Topological entropy dimension for noncompact sets

Similar with the fractal dimension, we introduce the concept of topological entropy dimension to classify the sets with entropy zero. We prove that the entropy dimension of the space in this article is not greater than that defined by De Carvalho, where he introduced the entropy dimension for the system, and give some examples indicating that such inequality is optimal. Some basic propositions of entropy dimension are discussed and it turns out that the entropy dimension is invariant under conjugacy. The property of the countable stability and a power rule for the entropy dimension of any set are obtained. It is shown that any set shares the same entropy dimension with its image set.     

Systems with almost specification property may have zero entropy

It is shown that there exist systems having almost specification property and zero entropy. Since Bowen has shown that systems with specification property must have positive entropy, this result reveals further the difference between almost specification and specification. Moreover, one can obtain a both sufficient and necessary condition to ensure positive entropy for systems with almost specification property.     

Topological pressure dimension for almost additive potentials

This paper is devoted to the study of the topological pressure dimension for almost additive sequences, which is an extension of topological entropy dimension. We investigate fundamental properties of the topological pressure dimension for almost additive sequences. In particular, we study the relationships among different types of topological pressure dimension and identify an inequality relating them. Also, we show that the topological pressure dimension is always equal to or greater than 1 for certain special almost additive sequence.     

零维纳米Fe2O3粉体的制备与吸波性能的研究

使用不同的化学共沉淀法制备零维纳米γ-Fe2O3和α-Fe2O3粉体,通过比表面测试、透射电镜(TEM)和X-射线衍射(XRD)分析其结构,并在10GHz的频率下测试了它们的微波吸收性能。结果表明：实验制备得到了零维纳米γ-Fe2O3和α-Fe2O3粉体,在10GHz的频率下γ-Fe2O3的微波吸收性能比α-Fe2O3要好。     

Computation of the Kolmogorov entropy for MDOF systems

The dynamics of a truss structure with several bars and nodes is investigated. The bars are made of some nonlinear material and the truss structure shows large displacements under some time-dependent loads. The resulting equations are an example of a model which governs the motion of a general MDOF structure after some discretization procedure, like FEM. Attention is focused on the response strangeness met during the numerical integration of the motion equations. As a principal tool of investigation, one uses the Kolmogorov entropy, the value of which is able to detect the sensitivity to initial conditions. The material can present either nonlinear elastic softening or elasto-plastic behaviour. This research has been supported by grants from the Italian Ministry of University and Scientific and Technological Research (MURST).     

Topological entropy of continuous transitive maps on the real line

The topological entropy of a continuous transitive map f : ? → ? is studied. We find lower bounds for the topological entropy of f and prove that transitive real maps can have finite entropy.     

一维,二维和三维Si基纳米线的制备

在Ar气氛中，SiC粉末分别在Fe、Co、Fe：Co(1：1)的催化下，经一步反应制备了一维、二维和三维si基纳米线。SEM、HRTEM、EDX分析表明一维线状和二维网状Si基纳米线由C、Si、O组成，存在两类纳米线，一类是SiO，包裹的Si纳米线；另一类是SiO，包裹的SiC纳米线。三维Si基纳米线组成象花一样的结构，仅由SiOx组成。SiOx和Si是无定形结构，SiC是β-SiC单晶。     

Construction of probability distributions in high dimension using the maximum entropy principle: Applications to stochastic processes,random fields and random matrices

The construction of probabilistic models in computational mechanics requires the effective construction of probability distributions of random variables in high dimension. This paper deals with the effective construction of the probability distribution in high dimension of a vector‐valued random variable using the maximum entropy principle. The integrals in high dimension are then calculated in constructing the stationary solution of an Itô stochastic differential equation associated with its invariant measure. A random generator of independent realizations is explicitly constructed in this paper. Three fundamental applications are presented. The first one is a new formulation of the stochastic inverse problem related to the construction of the probability distribution in high dimension of an unknown non‐stationary random time series (random accelerograms) for which the velocity response spectrum is given. The second one is also a new formulation related to the construction of the probability distribution of positive‐definite band random matrices. Finally, we present an extension of the theory when the support of the probability distribution is not all the space but is any part of the space. The third application is then a new formulation related to the construction of the probability distribution of the Karhunen–Loeve expansion of non‐Gaussian positive‐valued random fields. Copyright © 2008 John Wiley & Sons, Ltd.     

