On phase transitions for subshifts of finite type

It has recently been shown that a strongly irreducible subshift of finite type in two or more dimensions may have more than one measure of maximal entropy. In this paper we obtain some results on when (i.e. for what kinds of subshifts of finite type) this happens, and when it does not. In particular, we show that the parameter of a certain subshift of finite type introduced by Burton and Steif has a critical value, below which we have a unique measure of maximal entropy, and above which we have non-uniqueness.     

Deng entropy

Dempster Shafer evidence theory has been widely used in many applications due to its advantages to handle uncertainty. However, how to measure uncertainty in evidence theory is still an open issue. The main contribution of this paper is that a new entropy, named as Deng entropy, is presented to measure the uncertainty of a basic probability assignment (BPA). Deng entropy is the generalization of Shannon entropy since the value of Deng entropy is identical to that of Shannon entropy when the BPA defines a probability measure. Numerical examples are illustrated to show the efficiency of Deng entropy.     

非凸单个守恒律初边值问题的整体弱熵解的构造

本文研究具有两段常数的初始值和常数边界值的非凸单个守恒律的初边值问题.在流函数具有一个拐点的条件下,由相应的初始值问题弱熵解的结构和Bardos-Leroux-Nedelec提出的边界熵条件,给出初边值问题整体弱熵解的一个构造方法,澄清弱熵解在边界附近的结构.与严格凸的单个守恒律初边值问题相比,非凸单个守恒律初边值问题的弱熵解中包括下列新的相互作用类型:一个接触或非接触激波碰到边界,边界弹回一个非接触激波.     

熵权DEA混合多目标评价方法研究

提高多目标决策问题评价结果的客观性、准确性,一直是决策科学研究的重要课题.结合熵权、DEA等数学方法对多目标决策问题进行研究,构造混合评价方法.首先通过构造熵权模型,获取主观权重;其次DEA的方法对多目标决策问题进行综合评价,得到问题的综合评价值,最后根据评价结果进行问题分析和判断.算例结果表明,方法能够应用于多目标决策问题,评价结果客观、准确.     

Minimal relative entropy for equivalent martingale measures by low-discrepancy sequence in Lévy process

In this paper, we focused on computing the minimal relative entropy between the original probability and all of the equivalent martin gale measure for the Lévy process. For this purpose, the quasiMonte Carlo method is used. The probability with minimal relative entropy has many suitable properties. This probability has the minimal Kullback-Leibler distance to the original probability. Also, by using the minimal relative entropy the exponential utility indifference price can be found. In this paper, the Monte Carlo and quasi-Monte Carlo methods have been applied. In the quasi-Monte Carlo method, two types of widely used lowdiscrepancy sequences, Halton sequence and Sobol sequence, are used. These methods have been used for exponential Lévy process such as variance gamma and CGMY process. In these two processes, the minimal relative entropy has been computed by Monte Carlo and quasi-Monte Carlo, and compared their results. The results show that quasi-Monte Carlo with Sobol sequence performs better in terms of fast convergence and less error. Finally, this method by fitting the variance gamma model and parameters estimation for the model has been implemented for financial data and the corresponding minimal relative entropy has been computed.     

The topological entropy for autonomous Lagrangian systems on compact manifolds whose fundamental groups have exponential growth

In this article, we consider the topological entropy for autonomous positive definite Lagrangian systems on connected closed Riemannian manifolds whose fundamental groups have exponential growth. We prove that on each energy level E(x, v) = k with k c(L), where c(L) is Mane's critical value, the EulerLagrange flow has positive topological entropy. This extends the classical Dinaburg theorem from geodesic flows to general autonomous positive definite Lagrangian systems.     

基于熵值法和神经网络模型的股价评估分析

股票价格的变化主要依赖于两个方面,一个是股票内在价值,另一个就是系统风险对股票价值的影响.通过使用神经网络的方法来分析股票的系统风险,用熵值法来分析股票的内在价值,从而全面的分析股票的投资价值,结果表明这种评估方法是可靠并且具有较大的获利空间.     

