Hardy spaces of spaces of homogeneous type

Let be a space of homogeneous type, and be the generator of a semigroup with Gaussian kernel bounds on . We define the Hardy spaces of for a range of , by means of area integral function associated with the Poisson semigroup of , which is proved to coincide with the usual atomic Hardy spaces on spaces of homogeneous type.

     

Condensations of projective sets onto compacta

For a coanalytic-complete or -complete subspace of a Polish space we prove that there exists a continuous bijection of onto the Hilbert cube . This extends results of Pytkeev. As an application of our main theorem we give an answer to some questions of Arkhangelskii and Christensen.

Under the assumption of Projective Determinacy we also give some generalizations of these results to higher projective classes.

     

Besov-Morrey spaces: Function space theory and applications to non-linear PDE

This paper is devoted to the analysis of function spaces modeled on Besov spaces and their applications to non-linear partial differential equations, with emphasis on the incompressible, isotropic Navier-Stokes system and semi-linear heat equations. Specifically, we consider the class, introduced by Hideo Kozono and Masao Yamazaki, of Besov spaces based on Morrey spaces, which we call Besov-Morrey or BM spaces. We obtain equivalent representations in terms of the Weierstrass semigroup and wavelets, and various embeddings in classical spaces. We then establish pseudo-differential and para-differential estimates. Our results cover non-regular and exotic symbols. Although the heat semigroup is not strongly continuous on Morrey spaces, we show that its action defines an equivalent norm. In particular, homogeneous BM spaces belong to a larger class constructed by Grzegorz Karch to analyze scaling in parabolic equations. We compare Karch's results with those of Kozono and Yamazaki and generalize them by obtaining short-time existence and uniqueness of solutions for arbitrary data with subcritical regularity. We exploit pseudo-differential calculus to extend the analysis to compact, smooth, boundaryless, Riemannian manifolds. BM spaces are defined by means of partitions of unity and coordinate patches, and intrinsically in terms of functions of the Laplace operator.

     

齐型空间上交换子的紧性

设(x，d，μ)是齐型空间．本文证明了分数次积分算子Iα与VMO函数构成的交换子I^ba是L^p(X)到L^q(X)的紧算子，其中α∈(0，1)，1＜p＜q＜∞且1/q＝1/p—α。     

关于L-fuzzy拓扑分离性的弱同胚不变性质

本文研究了一种新的弱同胚不变性质，它更具有一般性；证明了目前文献中所论述的各种分离性都是弱同胚不变性质，并且否定回答了王国俊提出的两个分离性问题。     

A version of Burkholder's theorem for operator-weighted spaces

Let be an operator weight, i.e. a weight function taking values in the bounded linear operators on a Hilbert space . We prove that if the dyadic martingale transforms are uniformly bounded on for each dyadic grid in , then the Hilbert transform is bounded on as well, thus providing an analogue of Burkholder's theorem for operator-weighted -spaces. We also give a short new proof of Burkholder's theorem itself. Our proof is based on the decomposition of the Hilbert transform into ``dyadic shifts'.

     

On non-measurability of in its second dual

We show that with the weak topology is not an intersection of Borel sets in its Cech-Stone extension (and hence in any compactification). Assuming (CH), this implies that has no continuous injection onto a Borel set in a compact space, or onto a Lindelöf space. Under (CH), this answers a question of Arhangel'ski.

     

Internal mode of incoherent photovoltaic vector solitons

The internal modes of incoherent vector solitons (IVSs) in photovoltaic photorefractive materials are investigated in the framework of coupled nonlinear Schr\"{o}dinger equations. It is found that there is a pair of internal modes corresponding to a bright--bright IVS. The propagation dynamics of the bright-bright IVS perturbed by the internal modes is simulated by numerical method.     

基于高光谱成像技术的番茄茎秆灰霉病早期诊断研究

共采集了112个番茄茎秆高光谱数据（光谱范围400～1 030 nm）,结合图像处理和化学计量学方法建立了番茄茎秆灰霉病早期诊断模型。应用偏最小二乘法（PLS）模型的隐含变量载荷分布选取了七个特征波长（EW）,并建立了番茄茎秆灰霉病早期诊断的最小二乘支持向量机（LS-SVM）模型。结果表明,经过变量标准化（SNV）及多元散射校正（MSC）预处理所建立的EW-LS-SVM模型获得了满意的判别效果,且优于全波段的PLS模型。说明高光谱成像技术进行番茄茎秆灰霉病的早期诊断是可行的,为番茄病害早期诊断和预警提供了新的方法。     

静态傅里叶变换超光谱全偏振成像技术

光谱偏振成像技术是成像光谱技术与偏振成像技术的有机融合, 是当前空间光学遥感技术研究的热点和前沿. 针对目前光谱偏振成像技术受测量原理、探测模式的限制, 普遍需要运动、电控调制等部件, 导致体积大, 结构复杂, 加工装调困难, 抗振能力差等问题, 我们于2010年在国际上首先提出了一种多信息融合的静态傅里叶变换超光谱全偏振成像方法. 本文在此基础上, 阐述了新方法的基本原理, 给出了具体实现方案. 新方案无需运动、电控调制部件, 可实现目标图像、光谱、全偏振信息的一体获取. 推导出了新方案的调制干涉强度数据表达式及Stokes矢量解调公式, 分析了新方法实现光谱、全偏振探测的物理过程. 对新方案进行了计算机数值模拟验证, 研制了原理验证样机开展了室内、室外验证实验, 首次获得了室外推扫光谱图像数据立方体和全色全偏振度图像, 模拟及实验结果均表明新方案原理正确, 技术可行. 上述研究为新型空间遥感器的开发提供了基础理论及实践支持. 关键词： 成像光谱 偏振成像 Stokes矢量