On the asymptotic behaviour of capillary surfaces in cusps

Concus and Finn [2] discovered that capillary surfaces rise to infinity in corners with sufficiently small opening angle. They also found the leading term of an asymptotic expansion. Miersemann [5] improved this result to obtain a complete asymptotic expansion. In the present paper we will apply the methods of the above authors to discuss asymptotic behaviour of capillarities in cusps, which is a corner with opening angle 0. A large variety of asymptotic formulas will be provided. The general comparison theorem from Concus and Finn will play an important role in the proofs.     

临界超布朗运动的渐近行为

本文证明了在一般的初始测度下，Dawson所获得的临界超布朗运动的渐 近定理并不成立，对于一般分支特征的临界的超布朗运动以及一般寝始测度，本文获得了它的渐近行为的阶的两个估计。     

Three-parametric robot manipulators with parallel rotational axes

The paper deals with asymptotic motions of 3-parametric robot manipulators with parallel rotational axes. To describe them we use the theory of Lie groups and Lie algebras. An example of such motions are motions with the zero Coriolis accelerations. We will show that there are asymptotic motions with nonzero Coriolis accelerations. We introduce the notions of the Klein subspace, the Coriolis subspace and show their relation to asymptotic motions of robot manipulators. The asymptotic motions are introduced without explicit use of the Levi-Civita connection.     

Local asymptotic normality and asymptotical minimax efficiency of the MLE under random censorship

Here we study the problems of local asymptotic normality of the parametric family of distributions and asymptotic minimax efficient estimators when the observations are subject to right censoring. Local asymptotic normality will be established under some mild regularity conditions. A lower bound for local asymptotic minimax risk is given with respect to a bowl-shaped loss function, and furthermore a necessary and sufficient condition is given in order to achieve this lower bound. Finally, we show that this lower bound can be attained by the maximum likelihood estimator in the censored case and hence it is local asymptotic minimax efficient.     

Global existence of small solutions to nonlinear evolution equations

We study the global existence and asymptotic behaviour of “small” solutions of a large class of nonlinear partial differential equations. If the nonlinear terms are of high degree the solutions will be asymptotic to solutions of the linear equation.     

Third-order asymptotic expansion of <Emphasis Type="Italic">M</Emphasis>-estimators for diffusion processes

For an unknown parameter in the drift function of a diffusion process, we consider an M-estimator based on continuously observed data, and obtain its distributional asymptotic expansion up to the third order. Our setting covers the misspecified cases. To represent the coefficients in the asymptotic expansion, we derive some formulas for asymptotic cumulants of stochastic integrals, which are widely applicable to many other problems. Furthermore, asymptotic properties of cumulants of mixing processes will be also studied in a general setting.     

基于长偏置数据的一个光滑剩余生命函数估计量(英文)

受希勒引理的启发,针对长偏置数据给出一个带泊松权重的平均剩余生命函数的光滑估计量.同时研究了该光滑估计量的渐进性质,例如强相合性及渐进正态性等性质.     

Permanence and extinction in competitive Lotka–Volterra systems with delays

In this paper, a class of competitive Lotka–Volterra systems are considered that have distributed delays and constant coefficients on interaction terms and have time dependent growth rate vectors with an asymptotic average. Under the assumption that all proper subsystems are permanent, it is shown that the asymptotic behaviour of the system is determined by the relationship between an equilibrium and a nullcline plane of the corresponding autonomous system: if the equilibrium is below the plane then the system is permanent; if the equilibrium is above the plane then this species will go extinct in an exponential rate while the other species will survive. Similar asymptotic behaviour is also retained under an alternative assumption.     

Minimal compact global attractor for a damped semilinear wave equation

Abstract

The asymptotic behavior of eigenvalues of an elliptic operator with a divergence form is discussed. The coefficients of the operator are discontinuous through a boundary of a subdomain and degenerate to zero on the subdomain when a parameter tends to zero. We will prove that the eigenvalues approach eigenvalues of the Laplacian on the subdomain or on the complement. We will obtain precise asymptotic behavior of their convergence.     

Asymptotic existence theorems for frames and group divisible designs

In this paper, we establish an asymptotic existence theorem for group divisible designs of type mn with block sizes in any given set K of integers greater than 1. As consequences, we will prove an asymptotic existence theorem for frames and derive a partial asymptotic existence theorem for resolvable group divisible designs.     

