Light-scattering study of the coil-to-globule transition of linear poly(N-isopropylacrylamide) ionomers in water

The coil-to-globule transition of two poly(N-isopropylacrylamide) (PNIPAM) ionomers with different ionic contents (0.8 and 4.5 mol %), but similar weight average molar masses, in deionized water was investigated by a combination of static and dynamic light scattering. In spite of the large difference in their ionic contents, both the ionomers have a nearly same lower critical solution temperature (LCST, ∼ 32.5°C). At temperatures higher than the LCST, the ionomer chains undergo a simultaneous intrachain coil-to-globule transition and interchain aggregation to form nanoparticles thermodynamically stable in water. The average size of the nanoparticles decreases respectively as the ionic content increases and the ionomer concentration decreases. The interchain aggregation can be completely suppressed in an extremely dilute ionomer solution (< ∼ 5 × 10⁻⁶ g/mL), so that the intrachain coil-to-globule transition leads to the collapse of the ionomer chains into individual single-chain nanoparticles. Our results clearly indicate that there is a hysteresis in the colling process (the globule-to-coil transition). © 1998 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 36: 1501–1506, 1998     

矩阵方程ATXB+BTXTA=D的极小范数最小二乘解的迭代解法

1 引言 设Rm×n表赤m×n实矩阵的全体,AT表示矩阵A的转置,R(A)和N(A)分别表示矩阵A的值域和零空间.     

铁镓驱动弯曲圆盘换能器设计及振动特性研究

为了研究新型磁致伸缩材料——铁镓合金(Galfenol)在换能器中应用,本文设计了一种低频弯曲圆盘换能器。借助有限元软件仿真分析换能器振动模态,对换能器结构参数进行优化设计,并研制了换能器样品。利用激光测振仪测量了换能器空气中模态及不同电流驱动下振动位移,测得振动模态与仿真结果吻合,换能器空气中共振频率为913 Hz,辐射头能够产生的最大振动位移达到93μm,磁致伸缩材料达到饱和应变。结果表明:铁镓材料能够驱动弯曲圆盘换能器大振幅振动;铁镓作为磁致伸缩换能器驱动材料具有较好的应用前景。     

Approximation on the Voronoi Cells of the A d Lattice

We study several approximation problems on the Voronoi cells of the A _d lattice. The study depends on discretization of the Voronoi cells induced by a zonotopal algebra and finite quotient groups. The latter provides a natural tool for doing discrete Fourier analysis on the Voronoi cells. The interactions between the groups and their dual groups yield interpolation and quadrature formulas on the Voronoi cells. The zonotope structure allows us to investigate the approximation property of several types of kernels (including the Dirichlet type and the Fejér type) on the Voronoi cells. The convolution operator given by the Fejér type kernel is positive, and consequently an approximate identity. The Fejér type kernel can also be realized as a summability method. As an interesting comparison to the classical (C,1) summability which assigns equal weight to the partial sums of a Fourier series, the Fejér type summability method on the Voronoi cells assigns equal weights to about half of the partial sums and algebraically decaying weights to the rest.     

非对称线性代数方程组的块向量算法

预条件广义共轭余量法并行和向量计算的关键是预条件计算是否可并行和向量计算，我们利用分而治之的原则，构造了一处块预条件矩阵Ｍ，这里的矩阵Ｍ是通过对线性代数方程组Ａｘ＝ｆ的矩阵Ａ进行块分解，在块分解中利用近似逆技术。这样分解形成的预条件矩阵Ｍ在迭代计算时，可向量或并行计算。     

The fundamentality of translates of a continuous function on spheres

In this paper we discuss the fundamentality of translates of a continuous function on the unit spheres of Euclidean spaces. Our result partially answers a question of Cheney and Xu [1].