Gas-phase 21Ne NMR studies and the nuclear magnetic dipole moment of neon-21

Gas-phase ²¹Ne nuclear magnetic resonance spectra were measured at the natural abundance of ²¹Ne isotope for samples consisting of pressurized neon up to 60 bar at room temperature and applying the magnetic field of the strength B₀ = 11.7574 T. It showed that the nuclear magnetic resonance frequency is linearly dependent on the density of gaseous neon. The resonance frequency was extrapolated to the zero-density point, and it permitted the determination of the ²¹Ne nuclear magnetic moment, μ(²¹Ne) = 0.6617774(10) μ_N. The present value of μ(²¹Ne) is not influenced by the bulk magnetic susceptibility of neon and interactions between neon atoms; therefore, it is more precise and reliable than the previous result obtained for μ(²¹Ne).     

一阶最优性条件研究

本对由Botsko的关于多变量函数取极值的一阶导数检验条件定理^[1]进行了分析研究，给出了更实用而简捷的差别条件。最后，举出若干例子予以说明。     

Wavelet Collocation Methods for a First Kind Boundary Integral Equation in Acoustic Scattering

In this paper we consider a wavelet algorithm for the piecewise constant collocation method applied to the boundary element solution of a first kind integral equation arising in acoustic scattering. The conventional stiffness matrix is transformed into the corresponding matrix with respect to wavelet bases, and it is approximated by a compressed matrix. Finally, the stiffness matrix is multiplied by diagonal preconditioners such that the resulting matrix of the system of linear equations is well conditioned and sparse. Using this matrix, the boundary integral equation can be solved effectively.     

Efficient Collocation Schemes for Singular Boundary Value Problems

We discuss an error estimation procedure for the global error of collocation schemes applied to solve singular boundary value problems with a singularity of the first kind. This a posteriori estimate of the global error was proposed by Stetter in 1978 and is based on the idea of Defect Correction, originally due to Zadunaisky. Here, we present a new, carefully designed modification of this error estimate which not only results in less computational work but also appears to perform satisfactorily for singular problems. We give a full analytical justification for the asymptotical correctness of the error estimate when it is applied to a general nonlinear regular problem. For the singular case, we are presently only able to provide computational evidence for the full convergence order, the related analysis is still work in progress. This global estimate is the basis for a grid selection routine in which the grid is modified with the aim to equidistribute the global error. This procedure yields meshes suitable for an efficient numerical solution. Most importantly, we observe that the grid is refined in a way reflecting only the behavior of the solution and remains unaffected by the unsmooth direction field close to the singular point.     

Carathéodory's method for a class of dynamic games

The method of equivalent variational methods, originally due to Carathéodory for free problems in the calculus of variations is extended to investigate feedback Nash equilibria for a class of n-person differential games. Both the finite-horizon and infinite-horizon cases are considered. Examples are given to illustrate the presented results.     

气垫导轨在刚体转动惯量测定实验中的应用

本文介绍了一种测量刚体转动惯量的新方法。即把气垫导轨和刚体转动仪结合起来来测量刚体的转动惯量,使传统的气垫导轨实验和刚体转动惯量测定实验得以更新,提高了实验测量的精度,拓展了实验内容。     

第一类永动机幻梦的破灭

介绍了13~18世纪物理学史和科技史上曾名噪一时的第一类永动机的设计方案的破灭.第一类永动机幻梦破灭的历史引起了人们的反思与启示,有力地促进了19世纪中叶能量转化和守恒定律的确立.     

一维光学格子孤子的传输特性及控制研究

利用解析和数值方法研究了在具有横向折射率周期性调制的克尔型非线性介质中光学格子孤子的传输，得到了孤子参数的演化方程以及格子孤子的形成和稳定传输的条件.结果表明：当光束的入射角小于某临界角度时，光束可被类似波导形式的路径俘获而稳定传输，该临界角随折射率调制周期、调制深度的增加而增大，且光束越窄临界值越大.此外，线性空间啁啾虽然对光束传输的中心位置没有任何影响，但会导致光束发散从而破坏格子孤子的形成和稳定传输，对此提出了采用特定功率取值来补偿啁啾作用从而形成格子孤子的方案. 关键词： 光孤子 光学格子 光传输 矩方法     

无穷矩阵拓扑代数的理想(Ⅰ)(英文)

本文给出了所有弱紧算子 ,强紧算子 ,Mackey紧算子 ,构成无穷矩阵拓扑下相同紧集的特征的刻画 .     

首次穿过边界概率及其在金融中的应用

本文把数学和管理科学有机结合,为数学应用提出问题,得出新结果,推广了J.Michel Harrison(1985)[1]第43页的命题27,并给出了在金融中的应用.