Energy of Radial Vector Fields on Compact Rank One Symmetric Spaces

We consider the energy (or the total bending) of unit vector fields oncompact Riemannian manifolds for which the set of its singularitiesconsists of a finite number of isolated points and a finite number ofpairwise disjoint closed submanifolds. We determine lower bounds for theenergy of such vector fields on general compact Riemannian manifolds andin particular on compact rank one symmetric spaces. For this last classof spaces, we compute explicit expressions for the total bending whenthe unit vector field is the gradient field of the distance function toa point or to special totally geodesic submanifolds (i.e., for radialunit vector fields around this point or these submanifolds).     

一种基于支持向量机预测模型的精度提高方法与应用

介绍了支持向量机模型的特点 ,针对该模型在经济预测中的应用 ,提出了一种提高该模型预测精度的方法 ,并进行了理论分析和实际应用的验证 ,说明了该方法能够获得更加准确的预测结果 .     

关于变点个数及位置的检测和估计

本文根据信息论准则研究变点问题，在模型选择的框架下，研究变点个数和变点位置的检测，证明当方差不同时，均值向量变点个数及变点位置估计的强相合性。     

Remark on the Hopf Bifurcation Theorem

A simple generalization of the Hopf Bifurcation Theorem for scalar higher order ordinary differential equations is suggested. We study the degenerate case where several roots of the characteristic polynomial cross the imaginary axis at the same point for some value λ₀ of the parameter λ. The main result is that if N₁ roots cross the imaginary axis from the left to the right and N₂ roots cross it from the right to the left, then λ₀ is a Hopf bifurcation point whenever N₁ ≠ N₂. In particular, in the classical Hopf Bifurcation Theorem the numbers N_j are 0 and 1. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

A New Theoretical Modeling of Surface Resistance in Normal Metals at Terahertz Frequencies

A number of researchers have reported discrepancies between surface resistance measurements and classical theoretical predictions for simple mm-wave and sub-mm-wave structures. We have developed a rigorous phenomenological model for analyzing surface resistance of normal metals. The model is based on quantum mechanical analysis for spatial dispersion within the metal. We have used the model to predict the surface resistance in normal metals at terahertz frequencies. Our analysis shows that the conductivity is not only frequency but also wave vector dependent. Moreover, we have compared the results of this model with the results of the classical skin-effect model and classical relaxation- effect model. We demonstrate that our model has good quantitative agreement with the published experimental data for the room temperature surface resistance of normal metals at terahertz frequencies range from the literature.     

Mazur定理的一个推广及其几何证明

建立了代数内点的若干性质；给出了Mazur定理的一个推广及其几何证明；证明了此推广的Mazur定理与基本分离定理等价；还得到一个严格分离定理．     

关于Z／mZ上置换多项式向量组的一个注记

设ｍ和ｎ是两个正整数，Ｒ＝Ｚ／ｍＺ是整数模ｍ剩余类环．设ｎ个多项式ｆｊ（ｘ１，…，ｘｎ）∈Ｒ［ｘ１，…，ｘｎ］，ｊ＝１，…，ｎ，若对任给的（ａ１，…，ａｎ）∈Ｒｎ，同余式组ｆｊ（ｘ１，…，ｘｎ）≡ａｊ（ｍｏｄｍ），ｊ＝１，…，ｎ，恰有一个解，则称ｆ１，…，ｆｎ是一组置换多项式向量模ｍ．一个自然的问题是：Ｒ上哪些ｎ元多项式可以扩充为一组置换多项式向量模ｍ？本文解决了这一问题，并给出了一个充分必要条件．     

向量值有理插值的逐步降阶算法

通过对向量值有理插值的分析,得到一个重要性质,根据这个性质,给出了计算向量值有理插值函数的逐步降阶算法.该算法具有运算量少,易于实现的特点.     

基于支持向量机的近红外光谱鉴别茶叶的真伪

快速准确地鉴别名优茶的真伪是当前茶叶行业亟待解决的一项重大课题。针对这一现状,提出了一种快速准确鉴别名优茶真伪的新思路。试验中,以碧螺春茶为研究对象,利用近红外光谱分析技术结合支持向量机(SVM)模式识别原理建立碧螺春茶真伪鉴别模型。试验结果显示,通过标准归一化(SNV)预处理,选取6500~5500 cm-1波长范围内的光谱经过主成分分析后,提取11个主成分,选用径向基函数(RBF)作为核函数建立的模型最佳。对训练集中的138个茶叶样本,模型的回判鉴别率达到93.48%;对90个独立样本进行预测时,模型的预测鉴别率达到84.44%。研究结果表明基于支持向量机的近红外光谱鉴别名优茶真伪的方法是可行的。     

离轴抛物镜准直特性的研究

由于反射式离轴抛物镜不产生色差并具有较大的有效孔径,已经广泛应用于辐射校准、宽波段的目标模拟和能量聚焦工作中。影响离轴抛物镜准直特性的主要因素有离轴量,有效孔径和焦面出射点的位置。采用矢量的方法,分析了离轴量等参量和准直性能之间的关系。给出了焦面出射点的位置从0~0.05f,相对孔径D/f从0~0.40,相对离轴量h/f从0.1~0.5变化时,离轴抛物镜准直仪的准直性能曲线。运用CODE V对矢量法的分析结果进行了验证,在条件一致的情形,两者结果吻合。这些结果有助于准直仪的设计。