第一类华罗庚域的凸性与Kobayashi度量

研究了华罗庚域及广义华罗庚域的凸性,得到了这两类域成为凸域的充分必要条件．并计算了HEI（N1,…,Nr;2,n;3,1,…,1）上的Kobayashi度量和Caratheodory度量．     

第一类Cartan-egg域的凸性与Kobayashi度量

考察了Cartan-egg域CE_I(k; N₁, N₂; m, n)的凸性, 得到此域为凸域的充分必要条件. Cartan-egg域既不是可递域也不是Reinhdart域, 利用Suzuki的方法计算出Cartan-egg域CE_I(2; N₁, N₂; 2, n)和Cartan-Hartogs域Y_I(3; N; 2, n)上的Caratheodory度量和Kobayashi度量.     

复Hilbert空间单位球上的Schwarz-Pick估计

设f是从一个复Hilbert空间单位球到另一个复Hilbert空间单位球上的全纯映射.本文利用Carathéodory度量的性质,给出了f的高阶Fréchet导数的Schwarz-Pick估计,从而应用一种新方法,推广了复Hilbert空间上全纯映射的高阶Fréchet导数的Schwarz-Pick估计.     

二阶常微分方程边值问题解的存在性

设f: [0, 1]×R2 R满足 Carathéodory条件, a∈ L1[0, 1], a(·) ≥ 0 满足 0 ≤∫10a(t)dt < 1. 运用Leray Schauder原理考虑了边值问题x″(t) = f(t, x(t), x′(t))　　　t∈[0, 1]x′(0) =0　　　x(1) =∫10a(t)x(t)dt解的存在性.     

子矩形域上的Bezier网的凸性

设Ｔ是矩形域Ｔ的一个子矩形域，证明了如果Ｔ“平行于”Ｔ，则Ｔ具有Ｂｅｚｉｅｒ网的保凸性。即所有在Ｔ上凸的Ｂｅｚｉｅｒ网在Ｔ上的限制也是凸的。     

凸性的度量

本文从三个不同的侧面刻划凸函数的凸度,进一步讨论了测度等问题.     

一类奇异边值问题解的存在性

为了讨论一类奇异边值问题解的存在性问题,首先得出与所研究奇异边值问题等价的积分算子方程,其次证明积分算子是全连续算子,最后运用Leray-Schauder原理,在f:[0,1]×R2→R满足Carathéodory条件且(1-t)e(t)∈L1(0,1)时,解决了这类奇异二阶m-点边值问题解的存在性问题,并获得了该类问题至少存在一个解的充分条件.     

四阶半正超线性边值问题正解的存在性

在不要求非线性项f(x,y)连续且下方有界的情况下,证明了当f满足Carath啨odory条件时四阶半正边值问题正解的存在性.     

完备有界域上关于内蕴测度的一个特征性质

证明了Cn 中的一个有界域全纯等介于一个完备有界域Ω0 当且仅当它的Carath埁ｏｄｏｒｙ测度和Ｅｉｓｅｎｍａｎ Koba yashi测度在某一点处相等 .     

Carathéodory系统解的存在性

将Carathéodory系统转化为Kurzweil广义常微分方程,利用已知的Kurzweil广义常微分方程解的存在性理论讨论了Carathéodory系统解的存在性.     

Extremal problems on the generalized Hua domain of the first type

Some extremal problems between the generalized Hua domain of the first type and the unit ball are studied. The extremal mapping and extremal value in explicit formulas are also obtained.     

第二类华罗庚域的Bergman核函数的计算—纪念华罗庚90岁寿辰

显式获得了第二类华罗庚域的Bergman核函数.第二类华罗庚域是指由如下表达式所界定的域|w1|2p1+|w2|2p2+…+|wn|2pn<det(I-Z)这里,1/p1,1/p2,…,1/pn-1都是正整数,pn是任意正实数,RII(p)是第二类典型域,Z∈RII(p).关键之处有两点1)给出了将此域的任一内点(W,Z)映为(W*,0)的全纯自同构群;2)引进了semi-Reinhardt域并给出了它的完备规范正交函数系.     

一类对称函数的Schur—几何凸性及Schur—调和凸性

Schur—凸函数在分析不等式、广义平均值、统计实验、图和矩阵、组合优化、可靠性、信息安全、随机排序和其它相关领域均有重要作用,故研究n元对称函数的Schur—凸性具有重要意义.在本文中,讨论了一类对称函数的Schur—凸性、Schur—几何凸性及Schur—调和凸性.     

第二类华罗庚域的Bergman核

论文以显式给出了第二类华罗庚域的Bergman核函数。关键之处有两点：一是给出了该域的全纯自同构群,该群的任一元素能把该域的形为（W1,W2,Z0）的点映为（W1^*,W2^*,0）;二是引进了semi-Reinhardt域的概念并求出了它的完备标准正交函数系。     

等差数列的凸性和对数凸性

研究了等差数列的凸性和对数凸性.进而利用受控理论证明了一些等差数列不等式.     

Bergman kernels on generalized Hua domains

The Bergman kernel functions with explicit formulas of the generalized Hua domains are obtained. And the holomorphic automorphism group for each generalized Hua domain is also given.     

Bergman kernel function on Hua construction of the fourth type

This paper introduces the Hua construction and presents the holomorphic automorphism group of the Hua construction of the fourth type.Utilizing the Bergman kernel function,under the condition of holomorphie automorphism and the standard complete or- thonormal system of the semi-Reinhardt domain,the infinite series form of the Bergman kernel function is derived.By applying the prop- erties of polynomial andΓfunctions,various identification relations of the aforementioned form are developed and the explicit formula of the Bergman kernel function for the Hua construction of the fourth type is obtained,which suggest that many of the previously-reported results are only the special cases of our findings.     

Bergman kernel function on Hua construction of the fourth type

This paper introduces the Hua construction and presents the holomorphic automorphism group of the Hua construction of the fourth type. Utilizing the Bergman kernel function, under the condition of holomorphic automorphism and the standard complete orthonormal system of the semi-Reinhardt domain, the infinite series form of the Bergman kernel function is derived. By applying the properties of polynomial and Γ functions, various identification relations of the aforementioned form are developed and the explicit formula of the Bergman kernel function for the Hua construction of the fourth type is obtained, which suggest that many of the previously-reported results are only the special cases of our findings.     

The comparison theorem for Bergman and Kobayashi metrics on Cartan-Hartogs domain of the second type

In this paper, the holomorphic sectional curvature under invariant metric on a Cartan-Hartogs domain of the second type YII(N,p,K) is presented and an invariant K?]lher metric which is complete and not less than the Bergman metric is constructed, such that its holomorphic sectional curvature is bounded above by a negative constant. Hence a comparison theorem for the Bergman and Kobayashi metrics on YII(N,p,K) is obtained.