一类单叶调和函数的系数不等式和极值点

设■是单位圆盘U上的单叶保形复值调和函数,其中h和g在U上解析.利用广义Salagean算子定义和研究一类新的调和函数类,给出该类中函数的充分系数不等式条件,并证明当g系数为负数时,这些条件是充分必要的.由此条件进一步讨论极值点及其相关几何性质,得到新的结果.     

用Salagean算子定义的缺系数的单叶调和函数类

本文研究了用Salagean算子定义的缺系数单叶调和函数类.利用从属关系和算子理论得到类中函数的系数估计、极值点、偏差定理、卷积性质、凸性组合与凸半径,推广了已有的一些结果.     

一类算子的凸性条件(英文)

In this paper,we find a subclass of starlike functions on the unit disk,which are mapped by a operator,given by F（z）=1＋u/zu∫z0 f（t）tu-1dt（Re u≥0）,onto convex functions.The main results extend some known results.     

关于一些解析函数空间的系数乘子(英文)

In this paper, we give some new results of the coefficient multiplier of some analytic function spaces, characterize the coefficient multiplier spaces (Hα, p Hβ q) and (Ap,α), Aq,β) with 0 < p ≤ 1, p ≤ q ≤∞, 0 ≤α < β < ∞ and show (Hα∞, Hβ∞) = Hβ-α1 with 0 < α < β < ∞.     

NA群上调和函数(英文)

本文研究了非对称调和流形上满足平均值性质的可积函数与卷积方程的解之关系.利用Naten,Weit在秩为一的对称空间上使用的谱综合方法,获得了NA群上卷积方程的可积函数解必是调和函数,这推广了Ahern,Flores和Rudin在欧氏空间,与Koranyi在双曲空间上得到的类似结果.     

一类新的可控排序问题(英文)

本文讨论了一类新的加工时间可控的单机排序问题。我们所考虑的目标函数由所有工件的加权完工时间之和与对所有工件的实际加工时间偏离额定加工时间的最大不满意程度这两部分组成.对此问题,我们提出了一个多项式算法.     

一类Hartogs域的Bergman核函数的零点问题(英文)

We obtain the Bergman kernel for a new type of Hartogs domain.The corresponding LU Qi-Keng’s problem is considered.     

加权Baouendi-Grushin型算子的基本解与一类加权Hardy不等式(英文)

In this paper we obtain the fundamental solution for a class of weighted BaouendiGrushin type operator L_p,γ,αu = ▽_γ·(|▽_γu|^p-2ρ^α▽_γu) on R^m+n with singularity at the origin,where ▽_γ is the gradient operator defined by ▽_γ =（▽_x,|x|^γ▽_y） and ρ is the distance function.As an application,we get some Hardy type inequalities associated with ▽_γ.     

β_∞(Ω)中算子的小紧扰动(英文)

We consider an approximation problem related to strongly irreducible operators, that is, does the direct sum of a strongly irreducible operator in в∞(Ω) and certain operator have a small compact perturbation which is a strongly irreducible operator in в∞(Ω)? In this paper, we prove that the direct sum of any strongly irreducible operator in в∞(Ω) and certain biquasitriangular operator have small compact perturbations which are strongly irreducible operators in в∞(Ω).     

数值积分的可选择误差界(英文)

Similar to having done for the mid-point and trapezoid quadrature rules,we obtain alternative estimations of error bounds for the Simpson＇s quadrature rule involving n-time（1 ≤ n ≤ 4） differentiable mappings and then to the estimations of error bounds for the adaptive Simpson＇s quadrature rule.     

关于某些调和函数

用H表示形如f(z)=h(z) g(z)的调和函数族,其中h和g是单位圆盘内的解析函数.本文考虑H的三类子族函数.其中的两族为PH(α)=f∶Ref(z)z≥α和NH(α)=f∶Ref(z)θz≥θα,其中0≤α<1和θ=argz.本文得到了函数f属于其中一族的一个充分必要条件,并且获得了一些系数不等式和偏差定理.     

由从属关系刻画的多叶调和函数新子类

本文引入了由广义Dziok-Srivastava算子定义的多叶调和函数新子类, 给出了该类中函数的系数不等式, 偏差估计和极值点等性质.     

单叶调和映照的反函数

设是在一个单连通区域上的单叶调和映照，我们证明了反函数ｚ＝ｆ－１（）也是调和映照的充要条件是ｆ为下面三类函数之一：（ｉ）单叶共形映照；（ｉｉ）仿射交换映照；（ｉｉｉ）具有形式ｆ（ｚ）＝Ａ［ａｚ＋β＋ｌｏｇ（１－ｅ－ａｚ－β）－ｌｏｇ（１－ｅ－ａｚ－β）］＋Ｂ的调和映照，其中Ａ，Ｂ，α和β是常数且满足条件Ｒ（ａｚ＋β）＞０，Ｚ∈Ｄ．     

On the Coefficients of Some Subclasses of Univalent Functions

In this paper we consider the class L_c*(,,) consisting of analytic and univlent functions with negative coefficients and with fixed second coefficient. The object of the present paper is to show coefficient estimates, convex linear combinations, some distortion theoems and radii of starlikeness and convexity for f(z) in the class L_c*(,,). The results are generalized to families with finitely many fixed coefficients.AMS Subject Classification (1991) 30C45     

单叶函数的几条判别法

对于单位圆盘内的解析函数f（z），本文根据给出了判别函数f（z）为单叶函数的几条判别法则，其中D0f（z）=f(z),D1f(z)=Df(z)=zf1(z),Dnf（z）=D(Dn-1f(z)),n∈N.     

锥中一类调和函数的增长估计

给出了锥中一类调和函数在无穷远点处的增长估计,推广了Siegel和Talvila,张和邓在半空间的相关结果.     

Comparison of Green Functions and Harmonic Measures for Parabolic Operators

In this paper, we prove two-sided pointwise estimates for the Green function of a parabolic operator with singular first order term on a C^1,1-cylindrical domain . Basing on these estimates, we establish the equivalence of the parabolic measure, the adjoint parabolic measure and the surface measure on the lateral boundary of . These results are first studied by some authors for certain elliptic and less general parabolic operators. Mathematics Subject Classifications (2000) 31B25, 35B05, 35K10, 58J35.     

单叶调和映射

由于在极小曲面理论中的作用，对调和映射的研究已有较长时间。１９８４年以来，经典解析单叶映射的理论被推广至调和单叶映射，并获得许多结论。这些工作引起人们对它的浓厚兴趣。该文介绍这一课题某些重要成果的概貌，并指出一些尚未解决的问题。它共分六个部分：映射定理；单叶调和函数的数值估计；特殊映射；变分方法；境界性质和在极小曲面中的应用。     

A New Class of Harmonic Measure Distribution Functions

Let Ω be a planar domain containing 0. Let h _Ω (r) be the harmonic measure at 0 in Ω of the part of the boundary of Ω within distance r of 0. The resulting function h _Ω is called the harmonic measure distribution function of Ω. In this paper we address the inverse problem by establishing several sets of sufficient conditions on a function f for f to arise as a harmonic measure distribution function. In particular, earlier work of Snipes and Ward shows that for each function f that increases from zero to one, there is a sequence of multiply connected domains X _n such that \(h_{X_{n}}\) converges to f pointwise almost everywhere. We show that if f satisfies our sufficient conditions, then f=h _Ω , where Ω is a subsequential limit of bounded simply connected domains that approximate the domains X _n . Further, the limit domain is unique in a class of suitably symmetric domains. Thus f=h _Ω for a unique symmetric bounded simply connected domain Ω.