A note on Lagrange interpolation of functions of generalized bounded variation

In this paper we solve a remained problem in [2], whether the following estimate approximation for the classf∈[-1, 1]∩BV by Lagrange interpolation based on the Jacobi abscissas: L _n ^(a,d) (f,x)−f(x)=O(1/n) holds, if α≠β α,β≥−1. The project is supported by the Natural Science Foundation of Zhejiang Province.     

Mann iteration of weak convergence theorems in Banach space

In this paper, by using Mann＇s iteration process we will establish several weak convergence theorems for approximating a fixed point of k-strictly pseudocontractive mappings with respect to p in p-uniformly convex Banach spaces. Our results answer partially the open question proposed by Marino and Xu, and extend Reich＇s theorem from nonexpansive mappings to k-strict pseudocontractive mappings.     

EXISTENCE OF SOLUTIONS OF A FAMILY OF NONLINEAR BOUNDARY VALUE PROBLEMS IN L^2-SPACES

By using the perturbation results of sums of ranges of accretive mappings of Calvert and Gupta (1978),the abstract results on the existence of solutions of a family of nonlinear boundary value problems in L^2 (Ω) are studied. The equation discussed in this paper and the methods used here are extension and complement to the corresponding results of Wei Li and He Zhen‘s previous papers. Especially,some new techniques are used in this paper.     

Pointwise characterization for combinations of Szász-Mirakjan operators

The purpose of this paper is to characterize the pointwise rate of convergence for the combinations of Szász-Mirakjan operators using Ditzian-Totik modulus of smoothness.     

Necessary optimality conditions for a class of nonsmooth vector optimization

The Kuhn-Tucker type necessary conditions of weak efficiency are given for the problem of minimizing a vector function whose each component is the sum of a differentiable function and a convex function, subject to a set of differentiable nonlinear inequalities on a convex subset C of ℝ ⁿ , under the conditions similar to the Abadie constraint qualification, or the Kuhn-Tucker constraint qualification, or the Arrow-Hurwicz-Uzawa constraint qualification. Supported by the National Natural Science Foundation of China (No. 70671064, No. 60673177), the Province Natural Science Foundation of Zhejiang (No.Y7080184) and the Education Department Foundation of Zhejiang Province (No. 20070306).     

CONSTRUCTIONS OF THE INVARIANT SETS AND INVARIANT MEASURES

In this paper, we will discuss the constructiOn problems about the invariant sets and invariant measures of continues maps~ which map complexes into themselves, using simplical approximation and Markov cbeirs. In [7], the author defined a matrix by using r-normal subdivi of the w,dimensional unit cube, considered it a Markov matrix, and constructed the invariantset and invafiant measure, In fact, the matrix he defined is not Markov matrix generally. So wewill give [7] and amendment in the last pert of this paper. We also construct an invariant set thatis the chain-recurrent set of the map by means of a non-negative matrix which only depends on themap. At hst, we will prove the higher dimension?Banach variation formuls that can simplify thetransition matrix.     

Strong laws of large numbers for weighted sums of $$\tilde \rho $$ -mixing random variables

Strong laws are established for linear statistics that are weighted sums of a -mixing random sample. The results obtained generalize the results of Baxter et al. [SLLN for weighted independent indentically distributed random variables, J. Theoret. Probab. 17 (2004), 165–181] to -mixing random variables. This paper is supported by Key discipline of Zhejiang Province (Key discipline of Statistics of Zhejiang Gongshang University) and National Natural Science Foundation of China.     

Asymptotic Smoothing Effect of Solutions to Davey-Stewartson Systems on the Whole Plane

This paper discusses the Cauchy problem of elliptic-elliptic-type Davey-Stewartson systems with zero-order dissipation on R^2. Making use of the Fourier spectral projector, together with a long time comparison between the solutions to the Davey-Stewartson systems and to an auxiliary problem, we prove that the global attractor in H^1 （R^2） for the addressed Davey-Stewartson systems is a compact subset of H^2（R^2）, and thus reveal the asymptotic smoothing effect of the solutions for the systems.     

一类可逆的弱次正规算子的幂

It is known that the square of a ω- hyponormal operator is also ω- hyponormal. In this note it is showed that there exists an invertible operator which is not log-hyponormal but its integer powers are all ω-hyponormal.     

