Anisotropic interpolation and quasi-Wilson element for narrow quadrilateral meshes

In this paper an anisotropic interpolation theorem is presentedthat can be easily used to check the anisotropy of an element.A kind of quasi-Wilson element is considered for second-orderproblems on narrow quadrilateral meshes for which the usualregularity condition _K/h_K c₀ > 0 is not satisfied, whereh_K is the diameter of the element K and _K is the radius of thelargest inscribed circle in K. Anisotropic error estimates ofthe interpolation error and the consistency error in the energynorm and the L²-norm are given. Furthermore, we give a Poincaréinequality on a trapezoid which improves a result of eniek.  

AN ANISOTROPIC NONCONFORMING FINITE ELEMENT WITH SOME SUPERCONVERGENCE RESULTS

The main aim of this paper is to study the error estimates of a nonconforming finite element with some superconvergence results under anisotropic meshes. The anisotropic interpolation error and consistency error estimates are obtained by using some novel approaches and techniques, respectively. Furthermore, the superclose and a superconvergence estimate on the central points of elements are also obtained without the regularity assumption and quasi-uniform assumption requirement on the meshes. Finally, a numerical test is carried out, which coincides with our theoretical analysis.  

构造曲线的插值型细分法--非均匀四点法

本文提出了一种构造曲线的插值型细分法－非均匀四点法，四点法可作为这个方法的一个特例。用这种方法可以构造出Ｇ＾１连续的插值曲线，该法引入了一些偏移参数来控制细分过程，偏移参数参曲线形状的影响是局部的。  

Lacunary Interpolation by Antiperiodic Trigonometric Polynomials

The problem of lacunary trigonometric interpolation is investigated. Does a trigonometric polynomial T exist which satisfies T(x _k) = a _k, D ^m T(x _k) = b _k, 0 k n – 1, where x _k = k/n is a nodal set, a _k and b _k are prescribed complex numbers, and m N. Results obtained by several authors for the periodic case are extended to the antiperiodic case. In particular solvability is established when n as well as m are even. In this case a periodic solution does not exist.  

函数的径向基表示

本文是关于函数的径向表示的综述性文章，基于我们对这方面的研究工作的了解，介绍了国际上近年来这方面的主要的有关研究结果以及在一些领域中应用的情况，文后附有主要的参考文献以便感兴趣的读者查阅。  

分形插值曲面理论及其应用

本文叙述了分形曲面的生成原理，给出了分形插值曲面的计算公式，证明了分形插值曲面迭代函数系唯一性定理，导出了分形插值曲面的维数定理，并应用实际数据进行了分形插值曲面的实例研究·  

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…  

Piecewise polynomial,positive definite and compactly supported radial functions of minimal degree

We construct a new class of positive definite and compactly supported radial functions which consist of a univariate polynomial within their support. For given smoothness and space dimension it is proved that they are of minimal degree and unique up to a constant factor. Finally, we establish connections between already known functions of this kind.  

有理插值问题存在性的一个判别准则

１引言我们知道，多项式Ｌａｇｒａｎｇｅ插值是适定的［１，２］，但有理插值函数却未必存在［８，３］．并且到目前为止，也没有类似于多项式Ｌａｇｒａｎｇｅ插值的能够揭示插值结构的显式插值公式．不过有理插值已有许多算法，比如Ｓｔｏｅｒ算法，Ｔｈｉｅｌｅ倒差商算法，Ｓａｌｚｅｒ算法以及Ｗｕｙｔａｃｋ算法等等，见［８，４，５，６］．本文为寻求尽可能接近显式的插值公式，进而揭示有理插值问题的内在结构，得到了有理插值函数存在的一个充要条件，同时也给出了有理插值函数的一种表现形式，参见［１１］．本文约定，所有矩阵…  

Interpolating hereditarily indecomposable Banach spaces

The following dichotomy is proved.

Every Banach space either contains a subspace isomorphic to , or it has an infinite-dimensional closed subspace which is a quotient of a Hereditarily Indecomposable (H.I.) separable Banach space.

In the particular case of , it is shown that the space itself is a quotient of a H.I. space. The factorization of certain classes of operators, acting between Banach spaces, through H.I. spaces is also investigated. Among others it is shown that the identity operator admits a factorization through a H.I. space. The same result holds for every strictly singular operator .

Interpolation methods and the geometric concept of thin convex sets together with the techniques concerning the construction of Hereditarily Indecomposable spaces are used to obtain the above mentioned results.