有限群极大子群的θ-子群偶

N.P.Mukherjee和 P.Bhattacharya在“On theta pairs for a maximal sub-group”(Proc.Amer.Math.Soc,Vl09N3(1990))一文中定义了有限群的极大子群的θ-子群偶概念,研究了极大子群的极大θ-子群偶对群结构的影响,得到了一系列结果.本文在进一步探究θ-子群偶性质的基础上,对该文中一系列主要结果作出了本质性的改进,并给出了可解性、幂零性的一些新刻划.     

Projecting average family size in rural India by the analytic hierarchy process

In this study, cultural, economic as well as certain crucial demographic factors are considered as the determinants for projecting the average family size in rural India. We use the Analytic Hierarchy Process to analyze influences of the factors which enter implicitly in a rural couple's decision‐making to determine the number of children they want to have as time goes by. We did not attempt to make distinctions among the regional differences in rural India. The outcome projected in our analysis compares favorably with the results of other demographic studies.     

Liquid crystalline properties and photochromism of 4-alkyl-N-(4-alkloxysalicylidene)anilines

Eight new homologous series of 4-alkyl-N-(4-alkloxysalicylidene)anilines were synthesized. The phase transitions of these homologues were determined using differential scanning calorimetry and polarizing optical microscopy. The homologues began to exhibit liquid crystalline phases as the terminal alkyl or alkoxyl chains were lengthened. In addition, some members of these homologues series exhibited photochromism in the solid state.     

Irradiation of detonation nanodiamonds with γ-rays does not produce long living spin radicals

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Local Near-Rings and Triply Factorized Groups

Abstract

Groups G of the form G = AB = AM = BM for two subgroups A and B of G and a normal subgroup M of G with A ∩ M = B ∩ M = 1 are called triply factorized and play an important rôle in the theory of factorized groups. In this paper, a method to construct triply factorized groups with non-abelian M using local near-rings is introduced.     

Carboxylic Acids as Directing Groups for C−H Bond Functionalization

The selective transformation of C?H bonds is one of the most desirable approaches to creating complexity from simple building blocks. Several directing groups are efficient in controlling the regioselectivity of catalytic C?H bond functionalizations. Among them, carboxylic acids are particularly advantageous, since they are widely available in great structural diversity and at low cost. The carboxylate directing groups can be tracelessly cleaved or may serve as the anchor point for further functionalization through decarboxylative couplings. This Minireview summarizes the substantial progress made in the last few years in the development of reactions in which carboxylate groups direct C?H bond functionalizations with formation of C?C, C?O, C?N, or C?halogen bonds at specific positions. It is divided into sections on C?C, C?O, C?N, and C?halogen bond formation, each of which is subdivided by reactions and product classes. Particular emphasis is placed on methods that enable multiple derivatizations by combining carboxylate‐directed C?H functionalization with decarboxylative couplings.     

Isopropenyl acetate: A cheap and general acylating agent of alcohols under metal-free conditions

Functionalized primary, secondary and tertiary alcohols are efficiently acetylated by isopropenyl acetate and catalytic p-TsOH.     

On the simplicity of some kac-moody groups

Recently, Marcuson extended the classical construction of Tits systems in Steinberg groups to include the Kac-Moody Steinberg groups associated with the infinite dimensional versions of the great Lie algebras. If these Lie algebras and their Kac-Moody groups are viewed as limits of their finite dimensional counterparts, more direct methods may be employed. In fact, the Kac-Moody Chevalley groups of these Lie algebras are seen to be simple.     

Introduction of C-Sulfonate Groups into Disaccharide Derivatives

To prepare C-sulfonate derivatives of disaccharides two different strategies were followed. Thus 6- and 6′-C-sulfocellobiosides 4 and 10–12 were prepared starting from a suitably protected cellobioside. The 6′-C-sulfoaminocellobioside 18 was prepared by construction of the molecule through a glycosylation reaction. In both cases, the synthetic pathway involves regioselective tosylation, introduction of a sulfur atom by nucleophilic displacement with potassium thioacetate and oxidation with hydrogen peroxide.