基于用户感性需求的产品设计方案评估方法

目前满足用户的情感诉求和情感体验逐渐成为热销产品的关键属性,引起了产品开发者和企业决策者的关注。为了更好地贴合用户情感体验,结合信息熵、灰色关联分析和模糊TOPSIS,提出了以用户感性需求为向导的产品设计方案的评估方法。首先引入感性工学中复合感性意象量化用户的情感信息,通过对收集的产品意象进行聚类分析和主成分分析产生具有代表性的目标意象,运用语义差分调查获得代表意象的评价值;其次对规范化的意象评价值计算其熵值权重;最后结合灰色关联分析和模糊TOPSIS,产生用户情感信息指导下的产品设计备选方案的优先级排序。以智能手表设计为例,验证了该方法的可行性和有效性。信息熵和结合灰色关联分析的模糊TOPSIS可以较大限度地减少方案评估时的个人主观影响,确保了评估结果的准确性,对企业产品方案决策具有指导意义。     

车床管理优化模型

本文讨论了自动化车床连续加工零件工序定期检查和刀具更换的最优策略 .针对问题一 ,应用管理成本理论结合概率统计方法 ,建立定期检查调节零件的平均管理成本的优化设计模型 ,通过计算机求解、模拟 ,得到工序设计效益最好的检查间隔和刀具更换间隔 .针对问题二 ,在问题一的基础上 ,利用概率知识调整了检查间隔中的不合格品数带来的平均损失 ,同时加上了因工序正常而误认为有故障停机产生的平均损失 ,然后建立起目标函数 ,得到工序设计效益最好的检查间隔和刀具更换策略 .对于工序故障采用自动检查装置 ,设计出了自动检查调节系统 ,并给出了算法框图 ,有效地避免工序正常而误认为有故障停机损失 ,提高工序效益     

A note on quasi-weakly almost periodic point

Recently, He et al. [On quasi-weakly almost periodic points. Sci. China Math., 56, 597–606(2013)] constructed two binary sub-shifts to solve an open problem posed by Zhou and Feng in[Twelve open problems on the exact value of the Hausdorff measure and on topological entropy: A brief survey of recent results. Nonlinearity, 17, 493–502(2004)]. In this paper, we study more dynamical properties of those two binary sub-shifts. We show that the first one has zero topological entropy and is transitive but not weakly mixing, while the second one has positive topological entropy and is strongly mixing.     

不完全信息下损失风险的研究

在获得损失分布不完全信息情况下,提出用方差和熵共同度量损失风险的方法.在不完全信息条件下,通过最大熵原理在最不确定的情况下得到最大熵损失分布,并获得了损失分布的熵函数值.用熵值度量损失分布对于均匀分布的离散程度,从而度量概率波动带来的风险;用方差度量损失对于均值的离散程度,从而度量状态波动带来的风险.由于熵是与损失变量更高阶矩信息相联系的,所以新方法是从更全面的角度对损失风险的预测.通过算例,进一步看出在获得高阶矩信息下,熵参与风险度量的必要性.     

The entropy formula for linear heat equation

We derive the entropy formula for the linear heat equation on general Riemannian manifolds and prove that it is monotone non-increasing on manifolds with nonnegative Ricci curvature. As applications, we study the relation between the value of entropy and the volume of balls of various scales. The results are simpler version, without Ricci flow, of Perelman ’s recent results on volume non-collapsing for Ricci flow on compact manifolds. We also prove that if the entropy for the heat kernel achieves its maximum value zero at some positive time, on any complete Riamannian manifold with nonnegative Ricci curvature, if and only if the manifold is isometric to the Euclidean space.     

A local breakdown property of robust tests in linear regression

The breakdown slope, as a useful summary measure of local stability for estimators and test statistics, has been studied recently by He, Simpson, and Protnoy (1990, J. Amer. Statist. Assoc., 85). It is shown here that all regression estimates based on residuals alone in linear models have zero breakdown slopes in contamination neighborhoods, even though they can have breakdown points as high as one-half. The breakdown functions of tests based on the S-estimation are investigated. It is also shown that the Generalized M-estimators can have better local breakdown robustness. One way to obtain regression estimators with desirable local and global breakdown properties is discussed.     

Entropy and co-entropy of a covering approximation space

The notions of entropy and co-entropy associated to partitions have been generalized to coverings when Pawlak’s rough set theory based on partitions has been extended to covering rough sets. Unfortunately, the monotonicities of entropy and co-entropy with respect to the standard partial order on partitions do not behave well in this generalization. Taking the coverings and the covering lower and upper approximation operations into account, we introduce a novel entropy and the corresponding co-entropy in this paper. The new entropy and co-entropy exhibit the expected monotonicity, provide a measure for the fineness of the pairs of the covering lower and upper approximation operations, and induce a quasi-order relation on coverings. We illustrate the theoretical development by the first, second, and third types of covering lower and upper approximation operations.     