On a singularly perturbed initial value problem in the case of a double root of the degenerate equation

We study the initial value problem of a singularly perturbed first order ordinary differential equation in case that the degenerate equation has a double root. We construct the formal asymptotic expansion of the solution such that the boundary layer functions decay exponentially. This requires a modification of the standard procedure. The asymptotic solution will be used to construct lower and upper solutions guaranteeing the existence of a unique solution and justifying its asymptotic expansion.     

Interpolatory integration rules and orthogonal polynomials with varying weights

We investigate which types of asymptotic distributions can be generated by the knots of convergent sequences of interpolatory integration rules. It will turn out that the class of all possible distributions can be described exactly, and it will be shown that the zeros of polynomials that are orthogonal with respect to varying weight functions are good candidates for knots of integration rules with a prescribed asymptotic distribution.Research supported by the Deutsche Forschungsgemeinschaft (AZ: Sta 299/4-2).     

基于极值理论的EXPAR时序模型异常点诊断

本文基于极值理论给出诊断EXPAR模型异常点检验统计量的渐近分布,并依此渐近分布来选取检验的临界值。这种方法选取的临界值可保证控制在一定显著性水平下,而且可以计算渐近p值,比仿真选取的临界值更科学合理。     

Asymptotic Expansion for the Null Distribution of the <Emphasis Type="Italic">F</Emphasis>-statistic in One-way ANOVA under Non-normality

In this paper we derive the asymptotic expansion of the null distribution of the F-statistic in one-way ANOVA under non-normality. The asymptotic framework is when the number of treatments is moderate but sample size per treatment (replication size) is small. This kind of asymptotics will be relevant, for example, to agricultural screening trials where large number of cultivars are compared with few replications per cultivar. There is also a huge potential for the application of this kind of asymptotics in microarray experiments. Based on the asymptotic expansion we will devise a transformation that speeds up the convergence to the limiting distribution. The results indicate that the approximation based on limiting distribution are unsatisfactory unless number of treatments is very large. Our numerical investigations reveal that our asymptotic expansion performs better than other methods in the literature when there is skewness in the data or even when the data comes from a symmetric distribution with heavy tails.     

Asymptotic properties of groups acting on complexes

We examine asymptotic dimension and property A for groups acting on complexes. In particular, we prove that the fundamental group of a finite, developable complex of groups will have finite asymptotic dimension provided the geometric realization of the development has finite asymptotic dimension and the vertex groups are finitely generated and have finite asymptotic dimension. We also prove that property A is preserved by this construction provided the geometric realization of the development has finite asymptotic dimension and the vertex groups all have property A. These results naturally extend the corresponding results on preservation of these large-scale properties for fundamental groups of graphs of groups. We also use an example to show that the requirement that the development have finite asymptotic dimension cannot be relaxed.

     

Navier and Stokes meet Poincare and Dulac

This paper surveys various precise (long-time) asymptotic results for the solutions of the Navier-Stokes equations with potential forces in bounded domains. It turns out that the asymptotic expansion leads surprisingly to a kind of Poincare-Dulac normal form of the Navier-Stokes equations. We will also discuss some related results and a few open issues.     

Asymptotics for the ratio and the zeros of multiple Charlier polynomials

We investigate multiple Charlier polynomials and in particular we will use the (nearest neighbor) recurrence relation to find the asymptotic behavior of the ratio of two multiple Charlier polynomials. This result is then used to obtain the asymptotic distribution of the zeros, which is uniform on an interval. We also deal with the case where one of the parameters of the various Poisson distributions depends on the degree of the polynomial, in which case we obtain another asymptotic distribution of the zeros.     

一类函数增量的局部渐近性质

文章研究了一类函数增量的局部渐近性质,发现这类函数增量的局部渐近性对于一元实函数,二元及多元实函数,向量值函数和复函数在一定条件下都会保持不变,进而提出了两个相关的猜想:此类函数增量的渐近性是关于函数变换的拓扑不变量。     

Asymptotic independence of ‘pure head’ stopping times

The asymptotic independence and exponentiality of ‘pure head run’ stopping times will be proved.     

Asymptotic analysis for linear difference equations

We are concerned with asymptotic analysis for linear difference equations in a locally convex space. First we introduce the profile operator, which plays a central role in analyzing the asymptotic behaviors of the solutions. Then factorial asymptotic expansions for the solutions are given quite explicitly. Finally we obtain Gevrey estimates for the solutions. In a forthcoming paper we will develop the theory of cohomology groups for recurrence relations. The main results in this paper lay analytic foundations of such an algebraic theory, while they are of intrinsic interest in the theory of finite differences.