Constructions of stable equivalences of Morita type for finite dimensional algebras II

Suppose k is a field. Let A and B be two finite dimensional k-algebras such that there is a stable equivalence of Morita type between A and B. In this paper, we prove that (1) if A and B are representation-finite then their Auslander algebras are stably equivalent of Morita type; (2) The n-th Hochschild homology groups of A and B are isomorphic for all n≥1. A new proof is also provided for Hochschild cohomology groups of self-injective algebras under a stable equivalence of Morita type.     

Fast electron transfer and enhanced visible light photocatalytic activity by using poly-o-phenylenediamine modified AgCl/g-C3N4 nanosheets

Exfoliation of bulk graphitic carbon nitride (g-C₃N₄) into two-dimensional (2D) nanosheets is one of the effective strategies to improve its photocatalytic properties so that the 2D g-C₃N₄ nanosheets (CN) have larger specific surface areas and more reaction sites. In addition, poly-o-phenylenediamine (PoPD) can improve the electrical conductivity and photocatalytic activity of semiconductor materials. Here, the novel efficient composite PoPD/AgCl/g-C₃N₄ nanosheets was first synthesized by a precipitation reaction and the photoinitiated polymerization approach. The obtained photocatalysts have larger specific surface areas and could achieve better visible-light response. However, silver chloride (AgCl) is susceptible to agglomeration and photocorrosion. The PoPD/AgCl/CN composite exhibits an extremely high photocurrent density, which is three times that of CN. Obviously enhanced photocatalytic activities of PoPD/AgCl/g-C₃N₄ are revealed through the photodegradation of tetracycline. The stability of PoPD/AgCl/CN is demonstrated based on four cycles of experiments that reveal that the degradation rate only decreases slightly. Furthermore, ?O₂^? and h⁺ are the main active species, which are confirmed through a trapping experiment and ESR spin-trap technique. Therefore, the prepared PoPD/AgCl/CN can be considered as a stable photocatalyst, in which PoPD is added as a charge carrier and acts a photosensitive protective layer on the surface of the AgCl particles. This provides a new technology for preparing highly stable composite photocatalysts that can effectively deal with environmental issues.     

Fabrication of HRP/Bi_2WO_6 photoenzyme-coupled artificial catalytic system for efficiently degrading bisphenol A

A novel photoenzyme-coupled artificial catalytic system is fabricated by immobilizing horseradish peroxidase(HRP) on the Bi_2WO_6 hollow nanospheres via a facile electrostatic self-assembly process. The obtained Bi_2WO_6/HRP sample not only improves the visible light harvest ability but also promotes the high-efficiency separation of charge carriers. More importantly, the photogenerated electrons and produced H_2O_2 on Bi_2WO_6 directly take part in redox cycle reactions of HRP to induce photoenzyme synergic catalytic effect. In consequence, the degradation activity of Bi_2WO_6/HRP is significantly improved relative to Bi_2WO_6 and HRP for removing bisphenol A(BPA) under the visible light irradiation.This work launches a feasible design strategy for exploiting photoenzyme-coupled artificial catalytic system with special structure to degrade organic pollutants in water efficiently.     

超欧拉扩展有向图

A digraph D is supereulerian if D has a spanning eulerian subdigraph. BangJensen and Thomass′e conjectured that if the arc-strong connectivity λ(D) of a digraph D is not less than the independence number α(D), then D is supereulerian. In this paper, we prove that if D is an extended cycle, an extended hamiltonian digraph, an arc-locally semicomplete digraph, an extended arc-locally semicomplete digraph, an extension of two kinds of eulerian digraph, a hypo-semicomplete digraph or an extended hypo-semicomplete digraph satisfyingλ(D) ≥α(D), then D is supereulerian.     

胞腔代数和仿射胞腔代数简介

表示论中一个最基本的问题是确定不可约表示的参数集,这个问题至今没有完全解决.对于Graham和Lehrer引入的有限维胞腔代数,这个问题得到了完满解答,并被成功地应用于数学和物理中出现的许多代数.近来,人们引入仿射胞腔代数,将Graham和Lehrer有限维胞腔代数的表示理论框架推广到一类无限维代数上.仿射胞腔代数不仅包括有限维胞腔代数,也包括无限维的仿射Temperley-Lieb代数和Lusztig的A-型仿射Hecke代数.本文将对胞腔代数的发展历史和主要研究成果做一些综述,同时,对新引入的仿射胞腔代数及其最新成果做一点简介.     

Constructions of derived equivalences for algebras and rings

In this article, we shall survey some aspects of our recent (or related) constructions of derived equivalences for algebras and rings.     

连通简单$r$-一致超图的约化

It is proved in this paper that if G is a simple connected r-uniform hypergraph with G ≥ 2, then G has an edge e such that G-e-V1(e) is also a simple connected r-uniform hypergraph. This reduction is naturally called a combined Graham reduction. Under the simple reductions of single edge removals and single edge contractions, the minor minimal connected simple r-uniform hypergraphs are also determined.