Gröbner-Shirshov basis for degenerate Ringel-Hall algebras of type <Emphasis Type="Italic">F</Emphasis><Subscript>4</Subscript>

In this paper, by using the Frobenius morphism and the multiplication formulas of the generic extension monoid algebra, the authors first give a presentation of the degenerate Ringel-Hall algebra, and then construct the Gröbner-Shirshov basis for degenerate Ringel-Hall algebras of type F ₄.     

Structural modification on rupestonic acid leads to highly potent inhibitors against influenza virus

Molecular Diversity - Influenza viruses are responsible for seasonal epidemics and occasional pandemics, which cause significant morbidity and mortality. Although several drugs (adamantanes and...     

D4型量子包络代数的Gelfand-Kirillov维数

本文研究了D₄ 型量子包络代数的Gelfand-Kirillov 维数的计算问题. 利用文献[1] 中给出的Gelfand-Kirillov 维数的计算方法和文献[2] 中给出的D₄ 型量子包络代数的Groebner-Shirshov 基计算了D₄型量子包络代数的Gelfand-Kirillov 维数, 得到的主要结果是D₄ 型量子包络代数的Gelfand-Kirillov 维数为28. 希望此结果为计算D_n型量子包络代数的Gelfand-Kirillov 维数提供一些思路.     

Generalized tilting functors and Ringel-Hall algebras

It is known from [M. Auslander, M.I. Platzeck, I. Reiten, Coxeter functors without diagrams, Trans. Amer. Math. Soc. 250 (1979) 1-46] and [C.M. Ringel, PBW-basis of quantum groups, J. Reine Angew. Math. 470 (1996) 51-85] that the Bernstein-Gelfand-Ponomarev reflection functors are special cases of tilting functors and these reflection functors induce isomorphisms between certain subalgebras of Ringel-Hall algebras. In [A. Wufu, Tilting functors and Ringel-Hall algebras, Comm. Algebra 33 (1) (2005) 343-348] the result from [C.M. Ringel, PBW-basis of quantum groups, J. Reine Angew. Math. 470 (1996) 51-85] is generalized to the tilting module case by giving an isomorphism between two Ringel-Hall subalgebras. In [J. Miyashita, Tilting Modules of Finite Projective Dimension, Math. Z. 193 (1986) 113-146] Miyashita generalized the tilting theory by introducing the tilting modules of finite projective dimension. In this paper the result in [A. Wufu, Tilting functors and Ringel-Hall algebras, Comm. Algebra 33 (1) (2005) 343-348] is generalized to the tilting modules of finite projective dimension.     

Skew-commutator relations and Gröbner-Shirshov basis of quantum group of type F 4

We give a Grobner-Shirshov basis of quantum group of type F4 by using the Ringel-Hall algebra approach. We compute all skew-commutator relations between the isoclasses of indecomposable representations of Ringel- Hall algebras of type F4 by using an ＇inductive＇ method. Precisely, we do not use the traditional way of computing the skew-commutative relations, that is first compute all Hall polynomials then compute the corresponding skew- commutator relations; instead, we compute the ＇easier＇ skew-commutator relations which correspond to those exact sequences with middle term indecomposable or the split exact sequences first, then ＇deduce＇ others from these ＇easier＇ ones and this in turn gives Hall polynomials as a byproduct. Then using the composition-diamond lemma prove that the set of these relations constitute a minimal CrSbner-Shirshov basis of the positive part of the quantum group of type F4. Dually, we get a Grobner-Shirshov basis of the negative part of the quantum group of type F4. And finally, we give a Gr6bner-Shirshov basis for the whole quantum group of type F4.     

