Transient free‐surface flow of a viscoelastic fluid in a narrow channel

The interplay between inertia and elasticity is examined for transient free‐surface flow inside a narrow channel. The lubrication theory is extended for the flow of viscoelastic fluids of the Oldroyd‐B type (consisting of a Newtonian solvent and a polymeric solute). While the general formulation accounts for non‐linearities stemming from inertia effects in the momentum conservation equation, and the upper‐convected terms in the constitutive equation, only the front movement contributes to non‐linear coupling for a flow inside a straight channel. In this case, it is possible to implement a spectral representation in the depthwise direction for the velocity and stress. The evolution of the flow field is obtained locally, but the front movement is captured only in the mean sense. The influence of inertia, elasticity and viscosity ratio is examined for pressure‐induced flow. The front appears to progress monotonically with time. However, the velocity and stress exhibit typically a strong overshoot upon inception, accompanied by a plug‐flow behaviour in the channel core. The flow intensity eventually diminishes with time, tending asymptotically to Poiseuille conditions. For highly elastic liquids the front movement becomes oscillatory, experiencing strong deceleration periodically. A multiple‐scale solution is obtained for fluids with no inertia and small elasticity. Comparison with the exact (numerical) solution indicates a wide range of validity for the analytical result. Copyright © 2004 John Wiley & Sons, Ltd.     

共轴均匀带电薄圆盘间的相互作用力

本文利用静电场的高斯定律和环路定律巧妙地求出了均匀带电圆盘在空间任一点所产生的电场 ,进而计算出了共轴均匀带电薄圆盘之间的相互作用力     

A RANDOM FIXED POINT ITERATION FOR THREE RANDOM OPERATORS ON UNIFORMLY CONVEX BANACH SPACES

In the present paper we introduce a random iteration scheme for three random operators defined on a closed and convex subset of a uniformly convex Banach space and prove its convergence to a common fixed point of three random operators. The result is also an extersion of a known theorem in the corresponding non-random case.     

更新时间概率模型及其无偏估计定理的论证

本文提出应用小参数法 ,探讨 Markov链中相邻两次更新时刻内稀疏事件的概率估计问题 .建立了三种最重要的具有更新时间的概率模型 .通过小参数的引入和对概率式的幂展开 ,进而推证出幂渐近展开系数的模型估算法 .论证了无偏估计的重要定理 ,给出了概率估计式和无偏估计精度 .亦将许多算法扩展到Markov链的任意状态空间     

含k-次增生算子的Ishikawa迭代的收敛性问题

主要研究了非线性方程x Tx=f的Ishikawa迭代解．其中T为k-次增生的或增生的，并在一致光滑和任意的实Banach空间分别研究了上述方程的带误差的Ishikawa迭代解，从而推广了已知的一些结果。     

Functional Quantization and Small Ball Probabilities for Gaussian Processes

Quantization consists in studying the L ^r -error induced by the approximation of a random vector X by a vector (quantized version) taking a finite number n of values. We investigate this problem for Gaussian random vectors in an infinite dimensional Banach space and in particular, for Gaussian processes. A precise link proved by Fehringer⁽⁴⁾ and Dereich et al. ⁽³⁾ relates lower and upper bounds for small ball probabilities with upper and lower bounds for the quantization error, respectively. We establish a complete relationship by showing that the same holds for the direction from the quantization error to small ball probabilities. This allows us to compute the exact rate of convergence to zero of the minimal L ^r -quantization error from logarithmic small ball asymptotics and vice versa.     

散射体系A+BC的平-振能量传递

用Alhassid与Levine所提出的动力学李代数的方法(简称A-L理论),研究了含有二级非简谐的共线散射体系A+BC的平-振能量传递问题,计算了散射过程含有主要动力学参量的跃迁矩阵和跃迁几率的解析表示式.     

同步辐射小角x射线散射方法研究由城市固体垃圾制备的活性炭

应用同步辐射小角x射线散射方法研究了由不同城市固体垃圾制备而成的活性炭的孔结构-结果发现利用木类、纸张、塑料这三类典型垃圾组分的热解残余物为原料制备中孔发达的活性炭是可行的-活性炭的形态和结构取决于垃圾热解残余物的组分和热解程度等因素- 关键词： 小角x射线散射 活性炭 分形维数 平均孔径     

Bundles, Handcuffs, and Local Freedom

We answer a question of J. Anderson's by producing infinitely many commensurability classes of fibered hyperbolic 3-manifolds whose fundamental groups contain subgroups that are locally free and not free. These manifolds are obtained by performing 0–surgery on a collection of knots with the same properties.     

Free radical-mediated vinyl amination: a mild, general pyrrolidinyl enamine synthesis

The complete scope of free radical-mediated vinyl amination is described, using 5-exo-trig cyclizations of vinyl radicals to the nitrogen of azomethines. The focus is primarily on N,N-dialkyl enamines since their nucleophilicity renders them the most challenging enamines to synthesize using redox conditions. These studies establish several encouraging precedents for the broader application of this strategy.