基于功能尺寸最短路径的零件尺寸标注模式的设计

机械零件的尺寸标注模式有多种.尺寸标注模式影响着机械产品的精度和制造成本.为获得零件尺寸合理的标注模式,建立了包含零件尺寸标注所有可能模式的装配尺寸联系路径图;以满足装配体功能尺寸形成路径最短为目标,基于装配尺寸链最短路径原则和最短路径问题的求解,通过2种方法建立了装配体功能尺寸最短路径生成树.功能尺寸最短路径生成树确...     

基于排列熵理论的非线性系统特征提取研究

提出一种基于排列熵及其改进理论的伪相平面法,从而可以提取非线性系统中的微弱周期信号特征。通过选择合理的时间延迟和嵌入维数,对Duffing系统的响应信号进行相空间重构,得到一次排列熵和二次排列熵。随后将位移激励、一次排列熵和二次排列熵作为数据集,组成位移激励-一次排列熵和位移激励-二次排列熵两种伪相平面。通过将这两种方法与传统的相平面法、频谱分析和排列熵、排列熵谱、二次排列熵、二次排列熵谱的提取效果进行对比,验证了该方法的合理性。研究表明该方法能够对非线性系统中的微弱周期信号特征进行提取,取得了较好效果。     

大规模动力系统高精度増维精细积分方法快速算法

考虑高精度増维精细积分法求解大规模动力系统快速算法。为提高増维精细积分方法求解大规模动力系统精度,将非齐次项近似为高阶多项式,形成高精度増维精细积分方法;为减少计算时间、提高计算效率,提出高精度増维精细积分方法快速算法。算例表明,通过提高非齐次项近似阶数可显著提高计算精度,快速算法可使计算效率呈量级提高,高精度快速算法适合大规模动力系统长时间推进计算。     

平面孔系尺寸的建模及其应用研究

针对传统的孔系尺寸计算需要绘制尺寸链图、判断增减环,以及存在过程复杂易出错等问题,提出用工序尺寸的路径图来描述平面孔系的各个孔的加工顺序和加工基准.基于路径图建立全相关的尺寸模型,求解得到具有矢量特征的坐标尺寸,并利用全微分法求解坐标尺寸的公差.避免了现有方法的缺陷,适用于加工中心及数控机床上孔系加工的计算机编程计算.     

Entropy and entropy of mixing

Entropy as a function of temperature at constant volume, S(T), can be determined by integrating the molar specific entropy capacity C_V/T (C_V: molar specific heat capacity at constant volume). As a second approach, S(T) at constant volume can be determined by differentiating the free energy with respect to the temperature, T. Recently, it has been shown for a system obeying Boltzmann statistics that these mathematical approaches are equivalent to applying the formula of the mixing entropy, if the ground and excited states of the same sub‐systems or elementary systems are considered as mixing objects or quantum components. This result considerably extends the applicability of the formula of the mixing entropy, which is derived in textbooks just for mixing real indifferent components. In the present paper, it is shown that the formula of the mixing entropy can also be applied to calculate the entropy of Bose and Fermi systems. Thus, all entropy can be calculated and interpreted as mixing entropy of real components or quantum components. In reverse, the transitions between the ground and the excited states of any system can be explained as mixing processes. This interpretation is applied to the melting transition of chemically bonded solids and in particular to the glass transition whereby upon cooling the mixing entropy of the melt is (at least partly) frozen in the configuration. These results suggest a new interpretation of the glass transition and a new definition of structural glass.     

Conformal iterated function systems with overlaps

For a conformal iterated function system satisfying the bounded distortion property and the weak separation condition, we prove a formula for the Hausdorff dimension of the attractor, and establish the equality between the Hausdorff dimension and the growth dimension. Furthermore, a relation between the open set condition and the weak separation condition is given.     

基于多尺度降维的柴油机信号信息熵增强方法

针对柴油机曲轴轴承磨损故障信号特征微弱,易被噪声湮没且不同故障程度信号较难区分的特点,提出了一种基于压缩小波和局部保持投影的柴油机信息熵增强方法。利用压缩小波对信号多尺度重构减弱噪声干扰,通过局部保持映射对多尺度信号进行降维,消除冗余信息并增强信号的冲击特性,最终以时域、频域以及时频域的三种信息熵表征信号特征。仿真和实例信号表明,该方法对故障信号特征增强明显,依据信息熵值实现了曲轴磨损状态的分类识别。