Stirling公式的一个推广

关于n!的S tirling渐近式,无论在理论上或者实际上,都有重要应用.应用Eu ler-M aclau lrin求和公式及Γ函数的性质,推导出一般等差级数连乘积并有余项估计式的类似表达式.     

r模同态的{1}-逆与{2}-逆

本文探讨模同态广义逆在环模理论中的应用．利用模同态的{1}-逆与{2}-逆，分别给出了一类环及一类重要模的特征刻画．     

Discrete stochastic approximations of the Mumford–Shah functional

We propose a new Γ-convergent discrete approximation of the Mumford–Shah functional. The discrete functionals act on functions defined on stationary stochastic lattices and take into account general finite differences through a non-convex potential. In this setting the geometry of the lattice strongly influences the anisotropy of the limit functional. Thus we can use statistically isotropic lattices and stochastic homogenization techniques to approximate the vectorial Mumford–Shah functional in any dimension.     

关于具有泛分解的态射的广义逆

本文给出了预加范畴中具有泛分解的态射的（１,…,ｉ）－逆存在的条件及其表达式．特别地,得到了这类态射的Ｍｏｏｒｅ－Ｐｅｎｒｏｓｅ边和群逆存在的一些新的充要条件和新的表达式．     

一般化凸空间上极大极小不等式及其应用

我们首先改进了已有的KKM型定理,然后根据改进后的KKM型定理得到了一般化凸空间上的KyFan型极大极小不等式,最后利用它给出了Fan-Kneser型不等式族及其一些应用.我们的结论对文献中的相应结果进行了改进和一般化。     

New second order Mumford–Shah model based on Γ-convergence approximation for image processing

In this paper, a second order variational model named the Mumford–Shah total generalized variation (MSTGV) is proposed for simultaneously image denoising and segmentation, which combines the original Γ-convergence approximated Mumford–Shah model with the second order total generalized variation (TGV). For image denoising, the proposed MSTGV can eliminate both the staircase artefact associated with the first order total variation and the edge blurring effect associated with the quadratic H¹ regularization or the second order bounded Hessian regularization. For image segmentation, the MSTGV can obtain clear and continuous boundaries of objects in the image. To improve computational efficiency, the implementation of the MSTGV does not directly solve its high order nonlinear partial differential equations and instead exploits the efficient split Bregman algorithm. The algorithm benefits from the fast Fourier transform, analytical generalized soft thresholding equation, and Gauss–Seidel iteration. Extensive experiments are conducted to demonstrate the effectiveness and efficiency of the proposed model.     

Dynamic consistency in incomplete information games under ambiguity

We develop a general framework of incomplete information games under ambiguity which extends the traditional framework of Bayesian games to the context of Ellsberg-type ambiguity. We then propose new solution concepts called ex ante and interim Γ-maximin equilibrium for solving such games. We show that, unlike the standard notion of Bayesian Nash equilibrium, these concepts may lead to rather different recommendations for the same game under ambiguity. This phenomenon is often referred to as dynamic inconsistency. Moreover, we characterize the sufficient condition under which dynamic consistency is assured in this generalized framework.     

Two-Dimensional Div-Curl Results: Application to the Lack of Nonlocal Effects in Homogenization

In this paper, we study the asymptotic behaviour of sequences of conduction problems and sequences of the associated diffusion energies. We prove that, contrary to the three-dimensional case, the boundedness of the conductivity sequence in L¹ combined with its equi-coerciveness prevents from the appearance of nonlocal effects in dimension two. More precisely, in the two-dimensional case we extend the Murat–Tartar H-convergence which holds for uniformly bounded and equi-coercive conductivity sequences, as well as the compactness result which holds for bounded and equi-integrable conductivity sequences in L¹. Our homogenization results are based on extensions of the classical div-curl lemma, which are also specific to the dimension two.     

The characterization of Γ-modules in terms of fuzzy soft Γ-submodules

In this paper, we focus on combining the theories of fuzzy soft sets with Γ-modules, and establishing a new framework for fuzzy soft Γ-submodules. The main contributions of the paper are 3-fold. First, we present the concepts of (R, S)-bi-Γ-submodules, quasi-Γ-submodules and regular Γ-modules. Meanwhile, some illustrative examples are given to show the rationality of the definitions introduced in this paper. Second, several new kinds of generalized fuzzy soft Γ-submodules are proposed, and related properties and mutual relationships are also investigated. Third, we discover some intrinsic connections between the generalized fuzzy soft Γ-submodules presented in this paper and crisp Γ-submodules, and describe the relationships between regular Γ-modules and the generalized fuzzy soft Γ-submodules presented in this paper.