$C_3$型的退化Ringel-Hall代数的Gr\"{o}bner-Shirshov基

The Gr?bner-Shirshov basis of the degenerate Ringel-Hall Algebras of type C₃ is obtained by studying the generic extension monoid algebra.     

The Canonical Basis for the Quantum Group of Type B2

We use the Ringel-Hall algebra approach to study the canonical basis elements for the quantum group of type B₂ which are characterized in Xi [12]. However, our approach simplifies several computations there.     

G_2型量子群的Gelfand-Kirillov维数

用Gr(o|¨)bner-Shirshov基和PBW代数方法来计算G_2型量子群的Gelfand.Kirillov维数.得到的结论是G_2型量子群的Gelfand-Kirillov维数为14.     

一类退缩椭园型方程弱解的正则性

本文得出一类形如：－Ｄｉｖ（ｇ（｜Ｄｕ｜）｜Ｄｕ｜＾ｐ－２Ｄｕ＋ｆ（ｘ,ｕ））＝Ｂ（ｘ,ｕ,Ｄｕ）在一定的条件下在Ｗ＾１．ｐ空间中的弱解的Ｈｏｌｄｅｒ连续性。     

ON DEGENERATE WEAKLY （K1, K2）-QUASIREGULAR MAPPINGS

The authors first give the definition of degenerate weakly （K1,K2）-quasiregular mappings using the technique of exterior power and exterior differential forms, and then, using the method of McShane extension, a useful inequality is obtained, which can be used to derive the self-improving regularity.     

Universal Deformation Rings of Modules over Self-injective Cluster-Tilted Algebras Are Trivial

Let k be a fixed algebraically closed field of arbitrary characteristic,let Λ be a finite dimensional self-injective k-algebra,and let V be an indecomposable non-projective left Λ-module with finite dimension over k.We prove that if τΛV is the Auslander-Reiten translation of V,then the versal deformation rings R(Λ,V)and R(Λ,τΛV)(in the sense of F.M.Bleher and the second author)are isomorphic.We use this to prove that if Λ is further a cluster-tilted k-algebra,then R(Λ,V)is universal and isomorphic to k.     

Nilpotent Lie Algebras of Maximal Rank and of Kac–Moody Type: E6

Let be the Kac–Moody algebra associated to the affine Cartan matrix E₆⁽¹⁾. Each nilpotent Lie algebra of type E₆⁽¹⁾ is isomorphic to a quotient of the positive part of . We determine the isomorphism classes of nilpotent Lie algebras of type E₆⁽¹⁾.     

Modular Branching Rules and the Mullineux Map for Hecke Algebras of Type A

We prove the quantum version - for Hecke algebras H A_n of typeA at roots of unity - of Kleshchev's modular branching rulefor symmetric groups. This result describes the socle of therestriction of an irreducible H A_n-module to the subalgebraH A_n–1. As a consequence, we describe the quantum versionof the Mullineux involution describing the irreducible moduleobtained on twisting an irreducible module with the sign representation.1991 Mathematics Subject Classification: 20C05, 20G05.     

求鳞状循环因子矩阵的极小多项式的算法

提出了任意域上鳞状循环因子矩阵 ,利用多项式环的理想的Go bner基的算法给出了任意域上鳞状循环因子矩阵的极小多项式和公共极小多项式的一种算法 .同时给出了这类矩阵逆矩阵的一种求法 .在有理数域或模素数剩余类域上 ,这一算法可由代数系统软件Co CoA4 .0实现 .数值例子说明了算法的有效性     

The Local Index Formula for SU q (2)

We discuss the local index formula of Connes–Moscovici for the isospectral noncommutative geometry that we have recently constructed on quantum SU(2). We work out the cosphere bundle and the dimension spectrum as well as the local cyclic cocycles yielding the index formula. (Received: January 2005)     

Star discrepancy estimates for digital (t, m, 2)-nets and digital (t, 2) -sequences over Z2

Summary We prove upper bounds on the star discrepancy of digital (t, m, 2)-nets and (t, 2)-sequences over Z₂. The main tool is a decomposition lemma for digital (t, m, 2)-nets, which states that every digital (t, m, 2)-net is just the union of 2^tdigitally shifted digital (0, m - t, 2)-nets. Using this result we generalize upper bounds on the star discrepancy of digital (0, m, 2) -nets and (0, 2) -sequences.     

Differential-geometric Newton method for the best rank-(R1, R2, R3) approximation of tensors

An increasing number of applications are based on the manipulation of higher-order tensors. In this paper, we derive a differential-geometric Newton method for computing the best rank-(R ₁, R ₂, R ₃) approximation of a third-order tensor. The generalization to tensors of order higher than three is straightforward. We illustrate the fast quadratic convergence of the algorithm in a neighborhood of the solution and compare it with the known higher-order orthogonal iteration (De Lathauwer et al., SIAM J Matrix Anal Appl 21(4):1324–1342, 2000). This kind of algorithms are useful for many problems. This paper presents research results of the Belgian Network DYSCO (Dynamical Systems, Control, and Optimization), funded by the Interuniversity Attraction Poles Programme, initiated by the Belgian State, Science Policy Office. The scientific responsibility rests with its authors. Research supported by: (1) Research Council K.U.Leuven: GOA-Ambiorics, CoE EF/05/006 Optimization in Engineering (OPTEC), (2) F.W.O.: (a) project G.0321.06, (b) Research Communities ICCoS, ANMMM and MLDM, (3) the Belgian Federal Science Policy Office: IUAP P6/04 (DYSCO, “Dynamical systems, control and optimization”, 2007–2011), (4) EU: ERNSI. M. Ishteva is supported by a K.U.Leuven doctoral scholarship (OE/06/25, OE/07/17, OE/08/007), L. De Lathauwer is supported by “Impulsfinanciering Campus Kortrijk (2007–2012)(CIF1)” and STRT1/08/023.     

两个同类的E_((2))型空间线性等距映射的表现定理

该文得到了两个同类的E_((2))型空间单位球面间等距线性算子的表现定理,这是首次在非具体范数的情形下取得此类结果.