QUASI-MODULUS OF CONTINUITY AND BEST APPROXIMATIONS

In this paper a concept of the quasi-modulus of continuity of the functions of L^2(T) on the unit circle T is introduced, and the relations between it and modulus of continuity are discussed. And we give a sufficient condition such that the best uniform approxi marion of the continuous functions on T is continuous.     

DIFFERENTIABILITY OF CONVEX FUNCTIONS AND ASPLUND SPACES

ＤＩＦＦＥＲＥＮＴＩＡＢＩＬＩＴＹＯＦＣＯＮＶＥＸＦＵＮＣＴＩＯＮＳＡＮＤＡＳＰＬＵＮＤＳＰＡＣＥＳＣｈｅｎｇＬｉｚｉｎ（程立新）ＺｈａｎｇＦｅｎｇ（张风）（Ｍａｔｈ．Ｓｅｃｔｉｏｎ，Ｄｅｐｔ．ｏｆＰｕｂｌｉｃＣｏｕｒｓｅｓ，ＪｉａｎｇｈａｎｒＰｅｔ...     

非线性退缩抛物型方程弱解的梯度的Holder连续性

本文我们讨论如下的非线性退缩抛物型方程：设为上述方程的弱解．在一些结构性条件下，我们得到△ｕ的Ｈ　ｌｄｅｒ连续性．     

ON THE PRODUCT OF GATEAUX DIFFERENTIABILITY LOCALLY CONVEX SPACES

A locally convex space is said to be a Gateaux differentiability space (GDS)provided every continuous convex function defined on a nonempty convex open subset D of the space is densely Gateaux differentiable in D.This paper shows that the product of a GDS and a family of separable Frechet spaces is a GDS,and that the product of a GDS and an arbitrary locally convex space endowed with the weak topology is a GDS.     

Analysis of Symmetric Matrix Valued Functions

For any symmetric function f: ? ⁿ  → ? ⁿ , one can define a corresponding function on the space of n × n real symmetric matrices by applying f to the eigenvalues of the spectral decomposition. We show that this matrix valued function inherits from f the properties of continuity, Lipschitz continuity, strict continuity, directional differentiability, Fréchet differentiability, and continuous differentiability.     

DIFFERENTIABILITY OF CONVEX FUNCTIONS ON SUBLINEAR TOPOLOGICAL SPACES AND VARIATIONAL PRINCIPLES IN LOCALLY CONVEX SPACES

This paper presents a type of variational principles for real valued w lower semicon-tinuous functions on certain subsets in duals of locally convex spaces, and resolve a problem concerning differentiability of convex functions on general Banach spaces. They are done through discussing differentiability of convex functions on nonlinear topological spaces and convexification of nonconvex functions on topological linear spaces.     

ON THE PRODUCT OF GATEAUX DIFFERENTIABILITY LOCALLY CONVEX SPACES

A locally convex space is said to be a Gâteaux differentiability space (GDS) provided every continuous convex function defined on a nonempty convex open subset D of the space is densely Gâteaux differentiable in D. This paper shows that the product of a GDS and a family of separable Fréchet spaces is a GDS, and that the product of a GDS and an arbitrary locally convex space endowed with the weak topology is a GDS.     

CONTINUITY AND HAUSDORFF DIMENSION OF JULIA SET CONCERNING YANG-LEE ZEROS

Considering the Julia set J（Tλ） of the Yang-Lee zeros of the Potts model on the diamond hierarchical Lattice on the complex plane, the authors proved that HDJ（Tλ） 〉 1 and discussed the continuity of J（Tλ） in Hausdorff topology for λ∈R.     

Distinct differentiable functions may share the same Clarke subdifferential at all points

We construct, using Zahorski's Theorem, two everywhere differentiable real-valued Lipschitz functions differing by more than a constant but sharing the same Clarke subdifferential and the same approximate subdifferential.

     

On the Mergelyan approximation property on pseudoconvex domains in

Let be a smoothly bounded pseudoconvex domain of finite type in . We prove the Mergelyan approximation property in various topologies on when the estimates for -equation are known in the corresponding topologies.

     

THE UNIT BALL OF C*-ALGEBRA AND DIFFERENTIABILITY OF SUPPORT FUNCTION

In this paper we show that the unit ball of an infinite dimensional commutative C-algebra lacks strongly exposed points, so they have no predual. Also in the second part, we use the concept of strongly exposed points in the Frechet differentiability of support convex functions.     

