关于级数敛散性的积分判别法的一个新证明及其推广

给出了现行的数学分析 ,微积分与高等数学的教材中的数值级数敛散性的积分判别法的一个新证明 ,获得了这个判别法的一个推广 ,由此得到一批渐近公式与命题     

初等函数Taylor级数的向量形式(英文)

推广了初等函数 Taylor级数的向量形式的一些结果 ,所考虑的初等函数 Taylor级数的向量形式涉及了三个复向量 .给出了在二阶常微分方程初值问题中的一个应用 .     

Probability Measures on Dual Objects to Compact Symmetric Spaces and Hypergeometric Identities

We derive, in several different ways, combinatorial identities which are multidimensional analogs of classical Dougall's formula for a bilateral hypergeometric series of the type ₂H₂. These identities have a representation-theoretic meaning. They make it possible to construct concrete examples of spherical functions on inductive limits of symmetric spaces. These spherical functions are of interest to harmonic analysis.     

Resampling time series using missing values techniques

Several techniques for resampling dependent data have already been proposed. In this paper we use missing values techniques to modify the moving blocks jackknife and bootstrap. More specifically, we consider the blocks of deleted observations in the blockwise jackknife as missing data which are recovered by missing values estimates incorporating the observation dependence structure. Thus, we estimate the variance of a statistic as a weighted sample variance of the statistic evaluated in a “complete” series. Consistency of the variance and the distribution estimators of the sample mean are established. Also, we apply the missing values approach to the blockwise bootstrap by including some missing observations among two consecutive blocks and we demonstrate the consistency of the variance and the distribution estimators of the sample mean. Finally, we present the results of an extensive Monte Carlo study to evaluate the performance of these methods for finite sample sizes, showing that our proposal provides variance estimates for several time series statistics with smaller mean squared error than previous procedures.     

Relations Between the Ranks and Cranks of Partitions

New identities and congruences involving the ranks and cranks of partitions are proved. The proof depends on a new partial differential equation connecting their generating functions.     

时间序列分解预测法及周期因素的探讨

本文运用时间序列分解预测法，分析门诊人次的变动规律，预测了季度门诊人次。本法与移动平均比率预测法相比，预测精度提高３１％。本文还探讨了时间序列分解预测的周期因素等有关问题。     

On the Maximum of the Modulus and the Maximal Term of Dirichlet Series

For the Dirichlet series, we obtain a condition on the exponents for which the logarithms of the maximum of the modulus of its sum and of the maximal term are equivalent to the same convex function.     

An Extremum Problem for Periodic Functions with Small Support

Mathematical Notes -     

Solutions globales d'un problème de Cauchy linéaire

On résoud le problème de Cauchy pour des opérateurs aux dérivées partielles à coefficients polynomiaux par rapport aux variables d'espace dans des classes de Gevrey projectives. Nos résultats sont des versions globales du théorème de Cauchy-Kowalewski et du théorème de Nagumo.