Multilinear Calderón-Zygmund Theory

A systematic treatment of multilinear Calderón-Zygmund operators is presented. The theory developed includes strong type and endpoint weak type estimates, interpolation, a multilinear T1 theorem, and a variety of results regarding multilinear multiplier operators.     

On G 2 Continuous Spline Interpolation of Curves in ℝ d

In this paper the problem of G ² continuous interpolation of curves in ^d by polynomial splines of degree n is studied. The interpolation of the data points and two tangent directions at the boundary is considered. The case n = r + 2 = d, where r is the number of interior points interpolated by each segment of the spline curve, is studied in detail. It is shown that the problem is uniquely solvable asymptotically, e., when the data points are sampled regularly and sufficiently dense, and lie on a regular, convex parametric curve in ^d . In this case the optimal approximation order is also determined.     

Degenerate Principal Series Representations of U(p, q) and Spin0(p, q)

Let p>q and let G be the group U(p, q) or Spin₀(p, q). Let P=LN be the maximal parabolic subgroup of G with Levi subgroup where

Hypergeometric Polynomials and Integer Programming

We examine connections between A-hypergeometric differential equations and the theory of integer programming. In the first part, we develop a hypergeometric sensitivity analysis for small variations of constraint constants with creation operators and b-functions. In the second part, we study the indicial polynomial (b-function) along the hyperplane xi=0 via a correspondence between the optimal value of an integer programming problem and the roots of the indicial polynomial. Gröbner bases are used to prove theorems and give counter examples.     

Elastoplastic stress analysis for cylindrical shell with flat strip imperfection

Based on unequidistant B-spline function, generalized spline subdomain displacement mode of rotational shell is obtained by taking double-direction interpolation of spline. The elastoplastic constitutive equation of shells is established by using the endochronic theory.According to the initial deflection theory of shells, the elastoplastic stress analysis of cylindrical shells with flat strip geometrical imperfection is studied. Numerical results show that the geometrical imperfection has a great effect on the stress distribution of shells.     

UCFC晶体场理论方法（I）——UCFC方法基本概念与d^4组态空间标准基

作为以ｄ４／ｄ６离子为例系统地介绍“ＵＣＦＣ（统一晶场偶合）图象晶体场理论方法”（简称ＵＣＦＣ方法）的系列论文的第一篇，首先介绍了ＵＣＦＣ方法的基本概念，然后介绍了ｄ４／ｄ６离子ＵＣＦＣ方法基本内容的第一部分：ｄ４离子全组态空间标准基链的构造方法。第二篇将介绍如何在标准基链中建造能量矩阵链。第三篇将介绍ｄ４／ｄ６离子ＵＣＦＣ方法的ＥＰＲ理论部分。ＵＣＦＣ方法不仅是一种考虑ｄ电子组态全部多重态的完全计算方法，而且是一种统一的、规范化的、简洁的理论方法体系。它克服了强场、弱场等传统逐次对角化方法的局限性，不须区分晶体场的强弱，因而原则上可通用于任意过渡金属络合物。     

任意三角形单元上的三次Lagrange型插值逼近

本文推广了文［２］中的结果，对于任意三角形单元的三次Ｌａｇｒａｎｇｅ型插值多项式给出了原函数ｕ与被插函数Ｕ之间的误差估计     

On the choice of the initial value of a quadratic spline in positive interpolation

Any quadratic spline with coinciding interpolating points and breakpoints can be uniquely determined by one initial condition. We examine how to choose the initial value in positive interpolation by using a norm of the spline. Monotone interpolation is also considered. The results are illuminated by numerical examples and by an application.