多复变数的二阶微分从属

在文[1－2]的基础上讨论了多复变数中的二阶微分从属，取得了一些结果。这些结果是文[1-5]中的一些结果的推广。     

On the size of multivariate polynomial lemniscates and the convergence of rational approximants

In a previous paper, the author introduced a class of multivariate rational interpolants, which are called optimal Padé-type approximants (OPTA). The main goal of this paper is to extend classical results on convergence both in measure and in capacity of sequences of Padé approximants to the multivariate case using OPTA. To this end, we obtain some estimations of the size of multivariate polynomial lemniscates in terms of the Hausdorff content, which we also think are of some interest.     

Clifford分析中奇异积分的Poincaré-Bertrand置换公式

借助于多元复分析的思想，本文证明了Ｃｌｉｆｏｒｄ分析中奇异积分的Ｐｏｉｎｃａｒé－Ｂｅｒｔｒａｎｄ置换公式．     

多日神话原型及寓意探析

中华文化圈有着丰富的太阳母题神话。多日神话乃其中之经典篇章。完整的多日神话包括生日、多日和征日三部分。古代典籍中均仅存片断,各民族传说中保存得相对完整。对于多日神话原型和寓意的阐释,“酷热干旱说”、“十干历法说”、“诸日部族称王说”等都不够圆满。其实,这个神话保存了古代先民的原始记忆,是对远古时代“幻日”这种自然天象的一种幻想性解释。最新的“多日并出”现象为之提供有力的证据。这个神话的深刻寓意则与原始宗教有关,它折射出我国古代先民自然崇拜中的日神信仰。     

Banzhaf Measures for Games with Several Levels of Approval in the Input and Output

An axiomatic characterization of ‘a Banzhaf score’ notion is provided for a class of games called (j,k) simple games with a numeric measure associated to the output set, i.e., games with n players, j ordered qualitative alternatives in the input level and k possible ordered quantitative alternatives in the output. Three Banzhaf measures are also introduced which can be used to determine a player's ‘a priori’ value in such a game. We illustrate by means of several real world examples how to compute these measures. Research partially supported by Grant BFM 2003-01314 of the Science and Technology Spanish Ministry and the European Regional Development Fund.     

两险种广义复合Poisson风险模型下的破产概率

广义复合Poisson风险模型被推广到两险种广义复合Poisson风险模型,并给出了理赔额分别服从指数和混合指数分布且初始资金为u的破产概率ψ（ u）的明确表达式以及安全系数。     

Solutions globales de certaines équations de Fuchs non linéaires dans les espaces de Gevrey

We consider nonlinear partial differential equations with several Fuchsian variables of type , where is a Fuchsian principal part of weight zero. We prove existence and uniqueness of a global solution to this problem in the space of holomorphic functions with respect to the Fuchsian variable and in Gevrey spaces with respect to the other variable . The method of proof is based on the application of the fixed point theorem in some Banach algebras defined by majorant functions that are suitable to this kind of equation.

     

An interpolation formula of the derivatives of higher order

ＡＮＩＮＴＥＲＰＯＬＡＴＩＯＮＦＯＲＭＵＬＡＯＦＴＨＥＤＥＲＩＶＡＴＩＶＥＳＯＦＨＩＧＨＥＲＯＲＤＥＲＧｕｉＺｕ－ｈｕａ（桂祖华）（ＴｈｅＤｅｐａｒｔｍｅｎｔｏｆＡｐｐｌｉｅｄＭａｔｈｅｍａｔｉｃｓ,ＳｈａｎｇｈａｉＪｉａｏｔｏｎｇＵｎｉｖｅｒｓｉｔ...     

Properties of some families of hypergeometric orthogonal polynomials in several variables

Limiting cases are studied of the Koornwinder-Macdonald multivariable generalization of the Askey-Wilson polynomials. We recover recently and not so recently introduced families of hypergeometric orthogonal polynomials in several variables consisting of multivariable Wilson, continuous Hahn and Jacobi type polynomials, respectively. For each class of polynomials we provide systems of difference (or differential) equations, recurrence relations, and expressions for the (squared) norms of the polynomials in question.