Further improved recursions for a class of compound Poisson distributions

In the present paper we develop more efficient recursive formulae for the evaluation of the t-order cumulative function Γ^th(x) and the t-order tail probability Λ^th(x) of the class of compound Poisson distributions in the case where the derivative of the probability generating function of the claim amounts can be written as a ratio of two polynomials. These efficient recursions can be applied for the exact evaluation of the probability function (given by De Pril [De Pril, N., 1986a. Improved recursions for some compound Poisson distributions. Insurance Math. Econom. 5, 129-132]), distribution function, tail probability, stop-loss premiums and t-order moments of stop-loss transforms of compound Poisson distributions. Also, efficient recursive algorithms are given for the evaluation of higher-order moments and r-order factorial moments about any point for this class of compound Poisson distributions. Finally, several examples of discrete claim size distributions belonging to this class are also given.     

Uniform asymptotics of some q-orthogonal polynomials

Uniform asymptotic formulas are obtained for the Stieltjes-Wigert polynomial, the q⁻¹-Hermite polynomial and the q-Laguerre polynomial as the degree of the polynomial tends to infinity. In these formulas, the q-Airy polynomial, defined by truncating the q-Airy function, plays a significant role. While the standard Airy function, used frequently in the uniform asymptotic formulas for classical orthogonal polynomials, behaves like the exponential function on one side and the trigonometric functions on the other side of an extreme zero, the q-Airy polynomial behaves like the q-Airy function on one side and the q-Theta function on the other side. The last two special functions are involved in the local asymptotic formulas of the q-orthogonal polynomials. It seems therefore reasonable to expect that the q-Airy polynomial will play an important role in the asymptotic theory of the q-orthogonal polynomials.     

高分子溶液气液平衡的测定与关联

采用静态蒸气吸收法测定了在308.15K时苯，甲苯与聚乙烯（PS），聚甲基丙烯酸甲酯（PMMA），聚醋酸乙烯酯（PVAc)构成的6个单溶剂-高分子系统的气液平衡数据，用UNIQUAC活度系数模型和链状流体状态方程对实验数据进行了关联。     

颗粒堵塞与滤液侵入地层的数学模型初探

本文在分析、研究额杜及滤液侵入孔隙机理的基础上,对颗粒及滤液在静态、动态条件下侵入地层而使地层受到损害的一维、二维数学模型进行了研完,建立了各种井下条件的数学模型,并结合室内实验时模型进行了验证。     

Toward Verification of the Riemann Hypothesis: Application of the Li Criterion

We substantially apply the Li criterion for the Riemann hypothesis to hold. Based upon a series representation for the sequence {λ_k}, which are certain logarithmic derivatives of the Riemann xi function evaluated at unity, we determine new bounds for relevant Riemann zeta function sums and the sequence itself. We find that the Riemann hypothesis holds if certain conjectured properties of a sequence η_j are valid. The constants η_j enter the Laurent expansion of the logarithmic derivative of the zeta function about s=1 and appear to have remarkable characteristics. On our conjecture, not only does the Riemann hypothesis follow, but an inequality governing the values λ_n and inequalities for the sums of reciprocal powers of the nontrivial zeros of the zeta function. Mathematics Subject Classification (2000) 11M26.     

陕西关中地区城市群特征的分析与讨论

陕西关中地区城市群的特征包括该群组的时间尺度、空间分布、规模等级和职能分工。本文从城市群特征与关中地区经济协调发展与相互影响的角度出发,讨论了城市群发展方向及调整意见。     

从隋唐时期宫廷燕乐的发展看中国传统音乐的传承与演变

宫廷燕乐是中国传统音乐发展史上不可缺少的重要组成部分,它曾在隋唐时期达到空前的辉煌.隋唐时期的宫廷燕乐其形式之复杂,其涉及到的地域风格之多样,是从古至今不可多见的.追溯其产生的源头,观察其后世之演变,能够直接地我们研究传统音乐的流变提供启示.     

p-Adic Schrödinger-type operator with point interactions

A p-adic Schrödinger-type operator Dα+VY is studied. Dα (α>0) is the operator of fractional differentiation and (bij∈C) is a singular potential containing the Dirac delta functions δx concentrated on a set of points Y={x₁,…,xn} of the field of p-adic numbers Qp. It is shown that such a problem is well posed for α>1/2 and the singular perturbation VY is form-bounded for α>1. In the latter case, the spectral analysis of η-self-adjoint operator realizations of Dα+VY in L₂(Qp) is carried out.     

Pseudoprime factorizations of integer matrices

We give a method of factoring integer matrices in into components such that the factorization is not unique unless certain information is known. In Section 2, we introduce this method of factorization and provide theorems which establish its well-definedness. In Section 3, we construct a matrix in as a product of specific types of matrices and establish an algorithm for factoring the result uniquely given an amount of information.     

试论公孙大娘剑器舞的道具、套路及其在舞蹈史上的地位

利用历史文献资料,结合体育舞蹈教学的专业技术,对杜甫《观公孙大娘弟子舞剑器行》诗中所谓"公孙大娘剑器舞"的道具、套路及其在中国舞蹈史上的地位作初步探讨。认为公孙大娘剑器舞是一种女子戎装持剑表演的健舞,公孙大娘表演的剑器舞至少有四个套路,即剑器浑脱、西河剑器、邻里曲与裴将军满堂势,并从她成就了"草圣"张旭的书法艺术及其在中国舞蹈历史上的崇高地位来肯定公孙大娘剑器舞的深远影响。