The Huber theorem for non-compact conformally flat manifolds

It was proved in 1957 by Huber that any complete surface with integrable Gauss curvature is conformally equivalent to a compact surface with a finite number of points removed. Counterexamples show that the curvature assumption must necessarily be strengthened in order to get an analogous conclusion in higher dimensions. We show in this paper that any non compact Riemannian manifold with finite -norm of the Ricci curvature satisfies Huber-type conclusions if either it is a conformal domain with volume growth controlled from above in a compact Riemannian manifold or if it is conformally flat of dimension 4 and a natural Sobolev inequality together with a mild scalar curvature decay assumption hold. We also get partial results in other dimensions. Received: April 14, 2000; revised version: March 20, 2001     

二维周期光子晶格中的非线性Landau-Zener隧穿

在二维周期光子晶格中研究了Kerr型非线性Landau-Zener隧穿. 首先在六方晶系光子晶格中推导出非线性三能级Landau-Zener隧穿模型, 在特殊初值条件下将其转化为非线性二能级模型. 对于三能级隧穿模型, 选择特殊初值, 研究了隧穿率随参数的变化规律. 关键词： 光子晶格 Kerr型非线性 Landau-Zener隧穿     

非超临界干燥法制备SiO2气凝胶

应用廉价的国产硅溶胶为原料，通过凝胶过程和干燥过程条件的选择，以非超临界干燥技术最终获得了块状SiO2气凝胶.该气凝胶外观状态与应用正硅酸乙酯为原料制得的完全一致，其微观结构也相当良好，其直径和孔分布均匀.溶液的配比和pH对凝胶过程和气凝胶样品的密度有比较明显的影响，同时pH值与SiO2的粒径之间也有一定的关系.依据制备条件的变化，所得SiO2气凝胶的密度约在200～400 kg•m－3，比表面在250～300 m2•g－1之间变化，平均孔径约为11～20 nm，而孔隙率在91％左右.     

调制式DSC在高聚物研究中的应用

综述了一种新的热分析技术－－调制式差示扫描量热示（Modulated Differentail Scanning Calorimetry）。对其工作原理，优点及在高聚物研究中的应用作了简介。     

耦合映像格子中时空混沌的状态反馈控制

利用状态反馈的方法，实现了耦合映像格子中时空混沌的稳定控制.反馈方式可以是没有延迟的，也可以是有延迟的；控制方式可以是连续的，也可以是脉冲的.数值模拟结果证明了状态反馈方法的有效性. 关键词： 耦合映像格子 时空混沌 状态反馈控制     

Adsorption thermodynamics of monomers on diluted-bonds triangular lattices

The surface of amorphous solids cannot be usually represented by a regular lattice of adsorbing sites. One of the main characteristics of such surfaces is a variable connectivity for each site. A simple model consisting of a triangular lattice where a fraction of bonds (interactions) is suppressed at random is used here to find out, by using Monte Carlo simulations, how the adsorption thermodynamics of repulsively interacting monomers is modified with respect to the same process in the regular lattice. Adsorption isotherm, differential heat of adsorption and adsorbed phase entropy calculations are carried out showing and interpreting the effects of the variable connectivity. In particular, it is found that the order-disorder phase transition observed for the regular lattice survives, though with modifications, above a critical mean connectivity.     

A Non‐Enzymatic Hydrogen Peroxide Sensor Based on Gold Nanoparticles/Carbon Nanotube/Self‐Doped Polyaniline Hollow Spheres

In this study, a novel non‐enzymatic hydrogen peroxide (H₂O₂) sensor was fabricated based on gold nanoparticles/carbon nanotube/self‐doped polyaniline (AuNPs/CNTs/SPAN) hollow spheres modified glassy carbon electrode (GCE). SPAN was in‐site polymerized on the surface of SiO₂ template, then AuNPs and CNTs were decorated by electrostatic absorption via poly(diallyldimethylammonium chloride). After the SiO₂ cores were removed, hollow AuNPs/CNTs/SPAN spheres were obtained and characterized by transmission electron microscopy (TEM), field‐emission scanning electron microscopy (FESEM) and Fourier transform infrared spectroscopy (FTIR). The electrochemical catalytic performance of the hollow AuNPs/CNTs/SPAN/GCE for H₂O₂ detection was evaluated by cyclic voltammetry (CV) and chronoamperometry. Using chronoamperometric method at a constant potential of ?0.1 V (vs. SCE), the H₂O₂ sensor displays two linear ranges: one from 5 µM to 0.225 mM with a sensitivity of 499.82 µA mM^?1 cm^?2; another from 0.225 mM to 8.825 mM with a sensitivity of 152.29 µA mM^?1 cm^?2. The detection limit was estimated as 0.4 µM (signal‐to‐noise ratio of 3). The hollow AuNPs/CNTs/SPAN/GCE also demonstrated excellent stability and selectivity against interferences from other electroactive species. The sensor was further applied to determine H₂O₂ in disinfectant real samples.     

Asymptotic properties of multistate random walks. I. Theory

A calculation is presented of the long-time behavior of various random walk properties (moments, probability of return to the origin, expected number of distinct sites visited) formultistate random walks on periodic lattices. In particular, we consider inhomogeneous periodic lattices, consisting of a periodically repeated unit cell which contains a finite number of internal states (sites). The results are identical to those for perfect lattices except for a renormalization of coefficients. For walks without drift, it is found that all the asymptotic random walk properties are determined by the diffusion coefficients for the multistate random walk. The diffusion coefficients can be obtained by a simple matrix algorithm presented here. Both discrete and continuous time random walks are considered. The results are not restricted to nearest-neighbor random walks but apply as long as the single-step probability distributions associated with each of the internal states have finite means and variances.     

How do the positive embeddings of Banach lattices depend on the αth derivatives of K?

Let K and S be locally compact Hausdorff spaces and X be an abstract space. Suppose that T is a positive Banach lattice isomorphism from into . Then for each ordinal α the cardinalities of the αth derivatives and satisfy the following inequality Moreover, if then is a continuous image of a subset of which can be taken closed when K is compact. The first statement of this result for is a vector‐valued extension of a Cengiz's theorem and the second one is vector‐valued version of a Holsztyński's theorem. A simple example shows that the number is sharp in these vector‐valued theorems.     

三维光晶格中玻色凝聚气体基态波函数及干涉演化

基于Gross-Pitaevskii方程，运用有效化学势概念，研究了囚禁在组合势(由磁阱和三维光 晶格组成)中玻色凝聚气体在三维光晶格中的分布规律，并由此得到玻色凝聚气体的归 一化基态波函数.在取消组合势和仅取消光晶格而保留磁阱的两种情况下，运用传播子方 法求解出玻色凝聚气体密度分布的解析表达式.取消组合势后，理论计算所得到的玻色凝聚 气体聚随时间的演化规律与Greiner等的实验结果相一致.仅取消光晶格而保留磁阱时，研 究表明玻色凝聚气体的干涉模式呈现周期性的振荡行为.此外，在磁阱为各向异性的情况下 ， 关键词： 玻色凝聚气体 磁阱 光晶格 干涉模式