Hua operators and Poisson transform for bounded symmetric domains

Let Ω be a bounded symmetric domain of non-tube type in Cn with rank r and S its Shilov boundary. We consider the Poisson transform Psf(z) for a hyperfunction f on S defined by the Poisson kernel Ps(z,u)=s(h(z,z)^n/r/²|h(z,u)^n/r|), (z,u)×Ω×S, s∈C. For all s satisfying certain non-integral condition we find a necessary and sufficient condition for the functions in the image of the Poisson transform in terms of Hua operators. When Ω is the type I matrix domain in Mn,m(C) (n?m), we prove that an eigenvalue equation for the second order Mn,n-valued Hua operator characterizes the image.     

中国现代数学家寿命分析

根据 2 1 2位中国现代数学家 (1 1 7位逝世 )的生存资料进行分析 ,得到如下结果 . 62位院士的期望寿命为 84.68岁 ,标准误差为 1 .96岁 ;1 5 0位非院士数学家的期望寿命为 79.2 6岁 ,标准误差为 1 .1 3岁 .院士和非院士数学家的寿命差异有显著性意义 (P =0 .0 5 ) .分别给出了院士和非院士数学家两个群体的寿命表 .结论 :中国现代数学家属于长寿之列 .脑部疾病、心脏疾病和癌症为数学家的主要死因 .     

Bergman kernel function on the third Hua Construction

The Bergman kernel function for Hua Construction of the third type is given in an explicit formula.     

The Einstein-K(a)hler metric on Hua construction of the first type

Let HCI be the Hua construction of the first type. We describe the EinsteinKahler metric for HCI. We reduce the Monge-Ampère 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.     

第三类华罗庚域的Bergman核函数

本文主要是计算第三类华罗庚域的Bergman核函数的显式表达式.由于华罗庚域既不是齐性域又不是Reinhardt域,故以往求Bergman核函数的方法都行不通.本文用新的方法进行计算.关键之处有两点:一是给出第三类华罗庚域的全纯自同构群,群中每一元素将形为(W,Z0)的内点映为点(W*,0);二是引进了semi—Reinhardt的概念并求出了其完备标准正交函数系.     

Approximate analytical versus numerical solutions of Schrödinger equation under molecular Hua potential

We solve the D‐dimensional Schrödinger equation under the Hua potential by using a Pekeris‐type approximation and the supersymmetry quantum mechanics. The reliability of the spectrum is checked via a comparison with the finite difference method. This interaction resembles Eckart, Morse, and Manning–Rosen potentials. Some useful quantities are reported via the Hellmann–Feynman Theorem. © 2012 Wiley Periodicals, Inc.     

The rotation‐vibration spectrum of diatomic molecules with the tietz‐hua rotating oscillator

The Tietz‐Hua (TH) potential is one of the very best analytical model potentials for the vibrational energy of diatomic molecules. By using the Nikiforov‐Uvarov method, we have obtained the exact analytical s‐wave solutions of the radial Schrödinger equation for the TH potential. The energy eigenvalues and the corresponding eigenfunctions are calculated in closed forms. Some numerical results for diatomic molecules are also presented. © 2011 Wiley Periodicals, Inc. Int J Quantum Chem, 2011     

The rotation–vibration spectrum of diatomic molecules with the Tietz–Hua rotating oscillator and approximation scheme to the centrifugal term

The Tietz–Hua (TH) potential is one of the very best analytical model potentials for the vibrational energy of diatomic molecules. By using the Nikiforov–Uvarov method and Pekeris approximation to the centrifugal term, we have obtained the solutions of the radial Schrödinger equation for the TH potential. The energy eigenvalues and corresponding eigenfunctions are calculated in closed form. Some remarks and numerical results are also presented for some diatomic molecules.     

Bergman kernel on generalized exceptional hua domain

We have computed the Bergman kernel functions explicitly for two types of generalized exceptional Hua domains, and also studied the asymptotic behavior of the Bergman kernel function of exceptional Hua domain near boundary points, based on Appell's multivariable hypergeometric function.     

On applied mathematics

This paper covers some aspects, problems, and episodes of applied mathematics intended to be enjoyable, instructive, and advisory to the young.