The Relative Transpose over Cohen-Macaulay Finite Artin Algebras

The relative transpose via Gorenstein projective modules is introduced, and some corresponding results on the Auslander-Reiten sequences and the Auslander-Reiten formula to this relative version are generalized.     

半量子群u~(≥0)

设u~(≥0)表示一个固定单李代数的半量子群,给出了u~(≥0)的性质和表示.证明了Hopf代数u~(≥0)不是拟余交换的,因此左u~(≥0)-模范畴不是辫子monoidal范畴.在权模范畴W中,给出了所有单对象和投射对象.最后描述了所有单的Yetter-Drinfel'd u~(≥0)-权模.     

On the Cayley-Bacharach Property

The Cayley-Bacharach Property (CBP), which has been classically stated as a property of a finite set of points in an affine or projective space, is extended to arbitrary 0-dimensional affine algebras over arbitrary base fields. We present characterizations and explicit algorithms for checking the CBP directly, via the canonical module, and in combination with the property of being a locally Gorenstein ring. Moreover, we characterize strict Gorenstein rings by the CBP and the symmetry of their affine Hilbert function, as well as by the strict CBP and the last difference of their affine Hilbert function.     

基于结构的新型CDK7抑制剂的设计、合成及其抗肿瘤活性

根据细胞周期依赖性激酶7(CDK7)的蛋白结构, 利用Discovery Studio 2.1程序包中的LigandFit模块建立了CDK7抑制剂的分子对接模型, 采用受试者工作特征曲线(ROC)方法选择LigScore2为最佳打分函数(ROC曲线下的面积为0.95), 并验证了该模型的准确性. 利用该模型对设计的化合物与CDK7蛋白进行对接分析, 得到了2个打分最高的化合物16、17, 进而通过13步的合成路线, 以中等至高的收率得到目标化合物, 并测定其体外抗肿瘤活性. 结果表明, 所合成的化合物对急性前髓细胞性白血病细胞(HL60)、鼻咽癌细胞(KB)、肝肿瘤细胞(SMMC-7721)、结肠腺癌细胞(HCT-116)、肺癌细胞(A549)细胞株均有抑制作用(IC50值为0.84-19.70 μmol·L-1), 其中化合物16对HL60细胞株的IC50值最低, 为0.84 μmol·L-1.     

Gorenstein正则环、奇点范畴和Ding模

本文证明了任意环的整体Ding投射维数和整体Ding内射维数一致,研究了奇点范畴和相对于Ding模的稳定范畴间的关系,并刻画了Gorenstein (正则)环以及环的整体维数的有限性.     

Compact DG modules and Gorenstein DG algebras

When the base connected cochain DG algebra is cohomologically bounded, it is proved that the difference between the amplitude of a compact DG module and that of the DG algebra is just the projective dimension of that module. This yields the unboundedness of the cohomology of non-trivial regular DG algebras. When A is a regular DG algebra such that H(A) is a Koszul graded algebra, H(A) is proved to have the finite global dimension. And we give an example to illustrate that the global dimension of H(A) may be infinite, if the condition that H(A) is Koszul is weakened to the condition that A is a Koszul DG algebra. For a general regular DG algebra A, we give some equivalent conditions for the Gorensteiness. For a finite connected DG algebra A, we prove that D^c(A) and D^c(A ^op) admit Auslander-Reiten triangles if and only if A and A ^op are Gorenstein DG algebras. When A is a non-trivial regular DG algebra such that H(A) is locally finite, D^c(A) does not admit Auslander-Reiten triangles. We turn to study the existence of Auslander-Reiten triangles in D_lf^b(A) and D_lf^b (A ^op) instead, when A is a regular DG algebra. This work was supported by the National Natural Science Foundation of China (Grant No. 10731070) and the Doctorate Foundation of Ministry of Education of China (Grant No. 20060246003)     

群Yetter-Drinfel''d范畴中的Hopf代数

In this note we first show that if H is a finite-dimensional Hopf algebra in a group Yetter-Drinfel＇d category L^LyD（π） over a crossed Hopf group-coalgebra L, then its dual H^＊ is also a Hopf algebra in the category L^LyD（π）. Then we establish the fundamental theorem of Hopf modules for H in the category L^LyD（π）.     

Polytopal estimate of Mirkovi?–Vilonen polytopes lying in a Demazure crystal

In this paper, we give a polytopal estimate of Mirkovi?–Vilonen polytopes lying in a Demazure crystal in terms of Minkowski sums of extremal Mirkovi?–Vilonen polytopes. As an immediate consequence of this result, we provide a necessary (but not sufficient) polytopal condition for a Mirkovi?–Vilonen polytope to lie in a Demazure crystal.     

Interconnections and Initial Conditions of Linear Systems With First-Order Representations

This paper considers the initial value problem of an interconnection composed of linear systems described by the first-order differential/algebraic equations (DAEs). An initial condition of the system variable for which the DAE has a solution is called admissible. For the interconnected system, we formulate the invariance of the admissible initial condition sets (AICSs) of the sub-systems under interconnection. Namely, the AICSs are said to be invariant if they remain unchanged even when additional constraints due to interconnection are imposed on the system variables. It is shown that the feedback and regular feedback structures of the interconnection guarantee the invariance of the AICSs in the senses of impulsive-smooth distributions and smooth distributions, respectively. The results in this paper justify the use of a feedback controller in the control system design.     

On the Pure-injectivity Profile of a Ring

An analog of the injective profile of a ring, with relative injectivity replaced by relative pure-injectivity, is investigated. Emphasis is placed on comparing and contrasting the properties of both profiles. In particular, the analog in this context of the notion of poor modules is considered and properties of pure-injectively poor modules are determined. While we do not know of any ring that does not have pure-injectively poor modules, their existence has not been determined in general. Rings having pure-injectively poor modules of various types are characterized.