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.     

What is the maximum stretching for C–C single bond?

The objective of this work is to determine the maximum stretch of the C–C bond before it misses the character of single bond, employing both the Atoms in Molecules (AIM) and Electron Localization Function (ELF) methods. It was concluded that C–C distances up to 2.0 Å could be considered single bonds.     

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。     

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.     

Transfer of electron density as a result of hydrogen bond formation

It has been found that the amount of charge transfer between donor and acceptor molecules in four sets of hydrogen‐bonded complexes may be adequately described as an exponential function of the equilibrium distance between the hydrogen atom and the nearest atom of the acceptor molecule. The exponential factors of the transfer are of the same order but somewhat larger than the factors found otherwise in the investigations of dynamic electron transfer. © 2008 Wiley Periodicals, Inc. Int J Quantum Chem, 2009     

Used digital speckle correlation method to realize orientation function of optical mouse

Used digital speckle correlation method (DSCM) to realize orientation function of optical mouse is researched. The experiment is designed to obtain the dynamic speckle patterns which are shot by CCD, then the DSCM is used to process the sequential images and also the experiment is simulated. The experimental results show the DSCM can confirm orientation function of the optical mouse, and have a good agreement with the simulation results, and the resolution we obtained is higher than the resolution of mouse on the market.     

A Theoretical and Computational Framework for Isometry Invariant Recognition of Point Cloud Data

Point clouds are one of the most primitive and fundamental manifold representations. Popular sources of point clouds are three-dimensional shape acquisition devices such as laser range scanners. Another important field where point clouds are found is in the representation of high-dimensional manifolds by samples. With the increasing popularity and very broad applications of this source of data, it is natural and important to work directly with this representation, without having to go through the intermediate and sometimes impossible and distorting steps of surface reconstruction. A geometric framework for comparing manifolds given by point clouds is presented in this paper. The underlying theory is based on Gromov-Hausdorff distances, leading to isometry invariant and completely geometric comparisons. This theory is embedded in a probabilistic setting as derived from random sampling of manifolds, and then combined with results on matrices of pairwise geodesic distances to lead to a computational implementation of the framework. The theoretical and computational results presented here are complemented with experiments for real three-dimensional shapes.