基于3-吡唑-5吡啶-1,2,4-三唑和均苯四甲酸构筑的两个同构配位聚合物的晶体结构和磁性

以3-吡唑-5吡啶-1,2,4-三唑(H2L)和均苯四甲酸(H_4btec)为配体合成了2个新的同构配位聚合物[M(btec)_(0.5)(H_2L)]_n(M=Co(Ⅱ)(1),Cu(Ⅱ)(2)),通过X射线单晶衍射、元素分析、红外光谱等进行了结构表征。晶体结构分析表明配合物1和2是同构的,都属于正交晶系,空间群为Pbca。2个配位聚合物都是二维结构,通过N…H…O氢键形成三维超分子框架结构。此外对上述配合物进行了磁性研究,结果表明配合物1内通过羧基桥连的金属钴离子之间是弱的铁磁相互作用;配合物2中存在典型的順磁行为。     

Typical Frobenius coverings

A covering p from a Cayley graph Cay（G, X） onto another Cay（H, Y） is called typical Frobenius if G is a Frobenius group with H as a Frobenius complement and the map p ： G →H is a group epimorphism. In this paper, we emphasize on the typical Frobenius coverings of Cay（H, Y）. We show that any typical Frobenius covering Cay（G, X） of Cay（H, Y） can be derived from an epimorphism /from G to H which is determined by an automorphism f of H. If Cay（G, X1） and Cay（G, X2） are two isomorphic typical Frobenius coverings under a graph isomorphism Ф, some properties satisfied by Фare given.     

张量乘积图的同构因子分解

本文讨论了两个可分图的张量乘积图的同构因子分解问题.给出了张量乘积图可同构因子分解的判定条件.     

连通的三重Kn-残差图

Erds P,Harary F和Klawe M研究了Kn-残差图,并对连通的m-Kn-残差图提出了一些结论和猜想．利用容斥原理以及集合的运算性质等方法,研究了连通的3-Kn-残差图,得到当顶点最小度为n时,3-Kn-残差图最小阶的计算公式以及相应的唯一极图．当n=2时,得到最小阶为ll以及相应的极图;当n=3时,得到最小阶为20并找到两个不同构的极图,不满足Erdos等提出的结论;当n=4时,得到最小阶为22及相应的极图;当n=8时,可以找到两个不同构的3-Kn-残差图,不满足Erdos等提出的结论;最后证明了当n=9,10时,最小阶分别为48和52以及相应的唯一极图,验证了Erdos等在文献（Residually-complete graphs[J]．Annals of Discrete Mathematics,1980,6：117．123）中提出的结论．     

Isomorphism of lattices of recursively enumerable sets

Let , and for , let be the lattice of subsets of which are recursively enumerable relative to the ``oracle' . Let be , where is the ideal of finite subsets of . It is established that for any , is effectively isomorphic to if and only if , where is the Turing jump of . A consequence is that if , then . A second consequence is that can be effectively embedded into preserving least and greatest elements if and only if .

     

A lower bound on the number of Semi‐Boolean quadruple systems

A Steiner quadruple system of order 2ⁿ is Semi‐Boolean (SBQS(2ⁿ) in short) if all its derived triple systems are isomorphic to the point‐line design associated with the projective geometry PG(n?1, 2). We prove by means of explicit constructions that for any n, up to isomorphism, there exist at least 2^{? 3(n?4)/2?} regular and resolvable SBQS(2ⁿ). © 2003 Wiley Periodicals, Inc. J Combin Designs 11: 229–239, 2003; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/jcd.10050     

Finitely Generated Nilpotent Groups of Infinite Cyclic Commutator Subgroups

The aim of this paper is to determine the structure and to establish the isomorphic invariant of the finitely generated nilpotent group G of infinite cyclic commutator subgroup. Using the structure and invariant of the group which is the central extension of a cyclic group by a free abelian group of finite rank of infinite cyclic center, we provide a decomposition of G as the product of a generalized extraspecial Z-group and its center. By using techniques of lifting isomorphisms of abelian groups and equivalent normal form of the generalized extraspecial Z-groups, we finally obtain the structure and invariants of the group G.     

Almost Isomorphic Torsion-Free Abelian Groups and Similarity of Homogeneously Decomposable Groups

In the paper the concept of the similarity of homogeneously decomposable groups is introduced. One investigates the cases in which almost isomorphic groups are similar or isomorphic. Mathematics Subject Classification (2000) 20K99.     

Physico-chemical Characterization of Hydrated and Anhydrous Crystal Forms of Amlodipine Besylate

The antihypertensive drug substance amlodipine besylate crystallizes in two stable crystal forms, an anhydrate and a hitherto unknown monohydrate. Both forms have been characterized by thermal analysis, X-ray powder diffractometry, FTIR- and FT Raman spectroscopy. Moisture sorption- and desorption investigations reveal their unusual physical stability in a broad range of relative humidities. The monohydrate forms an isomorphic dehydrate upon dehydration, which was elucidated by variable temperature X-ray powder diffractometry. Physico-chemical properties as well as relative stabilities of the crystal forms are described and discussed based on a comprehensive analytical identification, and enable an estimation of practical relevance for manufacturing of amlodipine besylate solid dosage forms. This revised version was published online in August 2006 with corrections to the Cover Date.     

Recursive constructions for triangulations

Three recursive constructions are presented; two deal with embeddings of complete graphs and one with embeddings of complete tripartite graphs. All three facilitate the construction of 2) non‐isomorphic face 2‐colourable triangulations of K_n and K_n,n,n in orientable and non‐orientable surfaces for values of n lying in certain residue classes and for appropriate constants a. © 2002 John Wiley & Sons, Inc. J Graph Theory 39: 87–107, 2002