Finite-dimensional global attractors in Banach spaces

We provide bounds on the upper box-counting dimension of negatively invariant subsets of Banach spaces, a problem that is easily reduced to covering the image of the unit ball under a linear map by a collection of balls of smaller radius. As an application of the abstract theory we show that the global attractors of a very broad class of parabolic partial differential equations (semilinear equations in Banach spaces) are finite-dimensional.     

多元协方差阵扰动模型岭估计的影响分析

本文研究了多元线性同归模型岭估计的影响分析问题.利用最小二乘估计方法,获得了多元协方差阵扰动模型与原模型参数阵之间的岭估计的一些关系式,给出了度量影响大小的基于岭估计的广义Cook距离.     

Proof of a conjecture on fractional Ramsey numbers

Jacobson, Levin, and Scheinerman introduced the fractional Ramsey function r_f (a₁, a₂, …, a_k) as an extension of the classical definition for Ramsey numbers. They determined an exact formula for the fractional Ramsey function for the case k=2. In this article, we answer an open problem by determining an explicit formula for the general case k>2 by constructing an infinite family of circulant graphs for which the independence numbers can be computed explicitly. This construction gives us two further results: a new (infinite) family of star extremal graphs which are a superset of many of the families currently known in the literature, and a broad generalization of known results on the chromatic number of integer distance graphs. © 2009 Wiley Periodicals, Inc. J Graph Theory 63: 164–178, 2010     

相似理论在深孔梯段爆破飞石距离计算中的应用

利用相似理论 ,推导了深孔梯段爆破中飞石距离的计算公式。结合三峡工程实际统计数据的回归分析导出了公式的具体表达式 ,讨论了公式的应用条件和进一步完善的研究思路。     

利用小车的上班族在拥有辐射环状交通网络的城市工作区内通勤时的平均移动距离

在一拥有辐射环状交通网络的城市工作区内，使用小车上下班的职员在通勤时的平均移动距离约为多少？本文基于一个较现实的模型对此进行了理论上的解析，所得结果，从城市规划的观点来看，具有一定的实际意义。     

Maximum Matchings in the n-Dimensional Cube

The problem of efficient computation of maximum matchings in the n-dimensional cube, which is applied in coding theory, is solved. For an odd n, such a matching can be found by the method given in our Theorem 2. This method is based on the explicit construction (Theorem 1) of the maps of the vertex set that induce largest matchings in any bipartite subgraph of the n-dimensional cube for any n.     

Diode-pumped Birefringent Tunable Nd:YAG Laser with Large Frequency Difference

A dual-frequency Nd: YAG laser which can output two frequencies with frequency difference of more than 5 gigaherz is developed. By inserting and moving an intracavity quartz crystal wedge in diode pumped Nd:YAG laser, It can be obtained and tuned frequency difference in a wide frequency range. The stabilization of frequency difference in free state is much better than that of birefringent dual-frequency He-Ne lasers at similar laboratory conditions. With such a large tunable frequency difference i.e. short synthetic wavelength, the laser may be used as the light source of absolute distance interferometers. In our experiment, the methods for tuning frequency difference by rotating and applying a tunable force on the intracavity quartz plate are also studied.     

Decomposition and removability properties of John domains

In this paper we characterize John domains in terms of John domain decomposition property. In addition, we also show that a domain D in ℔ ⁿ is a John domain if and only if D\P is a John domain, where P is a subset of D containing finitely many points of D. The best possibility and an application of the second result are also discussed.     

广义n-赋范空间中的Vogt定理

本文推广Vogt定理到广义n-赋范空间，即证明了两个广义n-赋范空间之间的保持ρ-诱导距离映射是仿射的.