单元(r≠0)是样条分片插值在极坐标中简单的推广应用,但扇形单元则不然.本文根据扇形单元在r=0处的特殊性对各位移插值函数作了合理的处理,使得该单元即体现了r=0处的几何特性又可以消除该处应变、应力的奇异性.文中给出了用样条(圆环)扇形单元求解平面问题及薄板弯曲问题的数值算例用以说明该单元的效能.     

基于共轭几何变换程序的国债市场利率期限结构波动建模

本文变革已有的利率期限结构模型估计依赖于定价误差平方和最小化原则,引入几何双重变换程序解决非线性约束的误差绝对距离最小化问题,丰富国债市场利率波动和定价研究的理论体系和研究方法;运用负指数平滑立方L₁样条优化模型,克服B样条函数对节点数目与定位的过度敏感和放宽对贴现函数的二阶导数平滑要求,协同拟合误差绝对距离与贴现函数波动率最小化,保留B样条函数刻画中长期利率波动趋势的优势,增强对短期利率波动结构突变的估计、定价和预测能力,缓解B样条和NSS模型在利率期限结构拟合存在的过度波动问题。     

四边简支正交异性板双向压屈模态的确定及其临界载荷的显式表达式

Libove曾经证明[1],四边简支的正交异性板在双向压力下的屈曲模态沿x方向和y方向的半波数m和n这两者中必有一者为1.本文将给出m=1或n=1的条件,并确定n=1时m的取值,及m=1时n的取值.从而完全确定了四边简支正交异性板在双向压力下的屈曲模态,并给出了临界载荷的显式表达式.     

三维热传导方程的一族两层显式格式

提出了一族三维热传导方程的两层显式差分格式,当截断误差阶为O(Δt+(Δx)2)时,稳定性条件为网格比r=Δt/(Δx)2=Δt/(Δy)2=Δt/(Δz)2≤1/2,优于其他显式差分格式。而当截断误差阶为O((Δt)2+(Δx)4)时,稳定性条件为r≤1/6,包含了已有的结果。     

奇异摄动边值问题的渐近展开

本文研究了奇异摄动边值问题:εy"=f(t,y,ε),y(0)=ξ(ε),y(1)=η(ε),其中ε是一个正小参数.在条件f_y(0,y,0)≥m₀(>0),f_y(1,y,0)≥m₀和f_y(t,y,ε)≥0之下.我们证明了解的存在唯一性,并给出了解的一致有效渐近展开式,从而改进了已有的结果.     

常差分方程奇异摄动问题的渐近方法

在本文中,我们讨论如下差分方程问题(P_ε):(L.y)_k≡εy(k+1)+a(k,ε)y(k)+b(k,ε)y(k-1)=f(k,ε)(1≤k≤N-1)B₁y≡-y(0)+c₁y(1)=a,B₂y≡-c₂y(N-1)+y(N)=β这里ε是一个小参数,c₁,c₂,a,β为常数,a(k,ε),b(k,ε),f(k,ε)(1≤k≤N)是k和ε的函数.首先,我们讨论了常系数的情形;接着引进伸长变换对变系数的情形进行了讨论,给出了解的一致渐近展开式;最后给出了一个数值例子.     

非水平分层区域Helmholtz边值问题的解析解

在(x,y,z)直角坐标系中,N个物性参数不同的区域D_j(j=0,1,…,N-1)充斥着整个空间,这些区域间的分界面是非水平的光滑曲面S_j,j+1下面的边值问题称为非水平分层区域Helmholtz边值问题:
?2H(j)+K_jH(j)=0(j=0,1,…,N-1)
(H(0)-H(1))S_0.1=δ(S)(δ(S):广义δ-函数)
(H(j)-H(j+1))S_j,j+1=0(j=1,…,N-2)本文给出了此问题的解析解.     

三维抛物型方程的一族高精度分支稳定显格式

构造了一族解三维抛物型方程的高精度显格式,其稳定性条件为r=Δt/Δx2=Δt/Δy2=Δt/Δz2<1/2,截断误差为O(Δt2+Δx4).     

