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.     

Measure-theoretic pressure and topological pressure in mean metrics

In this paper, using spanning sets in mean metrics we construct a new definition of measure-theoretic pressure of ergodic measures over a topological dynamical system. And we establish a pressure version of Katok's entropy formula in the case of mean metrics. Furthermore, we also introduce a new definition of topological pressure by replacing the Bowen metrics with the corresponding mean metrics, and prove that the new topological pressure is equivalent to the classical topological pressure. Then the variational principle for the newly defined topological pressure is obtained.     

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.     

Some results on the entropy of non-autonomous dynamical systems

In this paper, we advance the entropy theory of discrete non-autonomous dynamical systems that was initiated by Kolyada and Snoha in 1996. The first part of the paper is devoted to the measure-theoretic entropy theory of general topological systems. We derive several conditions guaranteeing that an initial probability measure, when pushed forward by the system, produces an invariant measure sequence whose entropy captures the dynamics on arbitrarily fine scales. In the second part of the paper, we apply the general theory to the non-stationary subshifts of finite type, introduced by Fisher and Arnoux. In particular, we give sufficient conditions for the variational principle, relating the topological and measure-theoretic entropy, to hold.     

基于耗散结构的企业系统熵变模型

应用耗散结构理论,通过对企业系统耗散结构形成过程及形成条件进行分析研究,建立了以资金流为推动的企业系统熵变模型,并结合企业系统的实际情况给出了具有可操作性的企业系统熵变计算公式,依据所建模型及公式进行实例验证,结果与企业实际发展情况基本吻合.     

工程爆破引起的振动速度计算经验公式及应用条件探讨

论文分析总结了工程爆破界对于爆破振动速度计算的经验公式。根据相似理论,推导了爆破振动速度计算的公式。研究结果发现,在地形、地质和使用炸药种类不变的情况下,爆破引起的地面振动速度与最大起爆药量Q、爆源距测点的直线距离R、以及爆破作用指数n有关。只有在集中药包、标准抛掷爆破条件下,爆破振动速度的计算公式,才适合于前苏联学者萨道夫斯基提出的经验公式。论文把深孔直列药包,假定为无数个等效集中药包,提出了深孔爆破的振动速度计算公式,并进行了工程实际应用     

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).     

多楔带附件驱动系统旋转振动方程的通程式方法

建立了单根多楔带附件驱动系统的旋转振动方程的通程化方法,以适用于不同布置形式的单根多楔带附件驱动系统的旋转振动特性计算。在此基础上,开发了一个单根多楔带附件驱动系统旋转振动特性的计算程序,并利用该程序对两个不同布置形式的多楔带附件驱动系统的旋转振动特性进行了计算。计算得到了这两个不同布置形式的多楔带附件驱动系统的固有频率、带的稳态张力、轮和张紧臂的角度波动、带段的动态张力和最大轮毂载荷等。将部分计算值和实测值进行对比,验证了本文所建立的通程式方法的可行性。     

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．     

产品可适应设计评价的信息熵方法

随着用户对产品的功能、质量、成本、个性化以及环境友好性等方面的需求日益提升,制造企业必须更加即时、高效地响应不断变化的市场需求.可适应设计作为一种新型的设计范式,可通过设计过程的综合优化来满足产品生命周期内用户、制造企业和社会的需求,以提升经济效益和环境效益等.为了提高产品设计的可适应性,需对可适应性进行量化的科学表达...     

Global sensitivity analysis for fuzzy inputs based on the decomposition of fuzzy output entropy

To analyse the component of fuzzy output entropy, a decomposition method of fuzzy output entropy is first presented. After the decomposition of fuzzy output entropy, the total fuzzy output entropy can be expressed as the sum of the component fuzzy entropy contributed by fuzzy inputs. Based on the decomposition of fuzzy output entropy, a new global sensitivity analysis model is established for measuring the effects of uncertainties of fuzzy inputs on the output. The global sensitivity analysis model can not only tell the importance of fuzzy inputs but also simultaneously reflect the structural composition of the response function to a certain degree. Several examples illustrate the validity of the proposed global sensitivity analysis, which is a significant reference in engineering design and optimization of structural systems.     

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。     

Multiplication rule for the Collins diffraction formula obtained by virtue of the Fresnel operator in quantum optics theory

By using the Fresnel operator we derive a multiplication rule for the Collins diffraction formula; the inverse of Collins diffraction integration can also be conveniently derived in this way in the context of quantum optics theory.     

On the generation of entropy in a counterflow heat exchanger

Entropy generation in a counterflow heat exchanger has been analysed in detail and expressions have been derived in terms of relevant non dimensional parameters. In the case of nearly ideal heat exchangers with nearly balanced capacity rate, an expression for entropy production has been derived which matches closely with exact calculation.     

关于 Stirling公式的一个注记

记 rn=nne- n 2πn.这个注记证明 ,当 n≥ 1 0时rn 1 +11 2 n+ 12 88n2 +2 4 9.2 n 相似文献   

基于熵技术的矿山安全模糊综合评价

根据矿山安全评价所存在的模糊性和随机性的特点,在建立多级模糊综合评价的指标体系的基础上,借用信息论中熵的概念计算客观权重的方法,运用模糊数学理论,建立二级模糊综合评价模型,提高了矿山安全现状评价的客观性和科学性,具有一定的工程实际应用价值.     

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。