纪念陈建功教授诞辰一百周年

陈建功教授是我国近代数学的奠基人之一,是我国分析数学许多分支的拓荒者和学术带头人,在国内外享有很高的声誉.本文概括了陈建功教授的学术成就,并对其最重要的成果作了系统的、全面的介绍.陈建功教授又是一位杰出的教育家,本文扼要地阐述了他的教育思想和成就.     

一类华氏宏观经济数学模型的均衡增长路径

利用非负矩阵最大特征值及非负特征向量的存在性和特征值的取值范围,研究一类华氏宏观经济数学模型的均衡增长路径.证明了无论直接消耗系数矩阵是否是不可约的,一类华氏宏观经济数学模型存在均衡增长解的必然性,并给出了模型的均衡增长解.说明在实际生产中相对于本部门总投入,当本部门的生产消耗掉本部门产品数量较少时,经济系统稳定增长.     

第四类华罗庚域的Bergman核函数

本文给出了第四类华罗庚域H EIV上的Bergman核函数,全纯自同构群以 及semi—Reinhardt域上的完备标准正交函数系.     

Remarks on Hua’s matrix equality involving generalized inverses

In this note, some necessary and sufficient conditions for Hua’s matrix equality involving generalized inverses to hold are presented.     

Chemical characterization of constituents from Polygonatum cyrtonema Hua and their cytotoxic and antioxidant evaluation

Abstract

Twenty-four compounds were isolated from the roots of Polygonatum cyrtonema Hua, including a new octopamine dimer, named trans-bis(N-feruloyl)octopamine (1). The structure was established on the basis of spectroscopic and chemical methods. All the extracts and compounds were evaluated for cytotoxic and antioxidant activities by using MTT and chemiluminescence assay. The extracts showed activity against MCF-7 and HepG-2 cell lines from IC₅₀ 0.30 to 1.01 mg mL^?1. Compound 3 exhibited activity against HepG-2 cell lines with IC₅₀ 8.99?μM. Compound 7 exhibited activity against Hela cell lines with IC₅₀ 2.53?μM and BGC-823 cell lines with IC₅₀ 7.77?μM. Moreover, compound 7 showed antioxidant with IC₅₀ 12?µM compared to the positive control with IC₅₀ 77?µM. Compound 16 exhibited activity against HepG-2 cell lines with IC₅₀ 1.05?μM and MCF-7 cell lines with IC₅₀ 1.89?μM. These results indicated that this plant might be potential in natural medicine and healthy food.     

Bergman kernel function on Hua Construction of the second type

In this paper, we give an explicit formula of the Bergman kernel function on Hua Construction of the second type when the parameters 1/p1,…,1/(pr-1) are positive integers and 1/pr is an arbitrary positive real number.     

Extremal problems on the Hua domain of the first type

In this paper we study some extremal problems between the Hua domain of the first type and the unit ball.     

一个行列式不等式的进一步研究

本文的日的在于改进已有的两个复矩阵的行列式的上界,以更精细的两个Hermitian正定矩阵和的行列式为基本工具.利用得到的相关一无二次不等式描述的行列式之间的关系,给出了两个复矩阵和的行列式新上界,作为心用可改进华罗庚行列式不等式的上界.     

华罗庚

为了让广大读者了解华罗庚先生传奇的一生,本刊特从中国数学会网站转载此文.由于受篇幅所限,本刊略去了原文中关于华罗庚先生在数论、代数与几何、复分析方面工作成就的介绍,另外增补了部分参考文献.关键词及文后的英文信息亦为编者所加.     

Dealing with the shifted and inverted Tietz–Hua oscillator potential using the J‐matrix method

The tridiagonal J‐matrix approach has been used to calculate the low and moderately high‐lying eigenvalues of the rotating shifted Tietz–Hua (RSTH) oscillator potential. The radial Schrödinger equation is solved efficiently by means of the diagonalization of the full Hamiltonian matrix, with the Laguerre or oscillator basis. Ro–vibrational bound state energies for 11 diatomic systems, namely , , , NO, CO, , , , , , and NO⁺, are calculated with high accuracy. Some of the energy states for molecules are reported here for the first time. The results of the last four molecules have been introduced for the first time using the oscillator basis. Higher accuracy is achieved by calculating the energy corresponding to the poles of the S‐matrix in the complex energy plane using the J‐matrix method. Furthermore, the bound states and the resonance energies for the newly proposed inverted Tietz–Hua IRSTH‐potential are calculated for the H₂‐molecule with scaled depth. A detailed analysis of variation of eigenvalues with n, quantum numbers is made. Results are compared with literature data, wherever possible. © 2015 Wiley Periodicals, Inc.