THE UNIT BALL OF C*-ALGEBRA AND DIFFERENTIABILITY OF SUPPORT FUNCTION

In this paper we show that the unit ball of an infinite dimensional commutative C-algebra lacks strongly exposed points, so they have no predual. Also in the second part, we use the concept of strongly exposed points in the Frechet differentiability of support convex functions.     

Almost Frechet Differentiability of Lipschitz Mappings Between Infinite-Dimensional Banach Spaces

We give several sufficient conditions on a pair of Banach spacesX and Y under which each Lipschitz mapping from a domain inX to Y has, for every > 0, a point of -Fréchet differentiability.Most of these conditions are stated in terms of the moduli ofasymptotic smoothness and convexity, notions which have appearedin the literature under a variety of names. We prove, for example,that for > r > p 1, every Lipschitz mapping from a domainin an l_r-sum of finite-dimensional spaces into an l_p-sum offinite-dimensional spaces has, for every > 0, a point of-Fréchet differentiability, and that every Lipschitzmapping from an asymptotically uniformly smooth space to a finite-dimensionalspace has such points. The latter result improves, with a simplerproof, an earlier result of the second and third authors. Wealso survey some of the known results on the notions of asymptoticsmoothness and convexity, prove some new properties, and presentsome new proofs of existing results. 2000 Mathematical Subject Classification: 46G05, 46T20.     

两模光场与原子相互作用中光场周期性和频效应-理想Kerr介质腔中非关联双模相干态光场与V型三能级原子相互作用系统中光场的不等阶和压缩效应

利用多模压缩态理论,通过数值计算研究了高Q Kerr介质腔中非关联双模相干态光场与V型三能级原子相互作用系统中双模光场的不等幂次高次和压缩效应,分别绘出了两模光场第一模i次方第二模j次方不等幂次和压缩度的第一正交分量(Sh1_ij),第二正交分量(Sh2_ij)的时间演化曲线.结果表明:1)Kerr介质的存在和嵌放在介质中的V型三能级原子是产生双模光场不等阶和压缩效应的物质条件,二者缺一不可.2)腔中光场和原子发生光子交换是导致双模光场不等幂次和压缩效应的微观机制.3)在不考虑坐标度的情况下,不同条件下的时间演化曲线呈现非常相似的"崩坍-复原-凹谷"式结构,且复原区的波型振荡次数及凹谷区的振荡下降和振荡上升型式一样.4)在χ以及,不变的条件下,不等幂次高次和压缩度时间演化曲线的崩坍-复原-凹谷式结构的持续时间随压缩阶次的升高而缩短,压缩度随压缩阶数的升高而迅速下降.5)在平均光子不变(即,恒定),但Kerr介质不同(即χ变化)的条件下,不等幂次高次和压缩度曲线的周期随Kerr介质的三阶非线性极化系数χ的增加而缩短,幅度则不受Kerr介质的三阶非线性极化系数变化的影响.6)不等幂次高次和压缩效应的持续时间等强烈地依赖于Kerr介质的非线性程度,χ越大不等阶和压缩效应持续时间就越短.在相同压缩幂次的情况下,不等幂次高次和压缩度演化曲线正向幅度随平均光子数的增大而增大.     

回归分析在高等教育评价中建立预测模型的应用

对教育行为、教育规律进行数量化研究是很有意义的工作.本文尝试用回归分析理论,建立高等教育的预测模型,使用的主要方法是最小二乘法.     

Higher order curvature flows on surfaces

We consider a sixth and an eighth order conformal flow on Riemannian surfaces, which arise as gradient flows for the Calabi energy with respect to a higher order metric. Motivated by a work of Struwe which unified the approach to the Hamilton-Ricci and Calabi flow, we extend the method to these higher order cases. Our results contain global existence and exponentially fast convergence to a constant scalar curvature metric.Uniform bounds on the conformal factor are obtained via the concentration-compactness result for conformal metrics. In the case of the sphere we use the idea of DeTurck's gauge flow to derive bounds up to conformal transformation.We prove exponential convergence by showing that the Calabi energy decreases exponentially fast. The problem of the non-trivial kernel in the evolution of the Calabi energy on the sphere is resolved by using Kazdan-Warner's identity. Mathematics subject classifications (2000) {Primary 53C44 Secondary 35K25}     

正交相干态的非经典特性

本文研究了正交相干态的非经典特性。结果表明,正交相干态仅为光场振幅偶次幂的最小测不准态,无高阶压缩效应,但存在高阶反聚束效应和亚泊松分布。     

关于Banach空间的k-光滑性

本文研究了k-光滑的Banach空间,引入了k-G可微性的概念.得到了k-光滑的Banach空间的几个等价条件.     

DIMENSION AND DIFFERENTIABILIIY OF A CLASS OF FRACTAL INTERPOLATION FUNCTIONS

In this paper, a new iterated function system consisting of non-linear affinemaps is constructed. We investigate the fractal interpolation functions generated bysuch a system and get its differentiability, its box dimension, its packing dimension,and a lower bound of its Hansdorff dimension.     

ON THE UNIFORMLY FRECHETDIFFERENTIABILITY OF NORMS

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Three positive solutions for higher order m-point boundary value problems

In this paper, we consider the existence of at least three positive solutions for the 2nth order m-point boundary value problem