聚合物流动诱导结晶研究进展

在外力作用下,半结晶聚合物的结晶形态、结晶动力学等与静态条件下相比,均发生了较大的变化,并继而影响到成型制品的性能.自上世纪六十年代人们从溶液中发现外力诱导结晶现象以来,相继开展了大量相关的理论和实验研究,提出了一些模型,随着测试手段的改进,流动诱导结晶研究取得了较大的进展,但仍存在许多争议.本文回顾了围绕聚合物流动诱导结晶所开展的工作,重点综述了流动诱导结晶形态变化、分子量及其分布、剪切速率、温度等因素对聚合物结晶动力学的影响,并指出了今后的研究方向.     

Temporal variation of velocity components in a turbulent open channel flow: Identification of fractal dimensions

Fractals are objects which have similar appearances when viewed at different scales. Such objects have details at arbitrarily small scales, making them too complex to be represented by Euclidian space; hence, they are assigned a non-integer dimension. Some natural phenomena have been modeled as fractals with success; examples include geologic deposits, topographic surfaces and seismic activities. In particular, time series have been represented as a curve with fractal dimensions between one and two. There are different ways to define fractal dimension, most being equivalent in the continuous domain. However, when applied in practice to discrete data sets, different ways lead to different results. In this study, three methods for estimating fractal dimension are described and two standard algorithms, Hurst’s rescaled range analysis and box-counting method (BC), are compared with the recently introduced variation method (VM). It was confirmed that the last method offers a superior efficiency and accuracy, and hence may be recommended for fractal dimension calculations for time series data. All methods were applied to the measured temporal variation of velocity components in turbulent flows in an open channel in Shiraz University laboratory. The analyses were applied to 2500 measurements at different Reynold’s numbers and it was concluded that a certain degree of randomness may be associated with the velocity in all directions which is a unique character of the flow independent of the Reynold’s number. Results also suggest that the rigid lateral confinement of flow to the fixed channel width allows for designation of a more-or-less constant fractal dimension for the spanwise velocity component. On the contrary, in vertical and streamwise directions more freedom of movements for fluid particles sets more room for variation in fractal dimension at different Reynold’s numbers.     

Properties of some statistics for AR-ARCH model with application to technical analysis

In this paper, we investigate some popular technical analysis indexes for AR-ARCH model as real stock market. Under the given conditions, we show that the corresponding statistics are asymptotically stationary and the law of large numbers hold for frequencies of the stock prices falling out normal scope of these technical analysis indexes under AR-ARCH, and give the rate of convergence in the case of nonstationary initial values, which give a mathematical rationale for these methods of technical analysis in supervising the security trends.     

Conceptual variation and coordination in probability reasoning

This study investigates students’ conceptual variation and coordination among theoretical and experimental interpretations of probability. In the analysis we follow how Swedish students (12-13 years old) interact with a dice game, specifically designed to offer the students opportunities to elaborate on the logic of sample space, physical/geometrical considerations and experimental evidence when trying to develop their understanding of compound random phenomena.The analytical construct of contextualization was used as a means to provide structure to the qualitative analysis performed. Within the frame of the students’ problem encounters during the game and how they contextualized the solutions of the problems in personal contexts for interpretations, the analysis finds four main forms of appearance, or of limitations in appearance, of conceptual variation and coordination among theoretical and experimental interpretations of probability.     

Regularity of stresses in Prandtl-Reuss perfect plasticity

We study the differential properties of solutions of the Prandtl-Reuss model. We prove that in dimensions n = 2, 3 the stress tensor has locally square-integrable first derivatives: . The result is based on discretization of time and uniform estimates of solutions of the incremental problems, which generalize the estimates in the case of Hencky perfect plasticity. Counterexamples to the regularity of displacements and plastic strains in the quasistatic case are presented.      

Shibor期限结构动态研究

近年来央行一直推动利率市场化进程,央行将把上海银行间同业拆放利率(Shibor)培育成基准利率。为了推动利率市场化进程,本文以Shibor作为研究对象,构造了Shibor期限结构的基础模型。为了进一步找出Shibor的变化规律,对于基础模型我们做了不同的扩展,并应用时间序列模型对我国的Shibor期限结构进行了实证分析,发现:隔夜、1周、2周、1个月Shibor具有很强的均值回复特性,3个月、6个月、9个月及1年Shibor不具有显著的线性均值回复特征;1个月、3个月、6个月、9个月及1年Shibor期限结构的扩散项部分是对称的,而隔夜、1周、2周Shibor期限结构的扩散项部分存在明显的不对称性。     

Global smoothness and uniform convergence of smooth Poisson-Cauchy type singular operators

In this article we introduce the smooth Poisson-Cauchy type singular integral operators over the real line. Here we study their simultaneous global smoothness preservation property with respect to the L_p norm, 1?p?∞, by involving higher order moduli of smoothness. Also we study their simultaneous approximation to the unit operator with rates involving the modulus of continuity with respect to the uniform norm. The produced Jackson type inequalities are almost sharp containing elegant constants, and they reflect the high order of differentiability of the engaged function.     

A generalization of a result of G. Pólya and its application to a continuous extension of the de la Vallée Poussin means

Variation diminishing properties are established for the periodic kernels . On the real axis, there are related variation diminishing properties of the functions u^msgnu, which are the Green’s functions for the differential operator D^(m+1).     

Brown运动连续模在H(o)lder范数下的拟必然收敛速度

本文中,用Brown运动在H(o)lder范数下关于Cr,p-容度的大偏差与小偏差,得到了Brown运动连续模在H(o)lder范数下关于Cr,p-容度的泛函收敛速度.     

随机利息力下的期末付倒平顶虹式年金

对于年金的定价问题的研究,传统精算理论假定利率是恒定不变的．但事实上,由于受到多种因素的影响,利率往往具有不确定性．因此,本文采用可逆MA（1）模型来刻画利率期限机构,在此基础上,研究了期末付倒平顶虹式年金的各阶矩问题,推导出了其年金现值的期望和方差的简洁公式．通过数值模拟分析了此年金面临的利率风险,其结论对年金定价有一定的参考价值．