Thin-walled Beams: A Derivation of Vlassov Theory via Γ-Convergence

This paper deals with the asymptotic analysis of the three-dimensional problem for a linearly elastic cantilever having an open cross-section which is the union of rectangles with sides of order ε and ε ², as ε goes to zero. Under suitable assumptions on the given loads and for homogeneous and isotropic material, we show that the three-dimensional problem Γ-converges to the classical one-dimensional Vlassov model for thin-walled beams.      

分形维数与城市规模分布评析

本在分形概念的基础上，指出城市规模分布是基于统计意义上的一种分形分布，并计算了安徽省1978～1998年城市规模分布的分维值，评析了安徽省城市规模分布变化的特征。     

R￣d中Hausdorff维数和packing维数的确定

本文目的在于建立确定Ｒ￣ｄ中Ｈａｕｓｄｏｒｆｆ维数ｄｉｍ和ｐａｃｋｉｎｇ维数Ｄｉｍ的两个命题（定理１和定理２），进而寻求Ｒ￣ｄ中Ｈａｕｓｄｏｒｆｆ维数ｄｉｍ与ｐａｃｋｉｎｇ维数Ｄｉｍ相等的条件；这使得我们能够引入分形测度的测度论定义。     

The Computable Dimension of I-Trees of Infinite Height

We study computable trees with distinguished initial subtree (briefly, I-trees). It is proved that all I-trees of infinite height are computably categorical, and moreover, they all have effectively infinite computable dimension.     

Long time behaviour of a flow in infinite pipe conforming to slip boundary conditions

The paper analyses long time behaviour of solutions of the Navier–Stokes equations in a two‐dimensional pipe‐like domain. The system is studied with perfect slip boundary conditions with arbitrary inflow conditions at infinity. The main results show the existence of global in time solutions and of an attractor for the dynamical system generated by the model. The paper also establishes an upper bound for the Hausdorff dimension of the attractor. Copyright © 2005 John Wiley & Sons, Ltd.     

Macroscopic Dimension of 3-Manifolds

In this paper we give the answer to the Gromov's question about the macroscopic dimension of universal coverings of closed manifolds in dimension 3. We prove that the macroscopic dimension of a universal covering of a closed Riemannian 3-manifold cannot be equal to 2.     

The fifth dimension: Theodor Kaluza's ground‐breaking idea

Theodor Kaluza (1885–1954) attracted the attention of the physical community since 1921 with his unified field theory of gravitation and electromagnetism in five dimensions. Despite Einstein's great interest in Kaluza's theory, 50 years elapsed before it contributed toward a paradigm shift in modern theoretical physics. The biography of this still unknown scientist is briefly presented along with an outline of his work in physics. A short history of the theories of unification and the dimensionality of space‐time is followed by a discussion of the significance of Kaluza's five‐dimensional unified theory in modern physics from the point of view of superstring and M‐theory.     

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     

Information processing,memories, and synchronization in chaotic neural network with the time delay

Information processing and two types of memory in an analog neural network model with time delay that produces chaos similar to the human and animal EEGs are considered. There are two levels of information processing in this neural network: the level of individual neurons and the level of the neural network. Similar to the state of brain, the state of chaotic neural network is defined. It is characterized by two types of memories (memory I and memory II) and correlation structure between the neurons. In normal (unperturbed) state, the neural network generates chaotic patterns of averaged neuronal activities (memory I) and patterns of oscillation amplitudes (memory II). In the presence of external stimulation, the activity patterns change, showing changes in both types of memory. As in experiments on stimulation of the brain, the neural network model shows synchronization of neuronal activities due to stimulus measured by Pearson's correlation coefficient. An increase in neural network asymmetry (increase of the neural network excitability) leads to the phenomenon similar to the epilepsy. Modeling of brain injury, Parkinson's disease, and dementia is performed by removing and weakening interneuron connections. In all cases, the chaotic neural network shows a decrease of the degree of chaos and changes in both types of memory similar to those observed in experiments with healthy human subjects and patients with Parkinson's disease and dementia. © 2005 Wiley Periodicals, Inc. Complexity 11:39–52, 2005     

ANTI FUZZY VECTOR SPACES（Ⅱ）

ＡＮＴＩＦＵＺＺＹＶＥＣＴＯＲＳＰＡＣＥＳ（Ⅱ）ＣｈｅｎＹｏｎｇｎｉａｎ（ＤｅｐａｒｔｍｅｎｔｏｆＭａｔｈｅｍａｔｉｃｓ，ＸｉｎｊｉａｎｇＮｏｒｍａｌＵｎｉｖｅｒｓｉｔｙ，８３００５４，Ｘｉｎｊｉａｎｇ，Ｐ．Ｒ．Ｃｈｉｎａ）ＡＮＴＩＦＵＺＺＹＶＥＣＴ...