The concept of bounded mean motion for toral homeomorphisms

A conservative irrational pseudo-rotation of the two-torus is semi-conjugate to the irrational rotation if and only if it has the property of bounded mean motion [T. Jäger, Linearisation of conservative toral homeomorphisms, Invent. Math., published online 9 December 2008, DOI: 10.1007/s00222-088-0171-5]. (Here ‘irrational pseudo-rotation’ means a toral homeomorphism with a unique and totally irrational rotation vector). The aim of this note is to explore this concept further. For instance, we provide an example which shows that the preceding statement does not hold in the non-conservative case. Further, we collect a number of observations concerning the case where the bounded mean motion property fails. In particular, we show that a non-wandering irrational pseudo-rotation of the two-torus with unbounded mean motion has sensitive dependence on initial conditions.     

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.     

Determination of adsorption entropies on solid surfaces by reversed-flow gas chromatography

The reversed-flow gas chromatography (RF-GC) method has been applied to measure the time separation of adsorption entropies and their probability density functions, when acetic and formic acid vapors, responsible for artifacts degradation inside museums, are adsorbed on various heterogeneous surfaces. The solid materials studied were Penteli marble and solid metals (lead, copper and iron), which are commonly used for the construction of the artifacts. Physicochemical measurements were performed at various temperatures in the range 353-473 K, the surface coverage theta being also calculated over time. A new mathematical model, based on well known equations was used in order to extract the above quantities.     

Evaluation of a simulation-based surrogate safety metric

The development of surrogate safety measures is essential due to the problems of availability and quality of historical crash data. The Aggregate Conflict Propensity Metric (ACPM) is a surrogate metric recently proposed and it is based on conflict studies and traffic simulations. ACPM is expected to be capable of assessing the relative safety levels of traffic facilities and/or treatments in order to help traffic engineers to select appropriate treatments based on traffic safety estimates. This paper presents three experimental tests conducted to evaluate the reliability of ACPM. In each test, ACPM is compared to a traditional conflict indicator in terms of identifying and ranking safety of traffic conditions under various traffic volumes based on traffic simulations. ACPM shows its strength and reliability in all three tests, as it provides results highly consistent with the Highway Safety Manual. The experimental tests indicate that ACPM is a promising surrogate safety measure that can appropriately identify relative safety among traffic treatments and/or facilities and provide traffic engineers with useful information on potential safety impact.     

机械产品可适应性度量方法及应用

基于信息论中信息熵的概念,用构成产品的模块集合来描述产品的当前状态,提出用可适应信息熵函数来表征产品设计的复杂性和不确定性,在此基础上提出了新的基于可适应信息熵的产品可适应度的计算公式.提出了2种可适应度计算方法,即基于结构配置图的可适应度计算和基于功能结构图的可适应度计算.实例研究表明,该可适应度具有很好的可操作性和实用性,能够应用于产品的开发和设计实践.     

关于齐次树指标马氏链的广义熵遍历定理

本文主要研究有限状态齐次树指标Markov链的强大数定律和广义熵遍历定理．熵遍历定理研究的是信息论中信源的渐近均分割性,树指标Markov链是近年来概率论的研究方向之一．首先,参照非齐次Markov链广义熵密度概念,本文给出了树指标Markov链的广义熵密度的定义．然后,通过构造一组期望值为1的随机变量,利用Markov不等式和Borel-Cantelli引理,证明得到了定义在树指标Markov链上一类随机变量的延迟平均的强极限定理．最后,利用上述定理的推论,我们证明得到了Cayley树上有限状态Markov链状态出现次数的延迟平均的强大数定律和广义熵遍历定理．本文的结果是对一些已有结果的推广．     

A universal measure of the conformity of a mesh with respect to an anisotropic metric field

In this paper, a method is presented to measure the non‐conformity of a mesh with respect to a size specification map given in the form of a Riemannian metric. The measure evaluates the difference between the metric tensor of a simplex of the mesh and the metric tensor specified on the size specification map. This measure is universal because it is a unique, dimensionless number which characterizes either a single simplex of a mesh or a whole mesh, both in size and in shape, be it isotropic or anisotropic, coarse or fine, in a small or a big domain, in two or three dimensions. This measure is important because it can compare any two meshes in order to determine unequivocally which of them is better. Analytical and numerical examples illustrate the behaviour of this measure. Copyright © 2004 John Wiley & Sons, Ltd.     

An uncertainty importance measure using a distance metric for the change in a cumulative distribution function

A simple measure of uncertainty importance using the entire change of cumulative distribution functions (CDFs) has been developed for use in probability safety assessments (PSAs). The entire change of CDFs is quantified in terms of the metric distance between two CDFs. The metric distance measure developed in this study reflects the relative impact of distributional changes of inputs on the change of an output distribution, while most of the existing uncertainty importance measures reflect the magnitude of relative contribution of input uncertainties to the output uncertainty. The present measure has been evaluated analytically for various analytical distributions to examine its characteristics. To illustrate the applicability and strength of the present measure, two examples are provided. The first example is an application of the present measure to a typical problem of a system fault tree analysis and the second one is for a hypothetical non-linear model. Comparisons of the present result with those obtained by existing uncertainty importance measures show that the metric distance measure is a useful tool to express the measure of uncertainty importance in terms of the relative impact of distributional changes of inputs on the change of an output distribution.     

