12参双参数矩形板元的误差估计

双参数方法是构造高阶问题有限元的有效方法．以此方法构造的双参数元是一种非标准元，以往文献中只证明了它的收敛性．此文针对具体12参双参数矩形板元给出它的误差估计式，并分析了节点参数的扰动量．文中的分析方法也适合于其它双参数矩形板元的误差估计．     

基于台劳展式的矩形Reissner-Mindlin板元

1.引言 Rdissner-Mindlin板模型放弃了经典板模型的Kirchhoff假说,考虑了剪切变形,能应用于更广泛的板问题。Reissner-Mindlin板模型的挠度与转角是相互独立的,单元只需具有c~0连续性,这一点优于需要具有c~1连续性的Kirchhoff板元,但一个严重困难是普通c~0元,尤其是低阶c~0元,当板厚趋于零时不收敛,这就是所谓的自锁现象(locking)。近年来,研究避免自锁现象的Reissner-Mindlin模型板元吸引了不少的注     

拟协调元的精度分析

利用双参数有限元的框架，证明利用拟协调元方法构造的非协调三角形板元都具有一个非常特殊的性质。即相容误差比插值误差高一阶。这是常规有限元和一般非协调元所不具备的。     

十二参三角形板元

九参三角形板元的研究工作已有不少,但十二参三角形板元还较少见报道。唐立民等利用他们创立的拟协调方法构造一个十二参三角形拟协调元,节点参数是单元三个顶点上的函数值和两个一阶偏导数值及三边中点上的外法向导数值,他们是用力学方法构     

无锁定的退化的等参壳元

构造了一个无锁定的8节点退化的等参壳元,在自然坐标系中,对横向剪应变项插值修正使单元满足必要的模式（平移,转动和纯弯曲）以消除“剪切锁定”,在局部坐标系中,对薄膜应变插值修正以消除“薄膜锁定”,这样构造的8节点单元的刚度矩阵具有正确的秩,同时具有恰当的零特征值和相应的刚体位移模式,这种单元对大跨－厚比情形既无“剪切锁定”又无“薄膜锁定”,无虚假的零能模式和机构出现,可用于厚壳和薄壳。     

Mindlin板几何非线性分析的附加内部剪应变法

本文在几何非线性分析的Ｍｉｎｄｌｉｎ板元中引入单元附加内部剪应变，有效地解决了薄板情况下的剪切自锁问题．文中导出了相应的能量相容条件，给出了有限元非线性列式的全过程及有关簿板及中厚板大挠度问题的数值结果．     

一种保形C~1三次样条插值方法

本文得到了构造一个保形Ｃ１三次插值样条函数的充要条件，并给出了一种构造保形Ｃ１三次插值样条函数的方法．     

二维非线性对流扩散方程的非振荡特征差分方法

１．引言 近十几年来,双曲守恒律问题的高分辨率格式已取得很大发展,具有局部自适应选取节点的非振荡插值算法（如 ＵＮＯ［１］, ＥＮＯ［２］等）在这些格式的构造中起着重要的作用．特征差分法是求解对流扩散问题的一种较为有效方法,但在求解具有陡峭前线问题时,也会产生非物理振荡阻（见４）．本文将把特征差分法与非振荡插值算法相结合构造对流扩散问题的高分辨率差分格式． ［１］中的 ＵＮＯ及［２］中的 ＥＮＯ插值都是一维的,有关讨论二维 ＵＮＯ及ＥＮＯ插值的文章还不多见,本文将构造二维基于六节点的二次非振荡插值以及…     

关于几种三角形板元等价性的注记

1．引言求解薄板弯曲问题的广义协调元法近年来有了发展,本文讨论几种三角形板元之间的等价关系．我们证明,[2]中构造的GCⅢ－T9元等价于Specht元问．同一作者在[4]中构造的GCⅡ－T9元实际上也等价于Specht元,因此,它们彼此等价．另外,[7]中用对称列式构造的一个广义协调元是和作者在问中所引进的单元等价．例已指出,[7]中的那个元等价于问中的VZ1元,所以[7]和[6]中的两个广义协调元均等价于已知的VZ1元．2．广义协调GCⅢ－T9单元设三角形单元K的三个顶点依反时针方向分别为p i（xi,yi）,节点参数是pi点处的函数值及其一阶导…     

