关于双参数量子群的注记(I)

借助于Euler型, 给出了一类(对应于半单Lie代数的)双参数量子群的更为简便的定义方式, 证明了所定义量子群的正部分在双参数满足适当条件下是互为2-上圈形变的, 并给出了该正部分 在Kashiwara意义下的斜微分算子实现.     

关于交叉数为2的联图

确定图的交叉数是NP-完全问题.Kuratowski定理刻画了平面图的结构特征,而对于交叉数为k(k≥1)的非平面图G的结构特征刻画,目前相关结果甚少.对于交叉数为1的联图G_1∨G_2,我们已经刻画出因子图G_1和G_2满足的充要条件.本文刻画了当△(G_2)≠3且cr(G_1∨G_2)=2时因子图G_1和G_2须满足的充要条件.     

秩1量子群的有限维表示的扩张与诱导模的零化性质

量子群表示的扩张归结为秩1群的扩张.本文研究了秩1量子群有限维表示的扩张结构和诱导模的零化性质,给出了有限维 U_k~b 表示扩张成 U_k 表示的充要条件.对任一有限维 U_k~b模 V,给出了诱导模 H_k~0(V)是非零的充要条件.     

G_(2)-型导出Hall代数的PBW基北大核心CSCD

在Dynkin型Ringel-Hall代数中,不可分解模同构类之间的所有拟交换关系的集合S构成理想Id(S)的一个极小Grobner-Shirshov基,并且对于S的所有不可约元素构成Ringel-Hall代数的一个PBW基.本文把此结果推广到G_(2)-型导出Hall代数上.首先用Auslander-Reiten箭图计算不可分解模同构类之间的所有拟交换关系,然后证明这些拟交换关系之间的所有合成都是平凡的,最后给出G_(2)-型导出Hall代数的一个PBW基.     

冠图(G_1○G_2)○G_3的Wiener指数

给出了冠图(G_1·G_2)·G_3的Wiener指数W((G_1·G_2)·G_3),得出了W((G_1·G_2)·G_3)与三个图的边数和顶点数有关,且与G_1的结构有关,而与G_2、G_3的结构无关.     

W-代数W(2,2)的单参数量子形变(英文)

众所周知,泛包络代数的量子形变所对应的量子群结构是依据所给代数的单根系给出的.我们构造了q-形变W代数Wq,并给出其非平凡的量子群结构.     

关于交叉数为1的联图

确定图的交叉数是NP-完全问题.Kuratowski定理刻画了平面图的特征,而结合图的交叉数这一参数来研究非平面图的特征,目前相关结果甚少.本文从联图着手,研究当G_1VG_2的交叉数为1时,刻画出因子图G_1和G_2须满足的充要条件.     

Hall多项式

作为Hall代数的结构常数, Hall数和Hall多项式与对称群的表示和量子群的结构有紧密联系.本文首先引入经典Hall代数和Hall多项式的概念,并阐述其与对称函数的联系.其次,定义有限域上代数的Ringel-Hall代数,并简述其与量子群的关系.最后,本文在Dynkin箭图和仿射箭图情形下,讨论Hall多项式的存在性.     

IR量子群ν_q(sl(2 ) )的不可约表示(英文)

本文引进满足一定关系的六个元素生成的量子群 νq(sl(2 ) ) .证明了 νq(sl(2 ) )具有 PBW基且是无零因子环 .进而当 q不是单根时决定了νq(sl(2 ) )的有限维不可约束表示 .     

B型量子群的Kashiwara算子

利用一个带特殊自同构的A_2n-1型Dynkin箭图上的F-稳定表示,刻画了B型量子群的Kashiwara算子.同时指出邓、杜和张文章中的主要结果对于B₂型赋值箭图并不成立.     