<Emphasis Type="Italic">W</Emphasis><Superscript>1,<Emphasis Type="Italic">p</Emphasis></Superscript>(R<Superscript><Emphasis Type="Italic">n</Emphasis></Superscript>)-boundedness for maximal functions

In this paper, we get W ^1,p (R ⁿ )-boundedness for tangential maximal function and nontangential maximal function, which improves J.Kinnunen, P.Lindqvist and Tananka’s results. Supported by the key Academic Discipline of Zhejiang Province of China under Grant No.2005 and the Zhejiang Provincial Natural Science Foundation of China.     

On Eigenvalue Intervals and Eigenfunctions of Nonresonance Singular Dirichlet Boundary Value Problems

In this paper we shall consider the nonresonance Dirichlet boundary value problemwhere λ>0 is a parameter, p>0 is a constant. Intervals of A are determined to ensure the existence of a nonnegative solution of the boundary value problem. For λ=1, we shall also offer criteria for the existence of eigenfunctions. The main results include and improve on those of [2,4,6,8].     

ESTIMATE FOR DISTANCE-COEFFICIENT OF MATRICES

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A FUNCTIONAL CENTRAL LIMIT THEOREMFOR NEGATIVELY ASSOCIATED SEQUENCE

Let(x1,j≥1)be a sequence of negatively associated random variables with ex1=o,ex^21＜∞.in this paper a functional central limit theorem for negatively associated random variables under some conditions withbout stationarity is proved which is the same as the results for positively associated random variables.     

L p -dual Quermassintegral sums

In this paper, we first introduce a concept of L _p -dual Quermassintegral sum function of convex bodies and establish the polar projection Minkowski inequality and the polar projection Aleksandrov-Fenchel inequality for L _p -dual Quermassintegral sums. Moreover, by using Lutwak’s width-integral of index i, we establish the L _p -Brunn-Minkowski inequality for the polar mixed projection bodies. As applications, we prove some interrelated results. This work was partially supported by the National Natural Science Foundation of China (Grant No. 10271071), Zhejiang Provincial Natural Science Foundation of China (Grant No. Y605065) and Foundation of the Education Department of Zhejiang Province of China (Grant No. 20050392)     

ON THE EXPONENT SET OF PRIMITIVELOCALLY SEMICOMPLETE DIGRAPHS

A locally semicomplete digraph is a digraph D=(V,A) satisfying the following condi-tion for every vertex x∈V the D[O(x)] and D[I(x)] are semicomplete digraphs. In this paper,we get some properties of cycles and determine the exponent set of primitive locally semicompleted digraphs.     

On polynomial rings over a ring with a selfduality

We prove that a ringR has a self duality induced by a leftR-moduleM if and only if its polynomial ringR[x] has a graded self duality induced by a graded leftR[x]-moduleM[x ⁻¹]. Supported by the Natural Science Foundation of Fujian Province (1994–1997)     

ON A SET OF h-HARMONIC HOMOGENEOUS POLYNOMIALS

In this paper, we study the homogeneous polynomials orthogonal with the weight function h(x(d))=x1^2k1…xd^2kd on S^(d-1).We obtain the explicit formula on a basis of the orthogonal homogeneous polynomials of degree n. It is simpler than the formula in,and can be regarded as an extension of under the weighted case.     

The decomposition of Kv into K2×K5''''s

The decomposition of the complete graph Kv into Kr×Kc's, the products of Kr and Kc,is originated from the use of DNA library screening. In this paper, we consider the case where r=2 and c = 5, and show that such a decomposition exists if and only if v ≡ 1 (mod 25).     

Asymptotic behavior of gibbs functions forM-band wavelet expansions

In this paper the asymptotic behavior of Gibbs function for a class ofM-band wavelet expansions is given. In particular, the Daubechies’ wavelets are included in this class. The authors are partially supported by the Chinese National Natural Science Foundation (19571972), the Key Project Foundation (69735020) and the Zhejiang Provincial Science Foundation of China (196083)     

Weak Type Endpoint Estimates for Multilinear θ-type Calderon-Zygmund Operators

In this paper, the author discusses the multilinear singular integrals with certain θ-type Calderdn- Zygmund operators and obtain the boundedness from weak H^1 （R^n） to weak L^1 （R^n）.