Banach空间中含强增生算子的非线性方程的迭代解

设X为实Banach空间,X*为其一致凸的共轭空间.设T:X→X为Lipschitzian强增生映象,L≥1为其Lipschitzian常数,k∈(0,1)为其强增生常数.设{α_n},{β_n}为[0,1]中的两个实数列满足:(ⅰ)α_n→0(n→∞);(ⅱ)β_n<L(1+L)/k(1-k)(n≥0);(ⅲ).假设为X中两序列满足:=o(β_n)与μ_n→0(n→∞).任取x₀∈X,则由(IS)1x_n+1=(1-α_n)x_n+α_nSy_n+u_ny_n=(1-β_n)x_n+β_nSx_n+μ_n(_n≥0){所定义的迭代序列{x_n强收敛于方程T     

正则变换的一种群表示

经典力学中的哈密顿正则变换所涉及的4个母函数F₁(q,Q),F₂(q,P),F₃(p,P),F₄(p,Q)和4种正则变量q,p,Q,P之间所有的关系,可以由7个基本关系式经线性变换而得到,这些变换是勒让德变换,变换是由32个8×8的变换矩阵来实现的,而这32个矩阵以4:1的关系与具有8个群元的D₄点群同态。热力学中的4个状态函数G(P,T),H(P,S),U(V,S),F(V,T)和4个热力学变量P,V,T,S之间的变换关系恰好与正则变换关系相同。热力学状态方程是源于宏观测量的实验结果的概括,而哈密顿正则变换是经典力学的理论性总结,它们的群表示是相同的,即它们的数学结构是相同的, 这种共性表明热力学变换是一维哈密顿正则变换的实例。     

一个分段线性Hénon映射吸引集合的结构

本文采用对偶线映射的方法分析了分段线性Hénon映射(x,y)→(1-a|x|+by,x),a=8/5,b=9/25吸引集的详细结构.设A和B分别是映射在第一和第三象限内的不动鞍点,本文说明:(1)映射的吸引集是B的不稳定流形U_B的闭包ū_B,而A的不稳定流形U_A则是ū_B的一个子集;(2)吸引盆是A的稳定流形S_A的闭包S_A,其边界是B的稳定流形S_B,而S_B在A_A的极限集之内.文中还给出周期鞍点不稳定流形和不动鞍点不稳定流形之间的关系.文中的符号动力学记号可用以研究各个不变流形每段的动态以及各同宿点、异宿点的动态.     

变热特性参数条件下肋片温度周期性变化的传热研究*

本文研究了变热特性参数下,根部温度作周期性变化的肋片传热情况.应用摄动法求解控制微分方程;并且采用打靶法和叠加原理进行数值计算,求解过程是嵌进的、非迭代的.对某种形状的肋片而言,当肋片根部温度作周期性变化时,其传热过程受以下几个参数的影响:E──导热系数的温度系数;N──肋片传热的特性参数;ε──温度波动的幅度参数;B──温度波动的频率;以及对流系数的变化模式等.文中给出了这些参数变化时对肋片的温度分布及热流率、肋效率等的影响情况.所得结果,不但具有理论价值,而且对工程设计也有现实指导意义.     

在共振点的一阶微分系统的周期解

考虑具偏差变元的一阶非线性微分系统:x>(t)=Bx(t)+F(x(t-τ))+p(t),其中,x(t)∈R2,τ∈R,B∈R2×2,F是有界的,p(t)是连续的2π-周期函数.应用Brouwer度及Mawhin重合度理论,在共振的情况下,给出了上述方程存在2π-周期解的充分条件及其在Duffing方程上的应用.     

查甫雷金方程的唯一性定理(Ⅰ)

<正>考虑下列混合型议程的唯一性问题 K(y)u_(xx)+u_(yy)=0 (K(0)=0;当y≠0时,■(1) 所考慮的區域D由三條曲綾圍成.其一是雙曲區域(y<0)中由原點引出的特徵线Γ_1,它滿足下面條件     

The brauer group and ramified double covers of surfaces

Let Z be a nonsingular plane curve of even degree and U = P ² — Z. Let : X —> P ² be tbe double cover ramified over Z and V = ^—1(U). It is shown that the kernel of the restriction map on Brauer groups^" : B(U) —> B(V), is isomorphic to Z/2(²) where ρ— 2 < r <ρ— 1, p being the Picard number of X and if ^" : Pic P² —> Pic X is an isomorphism, exactly half of the algebra classes of order 2 in B(X) are restrictions of algebra classes of order 2 in B(U) whose ramification has been split by V. The kernel of the corestriction map 2 B(V) — ₂B(U) is shown to be the subgroup consisting of elements fixed by the Galois group.     

