The F -Decomposition of Artinian Modules over Hyper-(Cyclic or Finite) Groups

Let Fbe a formation locally defined by f(p), G∈ Fand A a ZG-module, where p∈π={all primes and symbol ∞}.Then a p-main-factor U/V of G is said to be F -central in G if G/CG(U/V)∈f(p). In this paper, we have proved that: let Fbe a locally defined formation consisting of locally soluble groups, G a hyper-(cyclic or finite) locally soluble group and A an artinian ZG-module with all irreducible ZG-factors of A being finite; if G ∈ F, f(∞) f(p), f(p)≠ for each p∈π, A has an F -decomposition.     

城市轨道交通对城市结构的影响因素分析

分析了两种城市结构即单中心同心圆与多中心轴线式的特点。从我国城市可持续发展的角度指出我国大城市理想的发展模式是多中心轴线式。从人口环境,土地等方面阐述了城市轨道交通在城市结构变迁中的重要诱导作用,最后从我国城市的现状指出发展轨道交通应注意的几个问题。     

Splitting Extensions of Abelian by Hyper-（ cyclic or finite） Groups （Ⅱ ）

Let F be a locally defined formation consisting of locally solvable groups, G a hyper-（ cyclic or finite） locally solvable group and A a noetherian ZG-module with all irreducible ZG-factors being finite. The following conclusion is obtained： if G∈F, f（ ∞ ） include f（p）, f（p） ≠φ for each p∈π, and A has no nonzero F central ZG- images, then any extension E of A by G splits conjugately over A, and A has no nonzero F central ZG-factors.     

New Definition and Properties of Fuzzy Entropy

Let X = （x1 ,x2 ,…… ,xn ） and F（X） be a fuzzy set on a universal set X. A new def＇mition of fuzzy entropy about a fuzzy set A on F（X）, e^＊＇ , is defined based on the order relation ＂≤＂ on [ 0,1/2 ]^n. It is proved that e^＊ is a σ-entropy under an additional requirement. Besides, some entropy formulas are presented and related properties are discussed.     

群的共轭可裂扩张

通过对本项目两年的研究，一方面解决了几个长期未解决的问题，另一方面极大地提高了学术研究能力，为以后的研究工作打下了坚实的基础。     

F-Decomposition of Noetherian Modules over Hyper-（Cyclic or Finite）Groups

Let F be a locally defined formation consisting of locally soluble groups，G a hyper-(cyclic or finite)locally soluble group and A a noetherian ZG-module with all irreducible ZG-factors being finite，G∈F,f(∞)≌f(p)，f(P)≠Фfor each P∈π．The following conclutions are obtained：(1)if there exists a maximal submodule B of A such that A／B is F central in G and B has no nonzero F centml ZG-factors，then A has an F decomposition；(2)if there exists an irreducible F central submodule B of A such that all ZG-composition factors of A／B are F ecentric，then A has an F decomposition．