On the Diffusion Coefficient: The Einstein Relation and Beyond

We present a detailed derivation of the closed-form expression for the diffusion coefficient that was initially obtained by Einstein.[4] in press.  [Google Scholar] The present derivation does not make use of a fictitious force as did the original Einstein derivation, but instead concentrates directly on establishing a dynamic equilibrium between the forces of pressure and friction acting on a Brownian particle. This approach makes it easier to understand the true essence of the argument, and thus makes it simpler to apply the argument in a more general case or setting. We demonstrate this by deriving the equation of motion of a Brownian particle that is under the influence of an external force in the fluid with a non-constant temperature. This equation extends the well-known Smoluchowski approximation[24] Smoluchowski, M. von. 1915. Über Brownsche Molekularbewegung unter Einwirkung äußerer Kräfte und deren Zusammenhang mit der verallgemeinerten Diffusionsgleichung. Ann. Phys., 48: 1103–1112.  [Google Scholar] to the case of non-constant temperature, and offers new insights into the Ludwig–Soret and Enskog–Chapman effects (providing also a scholar example explaining the need for a stochastic integral). The key point in the derivation is reached by applying the Einstein dynamic equilibrium argument together with the conservation of the number of particles law. We show that this approach leads directly to the Kolmogorov forward equation whenever the setting is Markovian. The same method can also be applied in the case of interacting Brownian particles satisfying the van der Waals equation. In this setting we first demonstrate that the presence of short-range repulsive forces between Brownian particles tends to increase the diffusion coefficient, and the presence of long-range attractive forces between Brownian particles tends to decrease it. The method of derivation then leads to a nonlinear partial differential equation which in the case of weak interaction reduces to the Fokker–Planck equation. One of the main aims of the present article is to demonstrate that the Einstein argument leads to a truly dynamical theory of diffusion.     

位移介质动词的语义与论元表达

运用词汇语义学（Lexical Semantics）理论考察汉语位移介质动词的论元表达情况,探讨位移介质动词与位移方向动词在论元表达方面的差异,可以揭示汉语部分位移动词在论元表达中表现出的语义因素,并分析出动词家族相似性的基本表现：不同语义类的动词存在着“大异小同”,同一个语义类动词的不同成员存在着“大同小异”.不同动词成员在意义上存在着相互关联,形成一个非常复杂的语义网络.     

Innovation on Case Teaching of ＂Chinese Health Preservation of the Elder＂

“老年中医养生”课程是老年服务与管理专业学习领域课程中的一门职业核心课程。教学中运用多媒体案例教学法、行动引导教学法等有效方法,培养学生的学习兴趣,建立学生的自信心,提高学生的自我学习能力,以使学生具备中医养生的基本素养,在实训中能够指导老年人进行因人、因时和因地摄养等养生实践活动。     

Development of interactive biological motion perception in preschoolers and its relation to social competence

The perception of interactive biological motion (BM) plays an important role in social life. Such social perception enables people to understand the underlying social intentions and social relationships in interactive actions, so that they can anticipate the behavior response in an appropriate manner. Although interaction perception has been widely explored in adults, little is known about preschoolers' developmental trajectory of interaction perception and its further impact on social development. This study explored the development of interaction perception in a dyadic BM situation and its relation to teachers' report of social competence among 3–6‐year olds (N = 119). Children were asked to watch videos of dyadic BM and decide whether two characters were interacting or not. The results suggested that the sensitivity of BM perception continues to develop during the entire preschool age period and is positively associated with children's social competence among children aged 5–6, even after controlling for age and language ability. However, for younger children aged 3–4, language ability rather than perception of social interaction positively correlated with their social competence. Our findings review the rapid development of interactive BM perception in early childhood and highlight the important role of interaction perception in preschoolers’ social development.     

A strong convergence to the tempered fractional Brownian motion

In this paper, we give a strong approximation of the tempered fractional Brownian motion via transport processes and derive the rate of convergence.     

后发工业国技术从模仿到创新的路径、动力与选择机制——基于汽车产业拉美模式、日韩模式和中国模式的比较分析

后发工业国从模仿到创新的技术战略演进路径呈现多样性,为解释后发工业国汽车产业技术演进路径差异和选择,通过构造一个以企业家精神和企业技术能力成长为主要内驱力,市场需求、技术发展和溢出为拉力、研发投入和产业激励政策为推力,高昂技术学习成本和企业创新惯例和惰性等为阻力以及市场竞争和约束性产业政策为压力的汽车产业技术演进动力模型,比较分析了后发工业国汽车产业技术演进的动力差异和选择机制,并为中国汽车产业技术能力的发展提供有益建议。     

Estimation and testing stationarity for double-autoregressive models

Summary.  The paper considers the double-autoregressive model y _t  =  φ y _{t −1}+ ɛ _t with ɛ _t  =     . Consistency and asymptotic normality of the estimated parameters are proved under the condition E  ln | φ  +√ α η _t |<0, which includes the cases with | φ |=1 or | φ |>1 as well as     . It is well known that all kinds of estimators of φ in these cases are not normal when ɛ _t are independent and identically distributed. Our result is novel and surprising. Two tests are proposed for testing stationarity of the model and their asymptotic distributions are shown to be a function of bivariate Brownian motions. Critical values of the tests are tabulated and some simulation results are reported. An application to the US 90-day treasury bill rate series is given.     

紧集上布朗单水平集的Hausdorff维数

讨论了紧集上布朗单水平集的Ｈａｕｓｄｏｒｆｆ维数的上下界，得到了几个重要结果。