基于几何连续的AT-β-Spline曲线曲面的构造

为了更好地修改给定的样条曲线曲面,构造了满足几何连续的带两类形状参数的代数三角多项式样条曲线曲面,简称为AT-β-Spline.这种代数三角曲线曲面不仅具有普通三角多项式的性质,而且具有全局的和局部的形状可调性.同时还具备较为灵活的连续性.当两类形状参数在给定的范围内任意取值时,这种带两类形状参数的AT-β-Spline曲线满足一阶几何连续性;如果给定两段相邻曲线段中的两类形状参数满足-1≤α≤1,μ_i=λ_(i+1)或μ_i=λ_i=μ_(i+1)=λ_(i+1)时,则带两类形状参数的AT-β-Spline曲线满足C~1∩G~2连续.另外利用奇异混合的思想,构造了满足C~1∩G~2插值AT-β-Spline曲线,解决曲线反求的几何连续性等问题.同时还给出了旋转面的构造,描述了两类形状参数对旋转面的几何外形的影响;当形状参数取特殊值时,这种AT-β-Spline曲线曲面可以精确地表示圆锥曲线曲面.从实验的结果来看,本文构造的AT-β-Spline曲线曲面是实用的有效的.     

Hölder continuity for a class of strongly degenerate Schrödinger operator formed by vector fields

In this paper we obtain the Hölder continuity property of the solutions for a class of degenerate Schrödinger equation generated by the vector fields: $$- \sum\limits_{i,j = 1}^m {X_j^* \left( {a_{ij} \left( x \right)X_i u} \right) + \vec bXu + vu = 0,}$$ where X = {X ₁, ...,X _m } is a family of C ^∞ vector fields satisfying the Hörmander condition, and the lower order terms belong to an appropriate Morrey type space.     

A CLASS OF TWO-STEP CONTINUITY RUNGE-KUTTA METHODS FOR SOLVING SINGULAR DELAY DIFFERENTIAL EQUATIONS AND ITS STABILITY ANALYSIS

In this paper, a class of two-step continuity Runge-Kutta（TSCRK） methods for solving singular delay differential equations（DDEs） is presented. Analysis of numerical stability of this methods is given. We consider the two distinct cases： （i）τ≥ h, （ii）τ 〈 h, where the delay τ and step size h of the two-step continuity Runge-Kutta methods are both constant. The absolute stability regions of some methods are plotted and numerical examples show the efficiency of the method.     

BEST LIPSCHITZ CONSTANTS FOR THE BEZIER NETS AND BERNSTEIN POLYNOMIALS OVER A SIMPLEX

1IntroductionBernsteinpolynothealspreservethepropertiesoftheircorrespondingfunctionsandB6ziernets,forexample,convekityandmononity,tolargeextends.Thisisknownasshapepreservingproperty.ShapepreservingpropertiesofBernsteinpolynomialsmakethemplayanimportantroleinComputerAidedGeometricDesignandApproximationThe6ry.Manyscholarshavemademucheffortsinstudyillgthoseproperties.In1987,Brown,etal[1]begantostudyLipschitzcontilluitypreservingpropertyofBernsteinpolynomials.Theyprovedthatifunivariatefuncti…     

CONTINUITY AND LINEARITY OF ADDITIVE DERIVATIONS OF NEST ALGEBRAS ON BANACH SPACES

This paper discusses the problem concerning the continuity and linearity of additive derivation of nest algebras on normed spaces. It is proved that every linear derivation of a nest algebraalgN is continuous provided that one of the following conditions is satisfied: (1) 0 (?) 0. (2)X_ (?) X. (3) there exists a non-trivial idempotent p in algN such that the range of p belongsto N. It is also proved that every additive derivation of a nest algebra is automatically linearif the underlying normed space is infinite dimemnsional.     

多参数双分数布朗运动相遇局部时的存在性和联合连续性

本文研究了两个相互独立的(N,d)双分数布朗运动BH1,K1和BH2,K2的相遇局部时的问题.利用Fourier分析,获得了相遇局部时的存在性和联合连续性的结果,推广了分数布朗运动相遇局部时的相关结果.     

非可微分二层Lipschitz规划的广义微分和广义方向导数

本文对构成函数为Ｌｉｐｓｃｈｉｔｚ函数的二层规划问题,利用非光滑分析工具,讨论了下层极值函数和上层复合目标函数的Ｌｉｐｓｃｈｉｔｚ连续性,给出了这些函数的广义微分和广义方向导数的估计式。本文得到的结果为进一步研究非可微二层Ｌｉｐｓｃｈｉｔｚ规划的最优性条件和有效算法等理论和方法问题奠定了基础。     

Yang-Lee零点的Julia集及其Hausdorff维数的连续性

本文研究了Yang-Lee零点的Julia集的复解析动力系统问题.利用网格及共形迭代函数系统的方法,获得了Yang-Lee零点的Julia集及其Hausdorff维数连续性的结果,推广了乔建永教授在文献[1]中的结果,     

ON WEIGHTED L~p INTEGRABILITY AND APPROXIMATION OF TRIGONOMETRIC SERIES

We generalize several classical results on the integrability of trigonometric series and relations among the best approximation and the coefficients of trigonometric series. Theorem 3 and Theorem 4 are the first results on the relations among the weighted best approximation and the coefficients of trigonometric series.