火焰原子吸收光度法测定维药芜菁的微量元素

为探讨微量元素与芜菁的药效关系,用火焰原子吸收分光光度法测定了维药芜菁中的K,Na,Ca,Fe,Cu,Co,Zn,Mn,Mg等9种元素含量。结果表明,芜菁含有丰富的人体必需微量元素,其中K,Na,Ca,Zn的含量更显著;方法的回收率在93．7％～102．5％之间,RSD值在0．39％-1．3％之间,能用于维药芜菁中多种微量元素的同时测定。为芜菁的进一步研究和综合开发利用提供了新的科学依据。     

Grbner-Shirshov Basis and the Minimal Projective Resolution of U_q~+(G_2)

In this paper, by using the Anick's resolution and Gröbner-Shirshov basis for quantized enveloping algebra of type G₂, we compute the minimal projective resolution of the trivial module of U_q⁺ (G₂) and as an application we compute the global dimension of U_q⁺ (G₂).     

Synthesis and Antiviral Activity of New Derivatives of Rupestonic Acid

Chemistry of Natural Compounds - A series of 20 new derivatives of rupestonic acid were synthesized via Davis oxidation. Their antiviral activity against influenza A virus (H3N2) was established....     

植物毒素茄格孢吡喃酮A的研究

致病真菌Ascochyta rabiei感染鹰嘴豆植物体产生三种植物毒索．茄格孢毗喃酮A．茄格孢毗喃酮B和茄格孢毗喃酮C．其中茄格孢毗喃酮A的毒性最大．往往在感染的植物体中表现出植物体变黄．植物茎部变脆．易折断等病理现象。严重时导致整个植物体因枯萎病而死亡．体外培养Ascochyta rabiei研究已知．该致病菌产生一些叫做茄格孢毗喃酮的植物毒索．当用分离提纯的茄格孢毗喃酮A毒素喂养植物体时虽然出现了与病菌感染植物体完全一样的病理现象．但研究者均不能从感染植物体或者体外喂养毒索的植物体中重新分离到该毒索。很可能这种毒索通过某种机制被鹰嘴豆植物细胞代谢转换成另外一种物质．为了研究这一过程，我们提取鹰嘴豆植物的蛋白质提取物(30％-70％硫氨饱和沉淀法)于实验室条件下分离提取并用HPLC方法鉴定植物毒索茄格孢毗喃酮A反应．不管还原物质NADPH存在或者不存在．发现植物毒素茄格孢吡喃酮A消失．即使在鹰嘴豆蛋白制备物加热沸腾处理后与毒索的反应中也出现植物毒素茄格孢毗喃酮A的大量丢失．说明蛋白质制备物很可能不是酶．HPLC(高压液相色谱)检测反应产物时出现了一个新物质．NMR(核磁共振)确定该物质为脱甲基的茄格孢毗喃酮A．进一步的研究得知．该脱甲基的茄格孢毗喃酮A不是鹰嘴豆植物蛋白质提取物的作用下产生的．而是分离蛋白质用的硫氨作用于该植物毒素产生的．用透析方法除掉硫氨后的鹰嘴豆植物蛋白质制备物与该毒素反应时．脱甲基茄格孢吡喃酮A不再出现．但仍有茄格孢吡喃酮A植物毒素的丢失．最后发现，分离提纯蛋白质制备物所用的离子交换柱(FPLC)试剂Tris-HCI和NaCl也会导致茄格孢吡喃酮A植物毒素的丢失．与一些非特异性蛋白质化学物反应时．茄格孢吡喃酮A植物毒索还是存在大量的丢失．所有这些研究结果显示．这一种植物毒素茄格孢吡喃酮A似乎具有较高的反应活性．很可能与植物体中的一些物质结合或者局部反应．正因为是这一原因不能从感染植物体或者体外喂养毒素的植物体中重新分离到该毒素，而感染植物或体外喂养毒素的植物仍然表现出明显的病理现象．植物毒素茄格孢吡喃酮A的这种易反应特性．可能就是它对植物体具有较强毒性的原因之一．     

The Skew-commutator Relations and Gröbner-Shirshov Bases of Quantum Group of Type C3

Acta Mathematicae Applicatae Sinica, English Series - In this paper, we give a Gröbner-Shirshov basis of quantum group of type ℂ3 by using the Ringel-Hall algebra approach. For this,...