Estimation of the number of components of finite mixtures of multivariate distributions

An estimator of the number of components of a finite mixture ofk-dimensional distributions is given on the basis of a one-dimensional independent random sample obtained by a transformation of ak-dimensional independent random sample. A consistency of the estimator is shown. Some simulation results are given in a case of finite mixtures of two-dimensional normal distributions.     

Galois Structure of K-Groups of Rings of Integers

N/Kbe a Galois extension of number fields with finite Galois group G.We describe a new approach for constructing invariants of the G-module structure of the K groups of the ring of integers of N in the Grothendieck group of finitely generated projective Z[G]modules. In various cases we can relate these classes, and their function field counterparts, to the root number class of Fröhlich and Cassou-Noguès.     

Eigenvector p-Bases of Rings of Constants of Derivations

Let A be a UFD of characteristic p > 0, let 𝒵 be a set of some eigenvectors of a derivation of A. We prove, under some additional assumptions, a necessary and sufficient condition for 𝒵 to be a p-basis of the minimal ring of constants containing 𝒵. The main preparatory result is the unique decomposition theorem with respect to a factor from a given subalgebra containing A^p.     

有资格限制的指派问题的求解方法

在实际的指派工作中，常会遇到某个人有没有资格去承担某项工作的问题，因此，本建立了有资格限制的指派问题的数学模型。在此数学模型中，将效益矩阵转化为判定矩阵，由此给出了判定此种指派问题是否有解的方法；在有解的情况下，进一步将效益矩阵转化为求解矩阵，从而将有资格限制的指派问题化为传统的指派问题来求解。最后给出了一个数值例子来说明这样的处理方法是有效的。     

On Sums of Coefficients of Products of Polynomials

We study the nilpotency of the sums of all coefficients of some sorts of products of polynomials over reversible, IFP, and NI rings, and introduce an SCN ring as a generalization. We characterize SCN rings in relation with related ring properties, and also provide several useful properties and ring extensions of SCN rings.     

Convergence of sequences of sets of associated primes

It is a well-known result of M. Brodmann that if is an ideal of a commutative Noetherian ring , then the set of associated primes of the -th power of is constant for all large . This paper is concerned with the following question: given a prime ideal of which is known to be in for all large integers , can one identify a term of the sequence beyond which will subsequently be an ever-present? This paper presents some results about convergence of sequences of sets of associated primes of graded components of finitely generated graded modules over a standard positively graded commutative Noetherian ring; those results are then applied to the above question.

     

Rates of Convergence of Means of Euclidean Functionals

Let L be the Euclidean functional with p-th power-weighted edges. Examples include the sum of the p-th power-weighted lengths of the edges in minimal spanning trees, traveling salesman tours, and minimal matchings. Motivated by the works of Steele, Redmond and Yukich (Ann. Appl. Probab. 4, 1057–1073, 1994, Stoch. Process. Appl. 61, 289–304, 1996) have shown that for n i.i.d. sample points {X ₁,…,X _n } from [0,1] ^d , L({X ₁,…,X _n })/n ^(d−p)/d converges a.s. to a finite constant. Here we bound the rate of convergence of EL({X ₁,…,X _n })/n ^(d−p)/d . Y. Koo supported by the BK21 project of the Department of Mathematics, Sungkyunkwan University. S. Lee supported by the BK21 project of the Department of Mathematics, Yonsei University.     

图表示范畴的两个子范畴

引进图表示范畴的两个子范畴,研究它们的同调性质。     

Asymptotics of families of solutions of nonlinear difference equations

One method to determine the asymptotics of particular solutions of a difference equation is by solving an associated asymptotic functional equation. Here we study the behaviour of the solutions in an asymptotic neighbourhood of such individual solutions. We identify several types of attraction and repulsion, which range from almost orthogonality to almost parallelness. Necessary and sufficient conditions for these types of behaviour are given.     

Extreme values of the sum of squares of degrees of bipartite graphs

In this paper we determine the minimum and maximum values of the sum of squares of degrees of bipartite graphs with a given number of vertices and edges.