On Hypercentral Groups G With |G:G n |<∞

In 1960, Baumslag, following up on work of Cernikov for the 1940s, proved that a hypercentral p-group G with G = G ^p is a divisible Abelian group. In this article, we provide an interesting generalization of this 45 year old result: If a hypercentral p-group G satisfies |G:G ^p |<∞ (of course, it contains G = G ^p ), there exists a normal divisible Abelian subgroup D such that |G:D|<∞.     

非连通图G1∪G2及G1∪G2∪K2的优美性

将k-优美图的概念进行了推广，引入了k-l优美图及标号间距的概念，并以此为基础，分别推出了一般情形下判定非连通图G1∪G2及G1∪G2∪K2是优美图的两个充分条件；同时得出了图（C3VK^-n）∪st（m）∪K2是优美图，其中k、l为自然数，l〈k，C3是长为3的圈，Kn为n个顶点的完全图，K^-n是Kn的补图，St（m）表示m＋1个顶点的星形树，C3VK^-n是C3与K^-n的联图．     

G20表情

为期两天的二十国集团领导人第七次峰会，6月19日在墨西哥洛斯卡沃斯落下帷幕，与会领导人讨论了世界经济形势、加强国际金融体系和就业、发展、贸易等议题，并于会后发表了《二十国集团洛斯卡沃斯峰会领导人宣言》。二十国集团中的欧元区成员在宣言中承诺，将采取一切必要措施，维护该地区的完整性和稳定性，改善金融市场运作，打破主权债务与银行债务之间的恶性循环。各方希望欧元区能与希腊新一届政府通力合作，确保该国在欧元区内继续朝改革和可持续发展的方向前进。     

关于G连通子集

G连通子集有三种不同的定义方式, 建立了这三种G连通子集之间的关系, 并纠正了■(2012)的一些错误.     

G序列紧空间

基于G方法,在一般的集合中引入了G序列紧集,讨论了其基本性质,研究了在拓扑空间下其与序列紧,可数紧之间的关系,并论证了将方法定义为理想收敛时,G序列紧空间的应用.推广了序列紧与可数紧的一些经典结果.     

A general sufficient condition for a graph G with λ_m(G)≤ξ_m(G)

It has been shown that a λ m-connected graph G has the property λ m (G)≤ξ m (G) for m≤3.But for m≥4,Bonsma et al.pointed out that in general the inequality λ m (G)≤ξ m (G) is no longer true.Recently Ou showed that any λ 4-connected graph G with order at least 11 has the property λ 4 (G)≤ξ 4 (G).In this paper,by investigating some structure properties of a λ m-connected graph G with λ m (G) ξ m (G),we obtain easily the above result.Furthermore,we show that every λ m-connected graph G with order greater than m(m-1) satisfies the inequality λ m (G)≤ξm (G) for m≥5.And by constructing some examples,we illustrate that our conditions are the best possible.     

G恰当有效点集和G恰当有效解集的连通性

与多目标规划问题的G恰当有效解相应，引进了集合的G恰当有效点的概念，并互研究了G恰当有效点集和G恰当有效解集的连通性．利用所得的结果，还获得多目标规划问题的Pareto有效解集是连通的一个新的结论。     

System G|Gκ|1 with Batch Service of Calls

For the queuing system G|G |1 with batch service of calls, we determine the distributions of the following characteristics: the length of a busy period, the queue length in transient and stationary modes of the queuing system, the total idle time of the queuing system, the output stream of served calls, etc.     

3-γ-临界图G中关于i(G)=γ(G)的一个充分条件

如果图G满足γ（G）＝k且对图G中任两个相邻的点x,y有γ（G＋xy)=k-1,则称图G为k-γ-临界图,如果图G满足γ（G）＝k且对图G中任何距离为d的两点x,y有γ（G＋xy)=k-1,则称图G为k-(γ,d)－临界图。Sumner和Blitch猜想在3－γ－临界图中有γ（G）＝i(G).Oellermann和Swart猜想3－（γ,2）－临界图中有γ（G）＝i(G),这篇文章中我们提出3－γ－临界图中使γ（G）＝i(G)的一个充分条件。     

Graphs G for which both G and G¯ are Contraction Critically k-Connected

 An edge of a k-connected graph is said to be k-contractible if the contraction of the edge results in a k-connected graph. A k-connected graph with no k-contractible edge is called contraction critically k-connected. For k≥4, we prove that if both G and its complement Gˉ are contraction critically k-connected, then |V(G)|<k ^5/3+4k ^3/2. Received: October, 2001 Final version received: September 18, 2002 AMS Classification: 05C40     

G／G／1排队系统的渐近泊松离去过程

本文给出了Ｇ／Ｇ／１排队系统的离去过程的有限维分布弱收敛到泊松过程的有限维分布的条件,特别给出了生灭排队系统及Ｇ／Ｍ／１排队系统的离去过程的有限维分布弱收敛到泊松过程的有限维分布的简单条件．     

Idempotents in $$F_+(G)$$F+(G)

In this paper, we compute the idempotents of the ring $$F_+(G)$$ as defined by Boltje (J Algebra 206:293–343, 1998) in the particular case when the Green biset functor F is such that for all subgroups H of a finite group G, F(H) is a torsion-free ring, finitely-generated as an Abelian group, and has only the trivial idempotents. In this case, the only idempotents in $$F_+(G)$$ are those arising from the Burnside ring B(G).     

One-basedness and groups of the form G/G 00

We initiate a geometric stability study of groups of the form G/G ⁰⁰, where G is a 1-dimensional definably compact, definably connected, definable group in a real closed field M. We consider an enriched structure M?? with a predicate for G ⁰⁰ and check 1-basedness or non-1-basedness for G/G ⁰⁰, where G is an additive truncation of M, a multiplicative truncation of M, SO ₂(M) or one of its truncations; such groups G/G ⁰⁰ are now interpretable in M??. We prove that the only 1-based groups are those where G is a sufficiently ??big?? multiplicative truncation, and we relate the results obtained to valuation theory. In the last section we extend our results to ind-hyperdefinable groups constructed from those above.     

Rigid G2-representations and motives of type G2

We consider a family of motives associated to the rigid local system whose monodromy is dense in the simple algebraic group of type G₂ and which has a local monodromy of order 7 at ∞. We prove an explicit Hilbert irreduciblity theorem for the associated étale realizations and deduce that the specialized motives at the points of irreducibility have motivic Galois group G₂.