线性正则域的Hartley变换及其不确定性原理

Hartley变换是傅里叶变换的推广, 它的一个非常好的性质就是把实信号变换成实信号, 从而减少计算量。近些年, 随着分数阶傅里叶变换在信号处理中被广泛的应用, 线性正则变换也逐渐被应用到信号处理, 所以把Hartley变换推广到正则域是一个有研究价值的问题。本文首先通过变化傅里叶变换域Hartley变换的核函数, 得到了一个具有共轭性的核函数, 之后, 通过把该核函数替换成线性正则变换的核函数, 从而得到了正则域的Hartley变换, 在这个定义的基础上, 得到了正则域Hartley变换满足实数性质和奇偶不变性, 之后再利用线性正则变换的Heisenberg不确定性原理, 得到了正则域Hartley变换的Heisenberg不确定性原理。     

Measuring the conformity of non‐simplicial elements to an anisotropic metric field

This paper extends an approach for measuring the element conformity of simplices to non‐simplicial elements of any type, in spaces of arbitrary dimension. Element non‐conformity is defined as the difference between a given size specification map, in the form of a Riemannian metric tensor, and the actual metric tensor of the element. An approach to the measurement of non‐conformity coefficients of non‐simplicial elements based on sub‐simplex division is proposed. An analysis of the measure's behaviour presented for quadrilaterals, hexahedra, prisms and pyramids shows that the measure is sensitive to size, stretching and orientation variations, as well as to other types of element shape degeneration. Finally, numerical applications show that the metric conformity measure can be used as a quality measure to quantify the discrepancy between a whole non‐simplicial mesh and a complex anisotropic size specification map. Copyright © 2005 John Wiley & Sons, Ltd.     

On the connection between a skew product IFS and the ergodic optimization for a finite family of potentials

ABSTRACT

We study a skew product IFS on the cylinder defined by Baker-like maps associated to a finite family of potential functions and the doubling map. We show that there exist a compact invariant set with attractive behaviour and a random SRB measure whose support is in that set. We also study the IFS ergodic optimization problem for that finite family of potential functions and characterize the maximizing measures and the critical value through a discounting limit. This shows the connection between this maximization problem and the superior boundary of the compact invariant set, which is described as a graph of the solution of the Bellman equation.     

分形维数和近似熵用于度量信号复杂性的比较研究

本文介绍了两种度量时间序列复杂性的方法，一种是建立在分形理论基础上的分形维数，一种是最近新发展起来的度量序列复杂性的统计方法——近似熵。应用这两种方法对机械设备振动信号进行了复杂性特征的提取，对比研究表明，它们都可以作为表征信号复杂性的一种度量，各具特点。但近似熵具有一定的抗噪、抗野点的能力，包含了更多的时间模式的信息，是一种值得重视的、很有应用前景的故障诊断新方法。     

Density and viscosity of linear perfluoropolyethers under high pressures

New experimental data on the density and viscosity of linear, unbranched perfluoropolyethers are presented at temperatures from 273 to 333 K and pressures up to 180 MPa. The measurements were carried out by a high-pressure burrette apparatus and a falling-cylinder viscometer. The uncertainties of the measurements are estimated to be less than 0.09% for the specific volume and 2.5% for the viscosity. The P-V data at each temperature are correlated satisfactorily by the Tait equation. The viscosity data are also analyzed and correlated with pressure or molar volume by several empirical and theoretical equations.     

反拟阵自同构群的公理系统及其性质

给出了反拟阵自同构群的定义,利用反拟阵的公理系统建立其自同构群公理系统;在此基础上,讨论了拟阵与反反拟阵之间的一些关系。     

Redundancy index of lifelines for mitigation measures against seismic risk

Basic consideration is made on how comprehensively we can evaluate potential seismic risk of lifeline systems and gain an insight into the safety by way of information entropy, which transmits information of various kinds under uncertainties. It is clarified that a redundancy index R_E defined via Shannon's information entropy can be an index to represent redundancy of a system and whose value plays a role to choose the best alternative for designing a system or for finding the best damage mitigation measure against earthquake hazard. The redundancy index R_E takes a value between zero and unity with zero for no redundancy, and unity for maximum redundancy. After the validity of R_E is justified to represent a redundancy measure, a case study is conducted for a Kobe water supply system to evaluate a mitigation measure against earthquake risk where the 1995 Hyogoken-Nanbu earthquake is used as the input hazard.     

Computing Solutions of the Yang-Baxter-Like Matrix Equation for Diagonalisable Matrices

The Yang-Baxter-like matrix equation $AXA = XAX$ is reconsidered, where $A$ is any complex square matrix. A collection of spectral solutions for the unknown square matrix $X$ were previously found. When $A$ is diagonalisable, by applying the mean ergodic theorem we propose numerical methods to calculate those solutions.     

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.