可用于连续识别Cu^2+和阴离子、中性分子荧光探针的研究进展

铜(Cu)含量的高低直接影响着生命体的正常运转和自然体系的平衡.检测铜离子的方法多种多样,其中具有较高敏感度和选择性的荧光化学传感器应用更加广泛.综述了以Cu^2+为基的荧光化学传感器通过"替换"法实现了对阴离子S^2-, CN^-, H2PO4^-, PPi和I^-以及中性分子ATP、ADP和生物硫醇等的连续识别的研究进展.     

Two questions on semi-clean group rings

It was proved in [4] that every group ring of a torsion abelian group over a commutative local ring is a semi-clean ring. It was asked in [4] whether every group ring of a torsion abelian group over a commutative clean ring is a semi-clean ring and whether every group ring of a torsion abelian group over a commutative semi-clean ring is a semi-clean ring. In this paper, we give a positive answer to question 1 and a negative answer to question 2.     

On actions of Drinfel'd doubles on finite dimensional algebras

Let q be an nth root of unity for $n>2$ and let $T_n(q)$ be the Taft (Hopf) algebra of dimension $n^2$. In 2001, Susan Montgomery and Hans-Jürgen Schneider classified all non-trivial $T_n(q)$-module algebra structures on an n-dimensional associative algebra A. They further showed that each such module structure extends uniquely to make A a module algebra over the Drinfel'd double of $T_n(q)$. We explore what it is about the Taft algebras that leads to this uniqueness, by examining actions of (the Drinfel'd double of) Hopf algebras H “close” to the Taft algebras on finite-dimensional algebras analogous to A above. Such Hopf algebras H include the Sweedler (Hopf) algebra of dimension 4, bosonizations of quantum linear spaces, and the Frobenius–Lusztig kernel $u_q({\mathfrak{sl}}_2)$.     

Some results about zero‐cycles on abelian and semi‐abelian varieties

In this short note we extend some results obtained in [7]. First, we prove that for an abelian variety A with good ordinary reduction over a finite extension of with p an odd prime, the Albanese kernel of A is the direct sum of its maximal divisible subgroup and a torsion group. Second, for a semi‐abelian variety G over a perfect field k, we construct a decreasing integral filtration of Suslin's singular homology group, , such that the successive quotients are isomorphic to a certain Somekawa K‐group.     

Group divisible 3‐designs with block size four and group type 1ns1

In this article, we mainly consider the existence problem of a group divisible design GDD $\left(3,4,n+s\right)$ of type $1^n{s}^1$. We present two recursive constructions for this configuration using candelabra systems and construct explicitly a few small examples admitting given automorphism groups. As an application, several new infinite classes of GDD $\left(3,4,n+s\right)$s of type $1^n{s}^1$ are produced. Meanwhile a few new infinite families on candelabra quadruple systems with group sizes being odd and stem size greater than one are also obtained.     

有限CN-p-群

每个子群都C-正规的有限群称为CN-群.本文首先给出二元生成的CN-p-群的完全分类.在此基础上得到CN-p-群的结构:当p为奇素数时,有限群G为CNp-群当且仅当G的每个元都平凡地作用在Φ(G)上;有限群G为CN-2-群当且仅当对任意给定的a∈G,都有对任意g∈Φ(G),g~a=g或者对任意g∈Φ(G),g~a=g~(-1).最后给出两个CN-p-群的直积是CN-p-群的判定条件.     

The antipode of a quasitriangular quasi-Turaev group coalgebra is bijective

In order to construct a class of new Turaev-braided group category with nontrivial associativity, the concept of a quasitriangular quasi-Turaev group coalgebras was recently introduced. Inside the definition, the conditions of invertibility of the R-matrix R and bijectivity of the antipode S are required. In this article, we prove that the antipode of a quasitriangular quasi-Turaev group coalgebra without the assumptions about invertibility of the antipode and R-matrix is inner, and a fortiori, bijective. As an application, we prove that for a quasitriangular quasi-Turaev group coalgebra, two conditions mentioned above are unnecessary.