Organic/inorganic hybrid nanospheres coated with palladium/P4VP shells from surface‐initiated atom transfer radical polymerization

Crosslinked poly(4‐vinylbenzyl chloride) (PVBC) nanospheres of about 160 nm were first synthesized by emulsion copolymerization of 4‐vinylbenzyl chloride (VBC) in the presence of a crosslinking agent, p‐divinylbenzene. Subsequent modification of the nanosphere surfaces via surface‐initiated atom transfer radical polymerization of 4‐vinylpyridine, using the VBC units of PVBC on the nanosphere surface as the macroinitiators, produced a well‐defined and covalently tethered poly(4‐vinylpyridine) (P4VP) shells of 24–27 nm in thickness. Activation of the P4VP shells in a PdCl₂ solution, followed by reactions with CO or H₂S gas, gave rise to the corresponding P4VP composite shells containing densely dispersed palladium metal or palladium sulfide nanoparticles. The chemical composition of the nanosphere surfaces at various stages of surface modification was characterized by X‐ray photoelectron spectroscopy. Field emission scanning electron microscopy and transmission electron microscopy were used to characterize the morphology of the organic/inorganic hybrid nanospheres coated with palladium/P4VP shells. © 2008 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 46: 2119–2131, 2008     

Highly photocatalytic activity of metallic hydroxide/titanium dioxide nanoparticles prepared via a modified wet precipitation process

Surface modification is one important approach to increase the photocatalytic activity of TiO₂. By using a modified wet precipitation process, novel M(OH)_x/TiO₂ nanoparticles were synthesized, where M(OH)_x represents ferric or cupric hydroxide. The prepared M(OH)_x/TiO₂ powders were characterized with XRD, FT-IR, BET, UV–vis DRS, and TGA, and were observed to yield high photocatalytic ability by using methyl orange (MO) as a model compound of organic pollutants to be degraded. Due to the accelerating effects of the new photocatalyst, the half-time of MO during its photocatalytic degradation at pH 6.0 over M(OH)_x/TiO₂ was decreased from 332 min for unmodified neat TiO₂ to 63 min for Fe(OH)₃/TiO₂ and 65 min for Cu(OH)₂/TiO₂, respectively. The enhancing effects of M(OH)_x/TiO₂ was further observed in a wide composition range with various M/Ti atomic ratios in the photocatalysts and in a wide pH range of the MO solution from 3 to 7. This enhancing effect is mainly attributed to the increased trapping of the photogenerated electron by the higher valence sites (Fe(III) or Cu(II)) in the hydroxide layer near the M(OH)_x/TiO₂ interface and the enriched surface hydroxyl groups which accept photogenerated holes to yield more hydroxyl radicals.     

最小风险证券组合的结构分析和迭代算法

本文分析了最小风险组合证券投资的结构特征，并提出了一种组合证券风险最小化的迭代算法，证明了其收敛性．该算法操作简单，且易于处理不允许卖空情况下的证券组合问题．     

关于整函数超级的进一步结果

运用正规族理论研究了整函数与其高阶导数分担无穷级函数增长级与超级的相关结果.从亚纯函数超级大于零而使球面导数无界的角度出发,然后综合运用Pang-Zaclman引理,数学归纳法和Nevanlinna理论等方法证明了该结果,推广和改进了已有的结果.     

On an entropy of ℤ + k -actions

In this paper,a definition of entropy for Z＋k（k≥2）-actions due to Friedland is studied.Unlike the traditional definition,it may take a nonzero value for actions whose generators have finite（even zero） entropy as single transformations.Some basic properties are investigated and its value for the Z＋k-actions on circles generated by expanding endomorphisms is given.Moreover,an upper bound of this entropy for the Z＋k-actions on tori generated by expanding endomorphisms is obtained via the preimage entropies,which are entropy-like invariants depending on the ＂inverse orbits＂ structure of the system.     

A gap theorem on submanifolds with finite total curvature in spheres

We study a complete noncompact submanifold Mⁿ$M^n$ in a sphere S^n+p${\mathbb{S}}^{n+p}$. We prove that there admit no nontrivial L²$L^2$-harmonic 1-forms on M if the total curvature is bounded from above by a constant depending only on n. The gap theorem is a generalized version of Carron?s, Yun?s, Cavalcante?s and the first author?s results on submanifolds in Euclidean spaces and Seo?s result on submanifolds in hyperbolic space without the condition of minimality.     

Periodic boundary value problems for first-order impulsive dynamic equations on time scales

This paper deals with the periodic boundary value problem for a class of first-order impulsive dynamic equations on time scales. We introduce a new notion of lower and upper solutions, which extends the classical lower and upper solutions. The existence of extremal solutions is presented by virtue of the method of lower and upper solutions coupled with monotone iterative technique. An example is also included to illustrate the main results.     

Generalized Heisenberg-Virasoro algebras

In this paper, we mainly study the generalized Heisenberg-Virasoro algebra. Some structural properties of the Lie algebra are obtained.      

A path following algorithm for a class of convex programming problems

We present a primal-dual path following interior algorithm for a class of linearly constrained convex programming problems with non-negative decision variables. We introduce the definition of a Scaled Lipschitz Condition and show that if the objective function satisfies the Scaled Lipschitz Condition then, at each iteration, our algorithm reduces the duality gap by at least a factor of (1–/n), where is positive and depends on the curvature of the objective function, by means of solving a system of linear equations which requires no more than O(n³) arithmetic operations. The class of functions having the Scaled Lipschitz Condition includes linear, convex quadratic and entropy functions.     

三维粘流—无粘干扰流动方程组部分正则性问题

本文讨论了三维粘流一无粘干扰流动方程组部分正则性问题，引入了新的三维粘流－无粘干扰流动假设，并得到了相应的结论。