基于熵算法的股票指数高频数据复杂度测算与评价

在日内高频环境下检验基于兼容法的柯尔莫哥洛夫熵、样本熵和模糊熵等复杂度测算方法对我国沪深300股票指数的测算效率,并运用筛选后的有效算法分阶段研究和比较了序列复杂度的变化过程与变化幅度.结果表明,模糊熵算法是一种更适用于我国沪深300股票指数的有效复杂度测算方法,其对相似容忍度的敏感性更低,测度值连续性更好.随时间推移,我国沪深300股票指数复杂度整体呈上升趋势,而相较于发达市场甚至周边新兴市场其复杂度偏低.     

On the possible values of the entropy of undirected graphs

The entropy of a digraph is a fundamental measure that relates network coding, information theory, and fixed points of finite dynamical systems. In this article, we focus on the entropy of undirected graphs. We prove any bounded interval only contains finitely many possible values of the entropy of an undirected graph. We also determine all the possible values for the entropy of an undirected graph up to the value of four.     

具有随机参数的盾构管片弹性密封垫防水性能优化分析

盾构管片接缝弹性密封垫断面的几何尺寸极易受生产工艺的影响而呈现出随机性,从而对盾构管片弹性密封垫的防水性能产生影响.该文选取密封垫的孔洞圆心坐标、孔径、断面宽度、断面高度等参数作为随机输入变量,运用ANSYS-PDS模块得出了各随机参数对密封垫防水性能的灵敏度数值,结果显示圆孔孔径对闭合压力及接触应力的影响较其他几何尺寸更大;圆孔垂向位置改变对闭合压力及接触应力的影响较横向位置更大.在此基础上,应用ANSYS优化设计模块,选取密封垫闭合压力和下表面平均接触应力作为状态变量,以在闭合压力不超过某一定值的条件下接触应力最大为目标函数,对密封垫进行几何参数优化分析,得出了某盾构隧道弹性密封垫优化断面,试验结果很好地验证了优化计算结果的可靠性.     

Experimental investigations on the mechanical behavior of filled rubber

A lot of experimental results on the elastic as well as on the inelastic behavior of elastomer materials are known. However, so far now systematic examination on defined rubber mixtures has been reported. In this presentation the phenomenology of elastomer materials is characterized on the basis of extension and compression tests performed with dumbbell– and S2–specimen. Stiffness, upturn (stiffness at final deformation), hysteresis and remaining deformation have been analyzed for well defined rubber systems and environmental conditions. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

The limiting vortex in the similarity solution for a swirling flow

It is known that the similarity solution for a viscous swirling flow over a stationary disk does not exist if the driving vortex far away from the disk is a potential vortex, while the solution exists for a rigid body vortex. Previously, the breakdown has been determined to occur if the azimuthal velocity of the driving vortex decreases faster than a certain power of the radial distance from the axis of symmetry. The decay parameter at which the similarity solution ceases to exist is computed here by a more direct method, and the reason for the breakdown becomes apparent. The analysis confirms (and slightly improves) the known value of the parameter. The case where the fluid, now assumed to be conducting, is subject to an axial magnetic field and the asymptotic behavior of the solution far away from the axis are also briefly discussed.     

基于Pythagorean模糊熵的风险型决策方法——考虑后悔与失望规避

针对决策信息为Pythagorean模糊数,属性权重完全未知的风险型多属性决策问题,提出了一种基于Pythagorean模糊熵的考虑决策者后悔与失望规避心理行为的决策方法。首先,计算备选方案和理想点各属性的效用值,从而获得各备选方案的后悔-欣喜值、失望-愉悦值及感知效用值。其次,构建了一种Pythagorean模糊熵,并给出基于该Pythagorean模糊熵的属性权重确定方法,利用属性权重加权求和获得备选方案综合感知效用值,从而对方案进行排序。最后,通过算例说明方法的可行性和优点,并分析了后悔规避系数δ和失望规避系数τ对决策结果的影响。