Different forms of entropy dimension for zero entropy systems

The aim of this paper is to introduce the lower s-topological entropy to distinguish zero entropy systems. That this quantity is an invariant factor under topological conjugacy and a power rule is shown. Some examples are given to show that the lower entropy dimension can attain any value in (0, 1), and are different with the upper one and the entropy dimension in the sense of Bowen. A counterexample is used to indicate that the product rule does not hold, and the lower s-topological entropy of the subsystem for the non-wandering set can be strictly less than that of the system when 0 < s < 1. Finally, this study also constructs a dynamical system to show that the transitive system with zero entropy dimension may not be minimal.     

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.     

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.     

Topological properties of invariant sets for two-dimensional hyperbolic toral automorphisms

We study topological properties of invariant sets of Anosov diffeomorphisms with holes. Results related to cardinality, local maximality, entropy and dimension are presented. The main result states that the Hausdorff dimension of the invariant set can be computed by the entropy of the invariant set together with the hyperbolicity constants.     

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．     

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.     

基于模糊集表达和熵处理的产品用户需求评价

 在产品设计早期,对用户需求功能及其重要程度进行分析和获取的成功与否直接关系到产品设计目标特性的质量以及后续产品开发的各个阶段。提出一种基于模糊集表达和熵处理的有效用户需求获取方法。根据用户需求调查结果,建立了用户需求功能抽象的原则,采用模糊矩阵对各用户需求进行表达,并用熵处理的方法简化用户需求模糊矩阵,从而获取用户需求的重要度排序。该方法的显著优点是能够反应用户需求的主观性和模糊性。     

Quantization dimension estimate of probability measures on hyperbolic recurrent sets

In this paper, under the strong open set condition we have determined the bounds of the lower and the upper quantization dimensions of a probability measure supported by the limit set of a hyperbolic recurrent iterated function system. Moreover, we have shown that the lower and upper bounds are related with the temperature functions of the thermodynamic formalism corresponding to the lower and upper contractive ratios of the hyperbolic maps.     

Criteria for Realizing Room-Temperature Electrical Transport Applications of Topological Materials

The unusual electronic states found in topological materials can enable a new generation of devices and technologies, yet a long-standing challenge has been finding materials without deleterious parallel bulk conduction. This can arise either from defects or thermally activated carriers. Here, the criteria that materials need to meet to realize transport properties dominated by the topological states, a necessity for a topological device, are clarified. This is demonstrated for 3D topological insulators, 3D Dirac materials, and 1D quantum anomalous Hall insulators, though this can be applied to similar systems. The key parameters are electronic bandgap, dielectric constant, and carrier effective mass, which dictate under what circumstances (defect density, temperature, etc.) the unwanted bulk state will conduct in parallel to the topological states. As these are fundamentally determined by the basic atomic properties, simple chemical arguments can be used to navigate the phase space to ultimately find improved materials. This will enable rapid identification of new systems with improved properties, which is crucial to designing new material systems and push a new generation of topological technologies.     

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。     

随机集值A-proper映象的随机广义拓扑度

本文引入随机集值A-proper映象的随机广义拓扑度的定义,由此得到一些新的随机不动点和随机固有元定理。     

Topological derivatives for fundamental frequencies of elastic bodies

In this article a new method for topological optimization of fundamental frequencies of elastic bodies, which could be considered as an improvement on the bubble method, is introduced. The method is based on generalized topological derivatives. For a body with different types of inclusion the vector genus is introduced. The dimension of the genus is the number of different elastic properties of the inclusions being introduced. The disturbances of stress and strain fields in an elastic matrix due to a newly inserted elastic inhomogeneity are given explicitly in terms of the stresses and strains in the initial body. The iterative positioning of inclusions is carried out by determination of the preferable position of the new inhomogeneity at the extreme points of the characteristic function. The characteristic function was derived using Eshelby's method. The expressions for optimal ratios of the semi-axes of the ellipse and angular orientation of newly inserted infinitesimally small inclusions of elliptical form are derived in closed analytical form.     

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...     

Quantum Topological Boundary States in Quasi‐Crystals

Topological phases play a novel and fundamental role in matter and display extraordinary robustness to smooth changes in material parameters or disorder. A crossover between topological material and quantum information may lead to inherent fault‐tolerant quantum simulations and quantum computing. Quantum features may be preserved by being encoded among topological structures of physical evolution systems. This requires stimulation, manipulation, and observation of topological phenomena at the single quantum particle level, which has not, however, yet been realized. It is asked whether the quantum features of single photons can be preserved in topological structures. The boundary states are experimentally observed at the genuine single‐photon level and the performance of the topological phase is demonstrated to protect the quantum features against diffusion‐induced decoherence in coupled waveguides and noise decoherence from the ambient environment. Compatibility between macroscopic topological states and microscopic single photons in the ambient environment is thus confirmed, leading to a new avenue to “quantum topological photonics” and providing more new possibilities for quantum materials and quantum technologies.