The Littlewood-Richardson rule for wreath products with symmetric groups and the quiver of the category F≀FIn

We give a new proof for the Littlewood-Richardson rule for the wreath product F?S_n where F is a finite group. Our proof does not use symmetric functions but use more elementary representation theoretic tools. We also derive a branching rule for inducing the natural embedding of F?S_n to F?S_n+1. We then apply the generalized Littlewood-Richardson rule for computing the ordinary quiver of the category F?FI_n where FI_n is the category of all injective functions between subsets of an n-element set.     

Hochschild and ordinary cohomology rings of small categories

Let C be a small category and k a field. There are two interesting mathematical subjects: the category algebra kC and the classifying space |C|=BC. We study the ring homomorphism HH^∗(kC)→H^∗(|C|,k) and prove it is split surjective, using the factorization category of Quillen [D. Quillen, Higher algebraic K-theory I, in: Lecture Notes in Math., vol. 341, Springer-Verlag, Berlin, 1973, pp. 85-147] and certain techniques from functor cohomology theory. This generalizes the well-known theorems for groups and posets. Based on this result, we construct a seven-dimensional category algebra whose Hochschild cohomology ring modulo nilpotents is not finitely generated, disproving a conjecture of Snashall and Solberg [N. Snashall, Ø. Solberg, Support varieties and Hochschild cohomology rings, Proc. London Math. Soc. 88 (3) (2004) 705-732].     

Canonizing structural Ramsey theorems

At the beginning of 1950s Erd?s and Rado suggested the investigation of the Ramsey-type results where the number of colors is not finite. This marked the birth of the so-called canonizing Ramsey theory. In 1985 Prömel and Voigt made the first step towards the structural canonizing Ramsey theory when they proved the canonical Ramsey property for the class of finite linearly ordered hypergraphs, and the subclasses thereof defined by forbidden substructures. Building on their results in this paper we provide several new structural canonical Ramsey results. We prove the canonical Ramsey theorem for the class of all finite linearly ordered tournaments, the class of all finite posets with linear extensions and the class of all finite linearly ordered metric spaces. We conclude the paper with the canonical version of the celebrated Ne?et?il–Rödl Theorem. In contrast to the “classical” Ramsey-theoretic approach, in this paper we advocate the use of category theory to manage the complexity of otherwise technically overwhelming proofs typical in canonical Ramsey theory.     

Category with a natural cone

Generally, in homotopy theory a cylinder object (or, its dual, a path object) is used to define homotopy between morphisms, and a cone object is used to build exact sequences of homotopy groups. Here, an axiomatic theory based on a cone functor is given. Suspension objects are associated to based objects and cofibrations, obtaining homotopy groups referred to an object and relative to a cofibration, respectively. Exact sequences of these groups are built. Algebraic and particular examples are given. We point out that the main results of this paper were already stated in [3], and the purpose of this article is to give full details of the foregoing.     

笛卡儿闭Domain范畴的两个重要性质

对于CONT的任意一个笛卡儿闭的满子范畴C,构造CONT的两个新的满子范畴R-C(以C对象的收缩为对象的范畴)和B-C(以C扩张序列的双极限为对象的范畴),并证明了它们都是笛卡儿闭范畴。由于R-C和B-C都包含C为其满子范畴,利用上述结果可得CONT的极大笛卡儿闭子范畴必对收缩和双极限封闭。本文还从范畴笛卡儿闭性的角度给出了Domain理论中一个公开问题的等价描述。     

大气环境质量评价的灰色模型

大气环境是一个包含未知信息的灰色系统，根据其灰色性．运用灰色系统理论可以克服目前一些环境质量评价方法（综合指数法、概率统计法、模糊综合评判法）的局限性，使评价结果更为科学和客观。     

"老人"历史债务的双随机模型

为社会养老保险制度转轨过程中的“老人”历史债务建立了双随机模型，得到了“老人”历史债务的前二阶段，并对息力累积函数以Wiener过程和Ornstein-Uhlenbeck过程建模得到了的具体表达式。最后做了一个实例，以浙江省某市的实际数据，估算了该市的“老人”历史债务额。     

集合套范畴的研究

模糊集理论与 Topos理论有着密切的联系 ,借助于模糊集理论中的集合套理论 ,引入了两种新的范畴——集合套范畴 SEB1和 SEB2。首先证明了 SEB1满足卡氏积封闭性 (Cartesian Closed) ,但没有SC(子对象分类器 ) ,所以 SEB1不是 Topos.其次 ,得出 SEB2是一个 Topos     

Partial Orderings in the Category of Matrices over the Quaternion Field

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