一类龙虾树优美

本文使用交错的与非交错的标号法,证明了一类龙虾树优美。     

A Counterexample to a Generalized Saari's Conjecture with a Continuum of Central Configurations

In this paper we show that in the n-body problem with harmonic potential one can find a continuum of central configurations for n= 3. Moreover we show a counterexample to an interpretation of Jerry Marsden Generalized Saari's conjecture. This will help to refine our understanding and formulation of the Generalized Saari's conjecture, and in turn it might provide insight in how to solve the classical Saari's conjecture for n≥ 4. This revised version was published online in July 2006 with corrections to the Cover Date.     

有关Gorenstein投射猜想的一个注记

证明了对一个Artinian代数A,如果它的左有限维数或右有限维数有限,则A满足Gorenstein投射猜想.由此可知,Gorenstein代数和表示维数小于等于3的代数上的Gorenstein投射猜想是成立的.     

关于Win猜想的两个结果

设G是2n个顶点的简单图,k为不小于-1的整数,若G中每一对不相邻的顶点u和v,都有d(u)+d(v)≥2n+k,则称G为Ore k-型图。S.Win^[1]给出下面的猜想:若G是Ore k-型图,则G有k+2个边不相交的1-因子。其中k≤2n-4。本文证明了k=2n-4和k=2n-5时Win猜想是成立的。     

The Characterization Problem for Isotropic Covariance Functions

Isotropic covariance functions are successfully used to model spatial continuity in a multitude of scientific disciplines. Nevertheless, a satisfactory characterization of the class of permissible isotropic covariance models has been missing. The intention of this note is to review, complete, and extend the existing literature on the problem. As it turns out, a famous conjecture of Schoenberg (1938) holds true: any measurable, isotropic covariance function on ^d (d 2) admits a decomposition as the sum of a pure nugget effect and a continuous covariance function. Moreover, any measurable, isotropic covariance function defined on a ball in ^d can be extended to an isotropic covariance function defined on the entire space ^d .     

Saari’s conjecture for the restricted three-body problem

Saari’s conjecture adapted to the restricted three-body problem is proven analytically using BKK theory. Specifically, we show that it is not possible for a solution of the planar, circular, restricted three-body problem to travel along a level curve of the amended potential function unless it is fixed at a critical point (one of the five libration points.) Due to the low dimension of the problem, our proof does not rely on the use of a computer.     

滑坡影响因素的效果测度分析

滑坡做为一种主要的地质灾害类型，灾域广，灾情重，灾频高，与其它地质灾害相比有显著特点。深重的滑坡灾害，不仅给人民生命财产造成严重损失，也成为阻碍国民经济发展的一大制约因素。研究其产生的影响因素与分类，对此地质灾害的防治具有重要的理论意义与经济价值。效果测度分析方法具有系统因素分析与样本分类双重功能，是一种简便易于操作的信息数据分析评价决策方法，在环境保护、减灾对策和灾害评价等方面应用很广。本文将效果测度分析方法应用于滑坡影响因素与分类的量化分析，力求对地质灾害的防治理论与技术方法做出有意义的贡献。     

The Evolution of the Stable and Unstable Manifold of an Equilibrium Point

We consider the evolution of the stable and unstable manifolds of an equilibrium point of a Hamiltonian system of two degrees of freedom which depends on a parameter,ν. The eigenvalues of the linearized system are complex for ν < 0 and purely imaginary for ν > 0. Thus for ν < 0 the equilibrium has a two‐dimensional stable manifold and a two‐dimensional unstable manifold, but for ν > 0 these stable and unstable manifolds are gone. We study the system defined by the truncated generic normal form in this situation. One of two things happens depending on the sign of a certain quantity in the normal form expansion. In one case the two families detach as a single invariant manifold and recedes from the equilibrium as ν tends away from 0 through positive values. In the other case the stable and unstable manifold are globally connected for ν < 0 and the whole structure of these manifolds shrinks to the equilibrium as ν → 0 and disappears. These considerations have interesting implications about Strömgren's conjecture in celestial mechanics and the blue sky catastrophe of Devaney.