A TAILORED FINITE POINT METHOD FOR THE HELMHOLTZ EQUATION WITH HIGH WAVE NUMBERS IN HETEROGENEOUS MEDIUM

In this paper, we propose a tailored-finite-point method for the numerical simulation of the Helmholtz equation with high wave numbers in heterogeneous medium. Our finite point method has been tailored to some particular properties of the problem, which allows us to obtain approximate solutions with the same behaviors as that of the exact solution very naturally. Especially, when the coefficients are piecewise constant, we can get the exact solution with only one point in each subdomain. Our finite-point method has uniformly convergent rate with respect to wave number k in L^2-norm.     

On generalized Erd?s spaces

During the last years both Erd?s space and complete Erd?s space were topologically characterized by Dijkstra and van Mill. Applications include results about Erd?s type spaces in ?p-spaces as well as results about Polishable ideals on ω. We present an unifying theorem in terms of sets with a reflexive relation that among other things contains these apparently dissimilar results as special cases.     

指数型二分性和周期系统的周期解

先讨论指数型二分性成立的条件，在某种意义下推广了Ｌａｚｅｒ关于二分性的结果，之后，我们用该结论探讨Ｌａｓｏｔａ－Ｏｐｉｕｌ方程及方程ｘ＝ｆ（ｔ，ｘ），ｆ（ｔ＋ｗ，ｘ）＝ｆ（ｔ，ｘ），ｆ（ｔ，ｘ）∈Ｃ’（Ｒ＊Ｒ＾ｎ，Ｒ＾ｎ）的周期解的存在性，推广了文「２」的主要结果，并得到一些新的结果。     

Finite-size effects in the self-organized critical forest-fire model

We study finite-size effects in the self-organized critical forest-fire model by numerically evaluating the tree density and the fire size distribution. The results show that this model does not display the finite-size scaling seen in conventional critical systems. Rather, the system is composed of relatively homogeneous patches of different tree densities, leading to two qualitatively different types of fires: those that span an entire patch and those that do not. As the system size becomes smaller, the system contains less patches, and finally becomes homogeneous, with large density fluctuations in time. Received 24 April 1999 and Received in final form 26 October 1999     

一类非线性多重调和方程△~mu=f(|x|,u,|u|)的正整解

本文建立了一类Ｒｎ（ｎ≥３）中非线性多重调和方程△~ｍｕ＝ｆ（|ｘ|，ｕ，|(ｕ|）（ｍ≥２）正 的径向对称整体解的存在性定理，并给出了解的有关性质，推广了文［１］－［４］的有关结果．     

Existence of multiple fixed points for nonlinear operators and applications

In this paper, by the fixed point index theory, the number of fixed points for sublinear and asymptotically linear operators via two coupled parallel sub-super solutions is studied. Under suitable conditions, the existence of at least nine or seven distinct fixed points for sublinear and asymptotically linear operators is proved. Finally, the theoretical results are applied to a nonlinear system of Hammerstein integral equations.     

线性过程的强逼近和重对数律

本文讨论由独立同分布随机变量列产生的线性过程的泛函型重对数律和强逼近, 同时又给出由NA随机变量列产生的线性过程的重对数律.     

无穷方差厚尾过程变点的小波估计

研究随机设计下噪声为厚尾随机变量时非参数函数中的变点估计问题.首先,通过设计变换将随机设计转化为等间距固定设计,进而利用小波方法估计变换后的变点的位置,再利用逆设计变换求得随机设计下变点位置的估计,并给出估计的收敛速度.模拟研究结果说明对于无穷方差厚尾过程中的变点估计问题小波方法是有效的.     

Extreme value distribution of a recursive-type detector in a linear model

We study a CUSUM–type monitoring scheme designed to sequentially detect changes in the regression parameter of an underlying linear model. The test statistic used is based on recursive residuals. Main aim of this paper is to derive the limiting extreme value distribution under the null hypothesis of structural stability. The model assumptions are flexible enough to include rather general classes of error sequences such as augmented GARCH(1,1) processes. The result is underlined by an illustrative simulation study. Research partially supported by NSF grants DMS–0604670 and DMS–065242.     

一类新的解析函数族

定义了一族解析函数B(λ,α,β),导出该族中函数的积分表达式;借助算子理论建立B(λ,α,β)的包含关系,讨论端点性质;由此推出族中函数的偏差定理.