环上的一种群具体作用的G-等变K-群(Ⅰ)

讨论幺环上的一种群具体作用的G-等变代数K-群(本文只定义前两个群,其它高阶群将见我们的后续文章),这与通常熟知的经典情形(见[1,3])不相同,这里群在环上的作用相对于经典情形来说较"具体".然后,计算有理数域Q的第0阶群具体作用的G-等变代数K-群,这是本文的主要定理.     

On the Characterizability of the Automorphism Groups of Sporadic Simple Groups by Their Element Orders

For G a finite group, π _e (G) denotes the set of orders of elements in G. If Ω is a subset of the set of natural numbers, h(Ω) stands for the number of isomorphism classes of finite groups with the same set Ω of element orders. We say that G is k-distinguishable if h(π _e (G)) = k < ∞, otherwise G is called non-distinguishable. Usually, a 1-distinguishable group is called a characterizable group. It is shown that if M is a sporadic simple group different from M ₁₂, M ₂₂, J ₂, He, Suz, M ^c L and O′N, then Aut(M) is characterizable by its element orders. It is also proved that if M is isomorphic to M ₁₂, M ₂₂, He, Suz or O′N, then h(π _e (Aut(M))) ∈¸ {1,∞}.     

Potential Analysis on Carnot Groups，Part II：Relationship between Hausdorff Measures and Capacities

Abstract In this paper, we establish the relationship between Hausdorff measures and Bessel capacities on any nilpotent stratified Lie group (i. e., Carnot group). In particular, as a special corollary of our much more general results, we have the following theorem (see Theorems A and E in Section 1): Let Q be the homogeneous dimension of . Given any set E ⊂ , B _α,p (E) = 0 implies ℋ ^{Q−αp+ ε}(E) = 0 for all ε > 0. On the other hand, ℋ ^Q−αp (E) < ∞ implies B _α,p (E) = 0. Consequently, given any set E ⊂ of Hausdorff dimension Q − d, where 0 < d < Q, B _α,p (E) = 0 holds if and only if αp ≤ d. A version of O. Frostman’s theorem concerning Hausdorff measures on any homogeneous space is also established using the dyadic decomposition on such a space (see Theorem 4.4 in Section 4). Research supported partly by the U. S. National Science Foundation Grant No. DMS99–70352     

The Selmer Groups of Elliptic Curves

Let E/K be an elliptic curve with K-rational p-torsion points.The p-Selmer group of E is described by the image of a map λk and hence an upper bound of its order is given in terms of the class numbers of the S-ideal class group of K and the p-division field of E.     

On the p—Local Rank of Finite Groups

In this paper,we shall mainly study the p-solvable finite group in terms of p-local rank,and a group theoretic characterization will be given of finite p-solvabel groups with p-local rank two.Theorem A Let G be a finite p-solvable group with p-local rank plr(G)=2 and Op(G)=1.If P is a Sylow p-subgrounp of G,then P has a normal subgroup Q such that P/Q is cyclic or a generalized quaternion 2-group and the p-rank of Q is at most two.Theorem B Let G be a finite p-solvable group with Op(G)=1.Then the p-length lp(G)≤plr(G);if in addition plr(G)=lp (G) and p≥5 is odd,then plr(G)=0 or 1.     

On ＂Problems on von Neumann Algebras by R. Kadison, 1967＂

A brief summary of the development on Kadison‘s famous problems (1967) is given. A new set of problems in von Neumann algebras is listed.     

STABILITY OF CERTAIN RINGS OF HIGHEST WEIGHT VECTORS

51. IntroductionLet Cm'" be the space of complex m x n matrices, P(Cm)") be the algebra of complexpolynomials on Cd'~. Let GLm(C) x GL.(C) act on P(Cm,") as the following:(gi, gZ)f(x) ~ f(g,'xg,),where x E Cat", (gi, g2) E GLm x GL., f E P(Cm'"). This action induces an action of thesubgroup Of x GL. on P(Cm)") by restriction.Let G be a complex reductive algebraic group, (V, p) be a rational representation of G.Let B = TU be a Borel subgroup of G, where T is a majximal torns of …     

非退化Cauchy-Riemann流形上¶b复形的正则性

对于余维数大于1的CR流形M 上的一点ξ , M 在ξ 附近的CR结构可由两步幂零Lie群G_ξ的CR结构来逼近.G_ξ随ξ变化而变化.M 上的¶_b和¶_b可由两步幂零Lie群上的¶_b和¶_b逼近.用两步幂零Lie群上¶_b的拟基本解构造非退化CR流形M上¶_b的拟基本解,并定义M 上的拟距离.¶_b和¶_b复形的正则性可从M 上的调和分析得到.     

用于彩色目标跟踪的改进粒子群优化算法

提出一种用于彩色目标跟踪的改进粒子群优化算法(Improved Particle Swarm Optimization Algorithms,IP-SOA)。针对彩色目标,选择加权彩色直方图作为目标的特征,选用Bhattacharyya系数作为特征相似性度量,其最大值位置表示目标位置。对粒子群优化算法进行了改进,即自动调整惯性权重函数与认知学习因子,每次递推时对粒子速度、单帧位移总量加以限制,对Bhattacharyya系数优化,快速求取函数最大值位置。利用彩色序列图像进行仿真实验,结果表明,该方法能够实时跟踪飞机、车辆等目标,在目标被部分遮挡时能稳健跟踪。     

Σ-N相互作用的研究及 4ΣHe结合能的计算

基于SU(3)夸克模型， 用共振群方法研究了两种理论下的Σ-N相互作用， 得到了它们的相互作用非定域位以及Σ超子与3He壳心核的相互作用势， 并在此基础上计算了4ΣHe基态结合能。 计算结果表明， SU(3)夸克模型能较好地描述两种理论下的Σ N相互作用及Σ超子与3He壳心核的相互作用势， 同时由其得到的 4ΣHe基态结合能也与实验值基本相吻合。