FR^A模的Fuzzy同态的几个重要结果

证明了ＦＲ＾Ａ模的第一同构定理、第二同构定理、同构扩展定理以及其他一些重要性质。     

Constant curvature 2-spheres in—P2

In this note, for each 0<R<1, we construct a continuous family of isometric immersions of the 2-sphere of constant curvature 1/R ²,S ²(R), into complex projective plane—P² with the Fubini-Study metric.The author has received financial support from CNP_q during the completion of this work.     

Isomorphism of inclusion compounds built with composite host lattices of thiadiazole and V-shaped molecules with the existence of tetrabutylammonium guest template

By using 4,4′-dihydroxydiphenylsulfone (BPS) and 4,4′-dihydroxydiphenylsulfide (BTS) react with amidinethiourea and tetrabutylammonium respectively, two isomorphs of inclusion compounds of (n-C₄H₉)₄N⁺·C₁₂H₉O₄S^?·C₂H₄N₄S (1) and (n-C₄H₉)₄N⁺·C₁₂H₉O₂S^?·C₂H₄N₄S (2) were prepared and characterized by Single crystal X-ray diffraction. Although two varied types of V-shaped molecules were selected to react in the actual experimental process, two isomorphs with similar packing modes were finally obtained. Interestingly, amidinothiourea molecule occurred in situ oxidation reaction to generate a new compound of 3,5-dimido-1,2,4,-thiadiazole during the experiments, and these two inclusion compounds here are the pioneer examples of thiadiazole and tetraalkylammonium and can be regarded as two isomorphs due to their similar crystallization modes. In these two isomorphs, thiadiazole molecules derived from amidinothiourea link with various V-type molecules to develop the similar dumbbell-type hydrogen-bonded ribbons by the alike hydrogen bonding modes, then the ribbons interpenetrate with tetrabutylammonium to result in two stable isomorphism structures.     

On finite groups with the cayley isomorphism property

Let G be a finite group, and let Cay(G, S) be a Cayley digraph of G. If, for all T ⊂ G, Cay(G, S) ≅ Cay(G, T) implies S^α = T for some α ∈ Aut(G), then Cay(G, S) is called a CI-graph of G. For a group G, if all Cayley digraphs of valency m are CI-graphs, then G is said to have the m-DCI property; if all Cayley graphs of valency m are CI-graphs, then G is said to have the m-CI property. It is shown that every finite group of order greater than 2 has a nontrivial CI-graph, and all finite groups with the m-CI property and with the m-DCI property are characterized for small values of m. A general investigation is made of the structure of Sylow subgroups of finite groups with the m-DCI property and with the m-CI property for large values of m. © 1998 John Wiley & Sons, Inc. J Graph Theory 27: 21–31, 1998     

Mbius立方体的拓扑结构性质

超立方体网络是目前在超级计算机处理器结构中应用得最广泛的拓扑结构,Mbius立方体是超立方体的一种变形,已经被证明它在某些方面具有优于超立方体的拓扑性质.本文指出了n维Mbius立方体递归结构的一些重要拓扑性质.     

分片代数集合的不可约性和同构

本文利用多元样条函数来定义分片代数集合,讨论了分片代数集合的不可约性和同构问题,给出了分片代数集合不可约的两个等价条件,并把分片代数集合的同构分类问题转化为交换代数的同构分类问题。     

Linear operators in finite dimensional probabilistic normed spaces

In this paper, we consider strongly bounded linear operators on a finite dimensional probabilistic normed space and define the topological isomorphism between probabilistic normed spaces. Then we prove that every finite dimensional probabilistic normed space which is a topological vector space is complete.     

Stabilizability of two classes of contraction semigroups

This paper studies the strong stabilizability of two classes of Hilbert space contraction semigroups: (i) strict contraction semigroups, which include those with strictly dissipative generators; and (ii) isometric or unitary semigroups. The former class is already weakly stable, while the latter is not strongly stable over the whole space. Our tool is the functional model of Hilbert space contractions; hence, strong stability of the semigroup is studied via stability of its cogenerator. It is shown that a strict contraction semigroup is, in general, not strongly stabilized by the feedback –B*, while an isometric or a unitary semigroup is strongly stabilized by the same feedback, providedB is not compact.     

Cayley图的同构分解及弱DCI-子集的充要条件

本文得到了Ｃａｙｌｅｙ图的同构分解定理及弱ＤＣＩ－子集的充要条件．证明了二面体群是弱２－ＤＣＩ－群，同时确定了二面体群上２度Ｃａｙｌｅｙ图的自同构群．     

Isomorphism in the poly(3,3-bis-hydroxymethyloxetane) family and copolymers: Poly (3,3-bis-hydroxymethyloxetane-co-3-methyl-3-hydroxymethyloxetane)

Copolymers of 3,3-bis-hydroxymethyloxetane, BHMO, 3-metyl-3-hydroxymethyloxetane, MHMO, or with 3-ethyl-3-hydroxymethyloxetane, EHMO, monomer units were characterized by x-ray fiber diffraction, differential scanning calorimetry and ¹³C solid-state nuclear magnetic resonance (NMR). The copolymers are statistically random and crystalline throughout the range of compositions. Both P(BHMO) and P(MHMO) appear to crystallize in the same crystal form. The fiber repeat indicates a planar zigzag backbone conformation, c(fiber axis) = 4.77 ± 0.03 Å. Similarities in the x-ray fiber diagrams as well as a linear dependence of T_m with composition of copolymer with no change in fiber diagrams indicates isomorphism, a phenomenon in which the random substitution of MHMO monomeric units into the crystalline lattice of P(BHMO) occurs without hindering crystallization of the resulting copolymer. © 1994 John Wiley & Sons, Inc.