Ditkin's condition for certain Beurling algebras

Let be a locally compact abelian group. A function is said to be a weight if it is locally bounded, Borel measurable and submultiplicative. We call a weight on semi-bounded if there exist a constant and a subsemigroup with such that

for all Using functional analytic methods, we show that all Beurling algebras whose defining weight is semi-bounded satisfy Ditkin's condition.

     

基于语言评价信息的知识资本要素识别方法

知识资本是组织创造价值和获取竞争优势的关键资源, 其要素通常具有复杂的关联性, 如何识别知识资本的核心要素、原因要素和结果要素,对于组织进行知识资本管理具有重要意义.本文在构建了知识资本要素识别体系的基础上,借鉴决策试验和评价实验室报告的思想提出了一种基于语言评价信息的知识资本要素识别方法,通过处理和集结专家针对知识资本要素关联给出的语言评价信息,对知识资本要素进行排序与归类.最后通过一个实例分析说明了该方法的应用, 并说明了如何根据识别结果制定相应的策略以便进行知识资本的投资和控制.     

Modular Fisher Discriminant Sparse Representation for robust face recognition

This paper proposes a novel framework for robust face recognition based on sparse representation and discrimination ranking. This method consists of three stages. The first stage partitions each training sample into some overlapped modules and then computes each module's Fisher ratio, respectively. The second stage selects modules which have higher Fisher ratios to comprise a template to filter training and test images. The dictionary is constructed by the filtered training images. The third stage computes the sparse representation of filtered test sample on the dictionary to perform identification. The advantages of the proposed method are listed as follows: the first stage can preserve the local structure. The second stage removes the modules that have little contribution for classification. Then the method uses the retaining modules to classify the test sample by SRC which makes the method robust. Compared with the related methods, experimental results on benchmark face databases verify the advancement of the proposed method. The proposed method not only has a high accuracy but also can be clearly interpreted.     

因素空间理论与知识表示的数学框架（Ⅸ）──均衡函数的构造与Weber－Fechner特性

本文是文［１－８］的继续，该文及后续论文仍将系统地研究因素空间理论及其在知识表示中的应用。该文研究均衡函数的构造，并且引入了激励型均衡函数和混合型均衡函数。特别，从混合型变权出发，我们得到与ＷｅｂｅｒＦｅｃｈｎｅｒ定律一致的综合函数。     

The covariance matrix of the Potts model: A random cluster analysis

We consider the covariance matrix,G ^mm =q ²<(_x,m);(_y,m)>, of thed-dimensionalq-states Potts model, rewriting it in the random cluster representation of Fortuin and Kasteleyn. In any of theq ordered phases, we identify the eigenvalues of this matrix both in terms of representations of the unbroken symmetry group of the model and in terms of random cluster connectivities and covariances, thereby attributing algebraic significance to these stochastic geometric quantities. We also show that the correlation length corresponding to the decay rate of one of the eigenvalues is the same as the inverse decay rate of the diameter of finite clusers. For dimensiond=2, we show that this correlation length and the correlation length of the two-point function with free boundary conditions at the corresponding dual temperature are equal up to a factor of two. For systems with first-order transitions, this relation helps to resolve certain inconsistencies between recent exact and numerical work on correlation lengths at the self-dual point _o. For systems with second order transitions, this relation implies the equality of the correlation length exponents from above and below threshold, as well as an amplitude ratio of two. In the course of proving the above results, we establish several properties of independent interest, including left continuity of the inverse correlation length with free boundary conditions and upper semicontinuity of the decay rate for finite clusters in all dimensions, and left continuity of the two-dimensional free boundary condition percolation probability at _o. We also introduce DLR equations for the random cluster model and use them to establish ergodicity of the free measure. In order to prove these results, we introduce a new class of events which we call decoupling events and two inequalities for these events. The first is similar to the FKG inequality, but holds for events which are neither increasing nor decreasing; the second is similar to the van den Berg-Kesten inequality in standard percolation. Both inequalities hold for an arbitrary FKG measure.     

双生子佯谬的投影诠释

在表示洛伦兹变换的复平面上,考察各边平行于坐标轴的直角三角形,以其中各边比例关系为“投影关系”,用于简明地诠释双生子佯谬的实质,并得出某种程度的一般性结论