二维空间的Navier—Stokes问题的混合有限元分析

本文将给出二维空间的Navier-Stokes问题的三角形单元的一种新的二阶混合有限元法。     

Normal projection: deterministic and probabilistic algorithms

We consider the following problem： for a collection of points in an n-dimensional space, find a linear projection mapping the points to the ground field such that different points are mapped to different values. Such projections are called normal and are useful for making algebraic varieties into normal positions. The points may be given explicitly or implicitly and the coefficients of the projection come from a subset S of the ground field. If the subset S is small, this problem may be hard. This paper deals with relatively large S, a deterministic algorithm is given when the points are given explicitly, and a lower bound for success probability is given for a probabilistic algorithm from in the literature.     

Hyperspectral feature recognition based on kernel PCA and relational perspective map

A novel joint kernel principal component analysis （PCA） and relational perspective map （RPM） method called KPmapper is proposed for hyperspectral dimensionality reduction and spectral feature recognition. Kernel PCA is used to analyze hyperspectral data so that the major information corresponding to features can be better extracted. RPM is used to visualize hyperspectral data through two-dimensional （2D） maps, and it is an efficient approach to discover regularities and extract information by partitioning the data into pieces and mapping them onto a 2D space. The experimental results prove that the KPmapper algorithm can effectively obtain the intrinsic features in nonlinear high dimensional data. It is useful and impressing for dimensionality reduction and spectral feature recognition.     

D维空间Cs2分子X1Σ+g态精确解析解

使用完全量子化规则法计算了D维空间中具有任意转动量子数Morse势的Schrödinger方程,得到了Cs2分子X1Σ+g态旋转-振动能谱,讨论了能谱与维度D和振动量子数之间的关系。结果表明：(1)具有不同转动量子数和振动量子数的能谱随维度D的增大而趋于相同;(2)高维Cs2分子X1Σ+g态的振动能特性与三维相似。     

Two-Dimensional Wave Motion on the Charged Surface of a Viscous Liquid

The wave motion on the charged surface of a viscous Newtonian liquid is solved as an initial-value problem. Both the leaky dielectric and perfect dielectric cases are considered. The amplitude of wave is assumed to be small. The electric field induced by surface charge is shown to have a generally destabilizing effect on surface wave. The neutral stability curve is drawn in the （G, N~） plane （G： the gravitational bond number; N~： the electrical Bond number）. The Ohnesorge number, Taylor-Melcher number and permittivity ratio have little influence on the neutral stability curve. It is testified that the classical normal mode method cannot predict wave behaviour at small times.     

塞伯格-威滕理论——4维空间量子场论研究的新飞跃

 从1994年初开始,由塞伯格(N.Seiberg)、威滕(E.Witten)和他们的合作者所完成的一系列工作震动了理论物理界和数学界。从物理的角度说,这些工作涉及如何精确地研究4维空间量子场论的非微扰行为(例如禁闭、手征对称性破缺、真空凝聚等),也就是如何解析地处理强耦合的相互作用。从数学的角度说,它们涉及如何简单地算出光滑4维流形的拓扑特征。     

二维空间Stokes问题的四边形单元的二阶混合有限元法

本文将给出二维空间的Stokes问题的四边形单元的二阶混合有限元法。     

缺Zn症患儿微量元素水平的样本特征分析及其临床补Zn治疗的评价

测定了150例缺Zn症患儿及健康儿发样中的Zn、Ca、Mg及Fe四元素水平．采用主成分分析法．将高维空间中的样本点映射到低维空间中来观察，研究其样本特征，评价临床补Zn治疗措施．结果瑶明：缺Zn症患儿体内缺Zn是病理的主要方面，但往往同时伴有其它微量元素水平偏低现象，临床缺Zn症状的表现可能为多种元素综合效应的反映．因此临床治疗不能单纯考虑朴Zn，还应结合患儿体内其他元素水平的具体情况，考虑其他元素的补给．治疗才能奏效显著．     

Kolmogorov定理的一个变形

本文研究了随机过程轨道连续性的Kolmogorov定理.通过将两点间的距离用矩形上的增量代替,得到了Kolmogorov定理在高维空间的一种推广.