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.     

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.     

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.     

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.     

Katok formula for the induced measure-theoretic entropy

Entropy is undoubtedly one of the most essential characteristics of dynamical systems. In this article, we define a topological version of the induced measure-theoretic entropy and obtain its Katok entropy formula. We show that the induced measure-theoretic entropy coincides with Hausdorff dimension of the ergodic measure in a symbolic space and the BS dimensions of the ergodic measures can be characterized by the induced measure-theoretic entropies. As an application, we give a variational principle of the BS dimension by the induced measure-theoretic entropy.     

粗糙集中不确定性测量的修正粗糙熵方法

分析了引起粗糙集中不确定性的因素，对已有的测量不确定性的粗糙度与粗糙熵方法进行了比较，提出了一种修正的粗糙熵方法，证明了此粗糙熵的性质，并将基于等价关系的修正粗糙熵拓展到基于一般二元关系下的广义修正粗糙熵，同时给出了广义修正粗糙熵的定义及性质．通过分析和实例可以看出，所提出的修正粗糙熵方法可以用来更合理、更精确地测量粗糙集中的不确定性．     

Finer fractal geometry for analytic families of conformal dynamical systems

We prove several results establishing real analyticity of Hausdorff dimensions of limit sets of analytic families of conformal graph directed Markov systems. With this tool and with iterated function systems resulting from the existence of nice sets in the sense of Rivera-Letelier, we prove that the canonical Hausdorff measure restricted to the radial Julia set of a tame meromorphic function (can be rational) is σ-finite and that the Hausdorff dimension of the radial Julia sets for fairly general families of meromorphic functions (can be rational) is real analytic.     

Different mechanisms of A-site and B-site high entropy effect on radiation tolerance of pyrochlores

The properties of high entropy pyrochlore have been studied extensively,but there is no consistent con-clusion on its radiation tolerance.Besides,the mechanism of the high entropy effect on the radiation tolerance of pyrochlore is still unclear.In this work,combined with experiments and calculations of pyrochlores with similar cationic radius ratios,the A-site and B-site high entropy effects on structural evolution under irradiation are analyzed.In situ irradiation experiments were carried out on A-site high entropy pyrochlores such as(La0.2Nd0.2Sm0.2Gd0.2Er0.2)2Zr2O7,B-site Gd2(Ti1/3Sn1/3Zr1/3)2O7,and ternary pyrochlore Sm2Zr2O7 and Gd2Sn2O7 for comparison.The A-site high entropy pyrochlore can maintain a stable structure under high fluence irradiation like corresponding ternary pyrochlore,demonstrated by high angle annular dark field scanning transmission electron microscopy(HAADF-STEM),energy disper-sive spectroscopy(EDS)mapping and Raman spectrum.The additional irradiation experiments on A-site high entropy pyrochlores(La1/3Nd1/3Gd1/3)2Zr2O7 and(Nd1/3Sm1/3Gd1/3)2Zr2C7 also confirm the similarity under irradiation between A-site high entropy and ternary pyrochlores.However,the B-site high entropy pyrochlore Gd2(Ti1/3Sn1/3Zr1/3)2O7 becomes amorphous at exceptionally low irradiation fluences,indicat-ing a significantly distinct radiation tolerance compared with the A-site high entropy.The difference be-tween the A-site and B-site high entropy effect is analyzed from cationic lattice distortion,bond strength,and inner electron binding energy by first-principles calculations.The results reveal the role and mecha-nism of the high entropy effect in pyrochlores and lay a foundation for material design and future appli-cations.     

零夹杂钢精炼的理论与工艺

零夹杂钢即夹杂物高度弥散分、尺寸小于1 μm的钢.论文从理论上分析其制备的可能性,展望其性能.具体工艺措施为:经过预脱铝处理的超低S、P工业纯铁,在50 kg真空感应炉中依靠碳氧脱氧反应进行初脱氧、深脱氧和合金化处理,炼成42CrMo钢,最后在电子束炉中经过两次重熔,得到全氧量为T.O.=4×10-6的42CrMo锭.精炼钢锻造成材后,非金属夹杂物非常细小用常规金相检验(×100倍)很难定量评级,在扫描电镜检测下发现有少量1～4 μm 的Al2O3夹杂,其主要来自铁合金原料.疲劳寿命由107转数提高到109转数.     

盒维数的肠道压力数据分形分析

对肠道压力数据进行分形特性的分析,通过对结肠压力数据进行预处理,采用盒维数计算正常受试者和异常受试者结肠压力数据的分形维数.结果表明,该方法基本能够区分正常的和异常的结肠压力信号,可以作为判断肠道动力性能的辅助手段.     

液氢无损储存技术小型试验结果及分析

搭建了液氢无损储存技术小型试验系统,对试验系统进行了实际运行。基于课题第一阶段研究所建立的关于试验系统的氢工质数学模型,参照实际运行条件进行了数值仿真并与实际运行结果进行了对比。仿真结果与实际运行结果在压力变化趋势方面是一致的,但在变化速率方面表现出较大的差异。系统运行结果显示,液氢可以在系统内实现长时间无放空储存,证实了液氢无损储存技术的可行性。