关于Lagrange平均插值过程的逼近阶估计

本文以多项式（１＋ｘ）Ｖｎ（ｘ）Ｖｎ（ｘ）＝ｃｏｓ２ｎ＋１２θｃｏｓθ２，ｘ＝ｃｏｓθ的零点作为插值的节点，构造了一个Ｌａｇｒａｎｇｅ插值多项式算子过程Ｃｎ（ｆ，ｘ），给出了其逼近阶估计．同时证明Ｃｎ（ｆ，ｘ）亦满足Ｄｉｔｚｉａｎ－Ｔｏｔｉｋ定理．     

A REPRESENTATION FORMULA RELATED TO SCHR(O)DINGER OPERATORS

Schr(o)dinger operator is a central subject in the mathematical study of quantum mechanics.Consider the Schrodinger operator H = -△ V on R, where △ = d2/dx2 and the potential function V is real valued. In Fourier analysis, it is well-known that a square integrable function admits an expansion with exponentials as eigenfunctions of -△. A natural conjecture is that an L2 function admits a similar expansion in terms of "eigenfunctions" of H, a perturbation of the Laplacian (see [7], Ch. Ⅺ and the notes), under certain condition on V.     

Journal of Mathematical Research with Applications Guide for Authors

正Journal overview:Journal of Mathematical Research with Applications(JMRA),formerly Journal of Mathematical Research and Exposition(JMRE)created in 1981,one of the transactions of China Society for Industrial and Applied Mathematics,is a home for original research papers of the highest quality in all areas of mathematics with applications.The target audience comprises:pure and applied mathematicians,graduate students in broad fields of sciences and technology,scientists and engineers interested in mathematics.     

Instructions for contributions

正Applied Mathematics-A Journal of Chinese Universities,Series B(Appl.Math.J.Chinese Univ.,Ser.B)is a comprehensive applied mathematics journal jointly sponsored by Zhejiang University,China Society for Industrial and Applied Mathematics,and Springer-Verlag.It is a quarterly journal with     

CONTENTS OF VOLUME 30

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Staircase transportation problems with superadditive rewards and cumulative capacities

A cumulative-capacitated transportation problem is studied. The supply nodes and demand nodes are each chains. Shipments from a supply node to a demand node are possible only if the pair lies in a sublattice, or equivalently, in a staircase disjoint union of rectangles, of the product of the two chains. There are (lattice) superadditive upper bounds on the cumulative flows in all leading subrectangles of each rectangle. It is shown that there is a greatest cumulative flow formed by the natural generalization of the South-West Corner Rule that respects cumulative-flow capacities; it has maximum reward when the rewards are (lattice) superadditive; it is integer if the supplies, demands and capacities are integer; and it can be calculated myopically in linear time. The result is specialized to earlier work of Hoeffding (1940), Fréchet (1951), Lorentz (1953), Hoffman (1963) and Barnes and Hoffman (1985). Applications are given to extreme constrained bivariate distributions, optimal distribution with limited one-way product substitution and, generalizing results of Derman and Klein (1958), optimal sales with age-dependent rewards and capacities.To our friend, Philip Wolfe, with admiration and affection, on the occasion of his 65th birthday.Research was supported respectively by the IBM T.J. Watson and IBM Almaden Research Centers and is a minor revision of the IBM Research Report [6].     

Laminations minimales résiduellement à 2 bouts

Résumé On décrit toutes les feuilles des laminations minimales dont un ensemble résiduel de feuilles ont 2 bouts.      

Best approximation by downward sets with applications

We develop a theory of downward sets for a class of normed ordered spaces. We study best approximation in a normed ordered space X by elements of downward sets, and give necessary and sufficient conditions for any element of best approximation by a closed downward subset of X. We also characterize strictly downward subsets of X, and prove that a downward subset of X is strictly downward if and only if each its boundary point is Chebyshev. The results obtained are used for examination of some Chebyshev pairs （W,x）, where ∈ X and W is a closed downward subset of X     

Boundedness of multilinear operators on weighted herz type spaces

In this paper, the author establishes the boundedness of multilinear operators on weighted Herz spaces and Herz-type Hardy spaces. The author also obtains their weak estimates on endpoints. As a special case, the conclusions may lead to the weighted estimates for multilinear Calderon-Zygmund operators.     

THE EXACT CONVERGENCE RATE AT ZERO OF LAGRANGE INTERPOLATION POLYNOMIAL TO |x|α

In this paper we present a generalized quantitative version of a result due to M. Revers concerning the exact convergence rate at zero of Lagrange interpolation polynomial to f(x) = |x|α with on equally spaced nodes in [-1, 1].