Group extensions and free actions by finite groups on solvmanifolds

The purpose of this paper is to generalize Yalçin's result [Trans. Amer. Math. Soc. 352 , 2689–2700 (2000)] from tori to solvmanifolds. As a result, we prove that if (?_p)^r acts freely on a solvmanifold M of dimension n, then r ≤ n (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Recent topics of the metallacycles composed of the heavier group 14 elements

This Letter reviews recent advance of metallacycles with chelating Si-, Ge-, and Sn-ligands. Dehydrogenative bond-forming reactions of organosilanes, -germanes, and -stannanes promoted by Pd and Pt complexes afford four- and five-membered metallacycles composed of heavier group 14 elements. It has a couple of advantages such as easier preparation of the starting compounds and reaction procedure than the common metathesis reactions of dianions with transition metal dihalide complexes. These metallacycles are regarded as possible intermediates in catalytic dehydrocoupling polymerizations or as convenient precursors to form discrete oligomers.     

A theorem on refractive index as a function of wavelength

A theorem upon refractive index as a function of wavelength is derived starting from the Taylor expansion around the origin of this function. Our result involves the above index, the group index, and the coefficient of material dispersion all extrapolated to zero wavelength.     

Synthesis,Characterization, and Symmetry Relations of the Crystal Structures of Some Bis(dioxane) Adducts of Group 1 / Group 13 Heterometallic Trifluoroacetates

Four bis(dioxane) adducts of mixed‐metal trifluoroacetates, M[M′(O₂CCF₃)₄(C₄H₈O₂)₂] (M = Na, K, Cs, M′ = In and M = Cs, M′ = Ga) were synthesized by reaction of alkali metal trifluoroacetate and group 13 element trifluoroacetate in 1,4‐dioxane and completely characterized including X‐ray structure determination. Geometric parameters, empirical bond valences and frequencies of the symmetric C=O stretching vibrations show that the moisture sensitive solids are composed of dimeric structural moieties with site symmetry 1 , containing alkali metal ions and bis(dioxane)tetrakis(trifluoroacetato)indate or ‐gallate ions. The dimeric units are further connected by weaker “intermolecular” dioxane interactions to neighboring alkali metal ions. Closer inspection of space group symmetry, unit cell parameters and atom sites allows to rationalize the compounds as members of two isotypic pairs that are further closely related due to the group‐subgroup relation of their monoclinc space groups to a common orthorhombic supergroup.     

Group inverses for some 2 × 2 block matrices over rings

We first consider the group inverses of the block matrices (A0BC) over a weakly finite ring. Then we study the sufficient and necessary conditions for the existence and the representations of the group inverses of the block matrices (ACBD) over a ring with unity 1 under the following conditions respectively: (i) B = C, D = 0, B^# and (B^πA) ^# both exist; (ii) B is invertible and m = n; (iii) A^# and (D - CA^#B)^# both exist, C = CAA^# , where A and D are m × m and n × n matrices, respectively.     

应用ICP-MS测定城市道路尘土中铂族元素

自然条件下,铂族元素(PGEs)一直被认为是表生条件下的痕量元素。但是,随着铂族元素在机动车排放催化剂及其他方面的广泛使用,最终导致Pt,Pd,Rh会排放到环境中。目前,铂族元素在环境中存在一定程度的积累现象,机动车尾气催化转换器被认为是其污染的主要来源。为研究北京市城区内道路尘土铂族元素的污染状况,于2010年11月采集了北京市内大型居民社区内的道路尘土样品。样品先经王水热消解以及阳离子交换树脂(Dowex AG50W-X8)分离纯化后,采用电感耦合等离子体质谱仪(ICP-MS)分析了道路尘土样品中三种铂族元素(铂(Pt)、钯(Pd)和铑(Rh))的浓度。结果表明：北京城区内居民社区道路尘土中Pd,Pt和Rh的含量范围分别为：14.20～161.80,9.39～70.80和3.18～17.05 ng·g-1,其平均浓度分别为50.76,23.82和7.54 ng·g-1,高于北京市土壤背景值, 说明北京城市居民社区内道路尘土中PGEs已经有了一定程度的富集。其中,Pd,Pt和Rh分别高于北京土壤背景值约49.8,32.6和5.1倍。为了定量评价道路尘土中PGEs的污染状况,采用地积累指数法对北京市道路尘土进行了评价。地积累指数法评价结果发现：大型居民社区内道路尘土中PGEs污染程度由强至弱的顺序依次为：Pd＞Pt＞Rh,总体而言,北京城区内大型居民社区内道路尘土存在较为明显的PGEs污染。     

集团分布式制造模式下生产调配优化模型研究及算法设计

基于分布式概念的集团分布式制造生产管理模式在市场中占据着越来越重要的地位,此种运营模式由制造型企业向服务型企业蔓延的趋势也越来越明显,然而针对这一具有自身特点的集团分布式概念下的生产管理模型的调度研究却很少。研究针对此生产管理模式下集团级的生产调配问题建立数学模型,综合考虑客户订单的分散情况、各分厂日生产能力限制和产品品种多样性的特点,采用改进的遗传算法求解该模型,提出一种基于订单和工厂的两段式非负整数染色体编码方法,保证了生产能力约束和订单约束,采用PMX交叉算法避免不合法染色体的出现。选取W集团一定计划期内的客户订单数据进行实例分析,验证了该生产调配模型和算法的有效性。