New classes of domains with explicit Bergman kernel

We introduce two classes of egg type domains, built on general bounded sym-metric domains, for which we obtain the Bergman kernel in explicit formulas. As an aux-iliary tool, we compute the integral of complex powers of the generic norm on a boundedsymmetric domains using the well-known integral of Selberg. This generalizes matrix in-tegrals of Hua and leads to a special polynomial with integer or half-integer coefficientsattached to each irreducible bounded symmetric domain.     

Cn中有界域的Bergman核函数的零点问题

多复变数空间Cn中有界域的Bergman核函数的零点问题集中表现为陆启铿猜想.陆启铿猜想是波兰数学家M.Skwarczynski对陆启铿1966年的一篇文章中关于Bergman核函数的零点问题而命名的,至今已经40年了.该猜想已写入了多复变函数论的多本专著,引起很多数学家的兴趣而研究之,已经成为多复变函数论中的一个活跃的研究方向.本文简述了陆启铿猜想的最初含意,综述了迄今为止关于有界域的Bergman核函数有无零点的各种研究成果以及所用的思想和方法.特别对近来出现的陆启铿猜想的新研究领域进行了较详细的阐述并在最后提出了关于陆启铿猜想的6个Open Problems,希望国内的年轻数学家对陆启铿猜想感到兴趣而研究之.     

有界域的Bergman核函数显式表示的最新进展

对多维复数空间的有界域，如何求出它的Bergman核函数的显表达式，是多复变研究中的一个重要方向。本文综述了迄今为止的所有重要结果以及方法上的进展，特别对新近引进的华罗域，综述了它们的Bergman核函数的显表达式及其计算方法上的创新。     

华罗庚与爱因斯坦相对论及其扩展——纪念华罗庚诞辰一百周年

华罗庚先生运用矩阵几何与投影几何,研究并简化了爱因斯坦狭义相对论的基本原理,得到惯性运动的对称性,并促进了对德西特不变的狭义相对论的研究.他的深入考察至今仍引领着我们如何面对精确宇宙学的挑战.爱因斯坦相对论作为以宇宙常数Λ>0为特征的宇观物理学的基础面临疑难.相对性原理应该扩充到具有两个不变普适常数c和l,具有24个生成元的惯性运动对称性的相对性原理.于是,存在庞加莱、德西特和反德西特不变的3种相对论,伴随着对偶庞加莱运动学,它们构成相对论三位一体.取……,德西特相对论提供宇观尺度之新运动学,亦可避开相对性的宇宙佯谬.华老不仅是大数学家,而且是大思想家和大教育家,是一位为复兴中华民族而奉献终身的伟大代表.     

Polygonatone H,a new homoisoflavanone with cytotoxicity from Polygonatum Cyrtonema Hua.

A new homoisoflavonoid, (3R)-5,7-dihydroxy-6-methyl-3-(2′-hydroxy-4′-methoxybenzyl)-chroman-4-one (1), namely polygonatone H, in addition to fourteen known homoisoflavones (2–15) were isolated from the rhizome of Polygonatum Cyrtonema Hua. The structures were identified with the aid of 1D/2D NMR spectroscopic technologies. Compounds 2, 6, 8, 10, 11, 13, and 15 were isolated from P. Cyrtonema for the first time. Compound 1 showed cytotoxicities to human cancer cell lines with IC₅₀ values to comparable those of cisplatin.     

关于“华罗庚-王中烈型不等式”一文的注记

指出了［１］的定理２中的一个错误,推广了［１］中定理１给出的华罗庚－王中烈型不等式,避开控制不等式与动态规划模型等专门工具,改用较为初等的平均值不等式证明之,使改正后的［１］中的定理２成其推论     

Diastereoselective α-Alkylation of β-Amino Esters: Preparation of Novel α-Substituted β-Amino Esters from α-Amino Acids

b-Amino acids and their derivatives have attracted considerable attention in recent years due to their occurrence in biologically active natural products, such as dolastatins 11, cyclohexylnorstatine 22 and taxol 33. bAmino acids also find application in the synthesis of blactams4, piperidines5, indolizidines6. Moreover, the peptides consisting of bamino acids, the so called bpeptides, have been extensively studied recently7. Consequently, considerable efforts have been directed to the synt…     

小化的诗歌王国之旅

This short novel combines the romantic poetry with the rigorous chemistry through Xiao Hua's journey to the kingdom of poetry. It elaborates the wonderful and useful chemistry via what Xiao Hua saw, heard, felt in the kingdom of poetry, helping people appreciate the beauty of chemistry and motivate students to learn and research chemistry. It also expresses that scientists may achieve success if they take the correct methods and pay persistent efforts in the scientific research.     

The Einstein-Khler metric on Hua construction of the first type

Let HCI be the Hua construction of the first type. We describe the Einstein-Kahler metric for HCI. We reduce the Monge-Ampere equation for the metric to an ordinary differential equation in the auxiliary function X(z,w,ζ). This differential equation can be solved to give an implicit function in x(z,w,ζ). For some cases, we obtained the solution of the differential equation and the explicit forms of the complete Einstein-Kahler metrics on HCI which are the non-homogeneous domains.     

Hua operator on vector bundle: Application to AdS/CFT correspondence of Dirac fields

Hua’s theory of harmonic functions on classical domains is generalized to the theory on holomorphic vector bundles over classical domains and further on vector bundles over the real classical domains and quaternion classical domains. In case of the simplest quaternion classical domain there is a relation between Hua operator and Dirac operator, by which an AdS/CFT correspondence of Dirac fields is established.