Relative Topological Pinsker Factors and Entropy Pairs

 A relative version of the topological m-Pinsker factor is given and its relationships with other notions of relative Pinsker factors are investigated. Relative topological Pinsker factors (of various kinds) of relative products are described. (Received 4 December 2000; in revised form 1 June 2001)     

Relative Entropy and Mean Li-Yorke Chaos Along Some Good Sequences

Acta Mathematica Sinica, English Series - In this article, we showed that positive relative entropy implies mean Li-Yorke chaos along some good sequences in the fiber. Our result extended Li and...     

混合偏熵与关联熵

定义联系模糊性和随机性的混合集、混合偏熵与关联熵以及混合关联系数，研究了其性质，并举例说明混合关联系数在现实生活中的应用。     

Fuzzy集的偏熵与关联熵

在文献[1]的基础上,推广模糊熵的概念。首次定义Fuzzy集的偏熵、关联熵和关联熵系数等新概念。对其主要性质进行讨论,并与模糊散度建立联系．得到一些重要结果。     

Chaos in PDEs and Lax Pairs of Euler Equations

Recently, the author and collaborators have developed a systematic program for proving the existence of homoclinic orbits in partial differential equations. Two typical forms of homoclinic orbits thus obtained are: (1) transversal homoclinic orbits, (2) Silnikov homoclinic orbits. Around the transversal homoclinic orbits in infinite-dimensional autonomous systems, the author was able to prove the existence of chaos through a shadowing lemma. Around the Silnikov homoclinic orbits, the author was able to prove the existence of chaos through a horseshoe construction.Very recently, there has been a breakthrough by the author in finding Lax pairs for Euler equations of incompressible inviscid fluids. Further results have been obtained by the author and collaborators.     

Quantization of Boltzmann Entropy: Pairs and Correlation Function

We consider the Gibbs statistical ensemble. We introduce the statistical-weight operator , construct the entropy operator of the ensemble using the Boltzmann formula , and define the free-energy operator. We find asymptotic expressions for free-energy eigenvalues with pair correlations taken into account in the limit as the number of systems in the ensemble tends to infinity.     

Newton Polytopes and Relative Entropy Optimization

Foundations of Computational Mathematics - Certifying function nonnegativity is a ubiquitous problem in computational mathematics, with especially notable applications in optimization. We study the...     

Asymptotic Efficiency of Maximum Entropy Estimates

Doklady Mathematics - The problem of entropy estimation of probability density functions with allowance for real data is posed (the maximum entropy estimation (MEE) problem). Global existence...     

Convergence to Stable Laws in Relative Entropy

Convergence to stable laws in relative entropy is established for sums of i.i.d. random variables.     

Balanced Pairs and Relative Tilting Objects in Recollements of Abelian Categories

In this paper,we study the relationship of balanced pairs in a recollement.As an application of balanced pairs,we introduce the notion of the relative tilting objects,and give a characterization of relative tilting objects,which is similar to Bazzoni characterization of n-tilting modules.Finally,we investigate the relationship of relative tilting objects in a recollement.     

关于滑动相对熵的若干极限性质

引入滑动似然比和滑动相对熵等概念,讨论了滑动相对熵的若干渐近性质.主要结果是,获得了随机变量任意状态的相对频率与滑动相对熵之间的关系,并且给出了滑动相对熵基于相对频率的上界的估计.作为推论,得到了随机序列滑动平均的强大数定理.     

Pairs of Projections: Geodesics,Fredholm and Compact Pairs

A pair \((P, Q)\) of orthogonal projections in a Hilbert space \( \mathcal{H} \) is called a Fredholm pair if $$\begin{aligned} QP : R(P) \rightarrow R(Q) \end{aligned}$$ is a Fredholm operator. Let \( \mathcal{F} \) be the set of all Fredholm pairs. A pair is called compact if \(P-Q\) is compact. Let \( \mathcal{C} \) be the set of all compact pairs. Clearly \( \mathcal{C} \subset \mathcal{F} \) properly. In this paper it is shown that both sets are differentiable manifolds, whose connected components are parametrized by the Fredholm index. In the process, pairs \(P, Q\) that can be joined by a geodesic (or equivalently, a minimal geodesic) of the Grassmannian of \( \mathcal{H} \) are characterized: this happens if and only if $$\begin{aligned} \dim (R(P)\cap N(Q))=\dim (R(Q)\cap N(P)). \end{aligned}$$      

基于灰关联熵的多指标灰靶决策方法

针对方案指标值为三参数区间灰数的多指标决策问题,提出一种基于灰关联熵的多指标灰靶决策方法.首先定义了各方案的正靶心及正靶心距;其次,构建所有方案的相对关联度系数,继而形成灰关联系数矩阵,再利用熵理论求解目标权重.应用实例说明了提出的决策方法的合理性和有效性.     

基于相对熵和VIKOR的多属性决策排序方法

在相对熵和VIKOR决策方法的基础上,结合各自的优点,提出了一种解决多属性决策问题排序的新方法.首先利用改进熵权法对决策属性进行赋权,其次计算决策方案和正理想决策方案与负理想决策方案的相对熵、决策方案和正理想方案与负理想方案的群体效用值和个别遗憾值,再次根据TOPSIS法中的相对贴近度的思想,利用相对贴近度的大小对决策方案进行排序,案例分析说明了决策方法的有效性和实用性,最后对提出的模型的灵敏度和其他文献中模型的灵敏度进行了对比,发现提出的模型的灵敏度更高.创新和特色一是对传统熵权法进行了改进,不需要人为的特殊约定,具有一定的科学性;二是结合VIKOR方法和相对熵方法的各自优点,将其组合使用;三是结合TOPSIS法中的相对贴近度的思想将VIKOR方法和相对熵方法进行融合.     

Asymptotic Behavior of Large Weak Entropy Solutions of the Damped p-system

The asymptotic behavior of solutions of the damped p-system is known to be described by a nonlinear diffusion equation. The previous works on this topic concern either the case of small smooth data where estimates of high-order derivatives are available by energy methods or the case of special and small rough data. For large data, the existence of solutions is proved by using the method of compensated compactness. Thus the above mentioned energy estimates are not expected. However, the compensated compactness gives a very weak justification (in the mean in time) of the asymptotics. In the present paper we prove that the natural energy estimates, which does not involve derivatives, combined with this “convergence in the mean”, gives the strong convergence in L^p_{loc} space (p is finite) as expected.     

基于相对熵的建筑垃圾处理PPP项目融资风险评价

针对建筑垃圾处理项目融资难,在建筑垃圾处理项目中采用PPP融资模式,有效缓解政府财政资金的同时,提高资源化效率.面对建筑垃圾处理项目的融资风险,在分析PPP项目风险因素的基础上,构建基于相对熵理论的融资风险评价模型.首先,运用层次分析法和熵值法分别确定风险指标的主、客观权重.然后,运用博弈集结模型组合主客观权重,得到指标综合权重.最后,运用相对熵评价模型对建筑垃圾处理PPP项目主要参与方进行风险评价,为项目的风险控制管理提供参考依据.