典型域的调和函数论(Ⅲ)——斜对称方阵双曲空间的调和函数

<正> 3.1.斜对称方阵双曲空间的调和函数 命 Z 代表 n×n 斜对称方阵(?)(?)个复变数 z_(12),z_(13),…z_(1n),z_(23),…,(?)…,z_(n-1,n)空间的域我们引进运算子     

Positive reynolds operators and generating derivations

It is shown that the spectrum of a positive Reynolds operator on C₀(X) is contained in the disc centered at 1/2 with radius 1/2. Moreover, every positive Reynolds operator T with dense range is injective. In this case, the operator D = 1 — T^?1 is a densely defined derivation, which generates a one — parameter semigroup of algebra homomorphisms. This semigroup yields an integral representation of T. Along the way, it is proved that a densely defined closed derivation D generates a semigroup if, and only if, R(1, D) exists and is a positive operator.     

Book Review

Dynamics of One—Dimensional Maps by A. N. Sharkovsky, S. F. Kolyada, A. G. Sivak and Y. V. Fedorenko, Publisher: Kluwer Academic Publishers, Format: Hardcover, Publication Date: April 1997, 260 Pages. ISBN: 07923-4532-0, Price: $196=00. This is a nice and interesting introductory book on the dynamics of 1—dimensional maps. As stated by the authors, the book has two main goals. The first is to introduce the readers to the fundamentals of the theory of 1—dimensional dynamical systems. The second is to provide to the readers a comprehensive view of the problems appearing in the theory of dynamical systems and to describe the methods used to solve these problems in the case of 1—dimensional maps. The first chapter of this book is an elementary introduction to the theory of 1—dimensional maps. It contains an exposition of basic concepts of the theory of dynamical systems and a list of examples illustrating various situations encountered in the study of 1—dimensional maps. The second chapter deals with symbolic dynamics. It contains in particular a presentation of the kneading theory. The third chapter is on the Sharkovsky theorem, one of the most important early results in the theory of 1—dimensional maps. Chapter 4 contains, to a certain degree of details, a classification theory of 1—dimensional maps with zero entropy that mainly reflects the research interests of the authors. Chapter 5 is an introductory lecture to unimodal maps. Chapter 6 is on the aspect of 1—dimensional dynamics that is related to measure theory. Existence theorems on absolutely continuous invariant measures are discussed. Chapter 7 is on the problem of structure stability, and Chapter 8 is on fundamentals of 1—dimensional families of maps: bifurcation periodic doubling and universality.BOOK REVIEW This book touches a variety of topics, introduces basic concepts and presents many important early results that are fundamentally important to the study of 1—dimensional maps, Most of the materials the book covers have a distinctively topological flavor that occurs rather commonly in the study of dynamical systems up to the early 1980's. A substantial part of the text can be used directly in an introductory course on dynamical systems. On the other hand, readers should be reminded that there have been explosive new developments in the study of 1—dimensional maps since this book was written. One should definitely find books and survey articles that are more recent for an up—to—date view on this subject     

Simple Approximations for the GI/G/c Queue—I: The Steady-State Probabilities

Viewing the GI/G/c queue as a service system alternating between two basic states—that of a loaded (non-empty) GI/G/1 queue and that of a GI/G/∞ queue (dependent, respectively, on whether all servers in the GI/G/c queue are busy or otherwise)—approximations for the components of the mixture distribution of the steady-state probabilities are derived. The M/G/c queue is separately treated. Two imposed prerequisites, that only minimal prior information about the queue will be required and that no numeric method be needed other than a root-finding algorithm, are strictly adhered to. The accuracy attained is generally satisfactory, while remarkable algebraic simplicity is preserved.