Synthesis and self‐assembly of poly(styrene)‐b‐poly(N‐vinylpyrrolidone) amphiphilic diblock copolymers made via a combined ATRP and MADIX approach

Amphiphilic diblock copolymers of polystyrene (PS) and poly(N‐vinylpyrrolidone) (PNVP) were prepared by a combination of ATRP and MADIX. Well‐defined PS with bromine end group was synthesized by ATRP in bulk at 110 °C using (1‐bromoethyl) benzene as an initiator. The Br‐ end group was then converted to xanthate as verified by ¹H NMR spectroscopy, elemental analysis, and UV‐spectroscopy. PS‐b‐PNVP copolymers were produced by MADIX of NVP in bulk at 60 °C using PS‐xanthate as a macro‐chain transfer agent and the kinetics of polymerization were investigated. The structures of PS‐b‐PNVP were characterized using GPC and ¹H NMR. Amphiphilic PS‐b‐PNVP could form spherical micelles with PS cores and PNVP shells in aqueous solution as confirmed by ¹H NMR and laser light scattering (LLS). The values of critical micelle concentration of PS‐b‐PNVP and the average aggregation number of PS‐b‐PNVP in the micelles were measured using pyrene as a probe and static LLS, respectively. The aggregation number increases concomitantly with temperature (10–50 °C), but the hydrodynamic radius of the micelles remains almost constant over the same temperature range, which may indicate shell dehydration at a higher temperature. © 2008 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 46: 5604–5615, 2008     

Phase behavior study of poly(N‐tertbutylacrylamide‐co‐acrylamide) in the mixture of water–methanol: The role of polymer–nonsolvent second‐order interactions

The phase behavior of poly(N‐tertbutylacrylamide‐co‐acrylamide) (PNTBAM) in pure water and mixture of water–methanol is studied at different temperatures. The different compositions of PNTBAM are prepared by free‐radical polymerization technique and their phase behavior is studied by turbidimetry. The effects of copolymer and solvent composition on the phase behavior of the copolymers are discussed. It has been suggested that the inhomogenities in polymer chains are responsible for lowering the rate of phase transition by increasing the N‐tertbutylacrylamide (NTBAM) and methanol contents in copolymer and mixture, respectively. For the first time we have revealed that there are second‐order binary interactions in the water–methanol which are dominant in the special range of copolymer composition. © 2009 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 47: 455–462, 2009     

多光子J-C模型的场熵的演化

研究了一个二能级原子与相干光场多光子相互作用下场熵演化的动力学特性     

The Index of Vector Fields and Logarithmic Differential Forms

We introduce the notion of logarithmic index of a vector field on a hypersurface and prove that the homological index can be expressed via the logarithmic index. Then both invariants are described in terms of logarithmic differential forms for Saito free divisors, which are hypersurfaces with nonisolated singularities, and all contracting homology groups of the complex of regular holomorphic forms on such a hypersurface are computed. In conclusion, we consider the case of normal hypersurfaces, including the case of an isolated singularity, and describe the contracting homology of the complex of regular meromorphic forms with the help of the residue of logarithmic forms.     

两同心球间旋转流动类Lorenz方程组的静态分歧

对同心球间旋转流动的N av ier-S tokes方程谱展开后进行三模态截断,讨论了所得到的类Lorenz型方程组的分歧问题.给出了静态奇异点的条件,并计算出解分支.首先,简要介绍了Lorenz方程组以及用Lorenz截断法讨论非线性问题的意义,其次,推导同心球间旋转流动N av ier-S tokes方程的流函数-涡度形式,最后,讨论同心球间旋转流动的类Lorenz型方程组的分歧问题.     

第三型伯恩斯坦插值过程的双结点修正

In this work,the well-known problem put forward by S N Bernstein in 1930 is studied in a deep step.An operator is constructed by revising double interpolation nodes.It is proved that the operator converges to arbitrary continuous functions uniformly and the convergence order is the best.     

任意信源随机和的一类随机Shannon-McMillan定理

采用构造相容分布与非负上鞅的方法研究任意信源随机和相对熵密度的强极限定理,并由此得出若干任意信源,m阶马氏信源,无记忆信源的随机Shannon-Mcmillan定理.将已有的关于离散信源的结果加以推广.     

High accuracy time and space transform method for advection–diffusion equation in an unbounded domain

A new numerical method called high accuracy time and space transform method (TSTM) is introduced to solve the advection–diffusion equation in an unbounded domain. By a spatial transform, the advection–diffusion equation in the unbounded domain Rⁿ is converted to one on the bounded domain [?1, 1]ⁿ, and the Laplace transform is applied to eliminate time dependency. The consequent boundary value problem is solved by collocation on Chebyshev points. To face the well‐known computational challenge represented by the numerical inversion of the Laplace transform, Talbot's method is applied, consisting of numerically integrating the Bromwich integral on a special contour by means of trapezoidal or midpoint rules. Numerical experiments illustrate that TSTM has exponential rate in time and space. Copyright © 2008 John Wiley & Sons, Ltd.     

Epidemic dynamics in a heterogeneous incompletely isolated population with allowance for seasonal variations in the infection rate

Mathematical parasite-host models are generalized to the case when the population members differ in susceptibility and contagiousness, there is an external source of infection, and the model parameters depend periodically (seasonally) on time. The model is proved to have a periodic solution that is unique and exponentially stable for sufficiently small periodic oscillations of the coefficients.