Weak separation properties for self-similar sets

We develop a theory for self-similar sets in that fulfil the weak separation property of Lau and Ngai, which is weaker than the open set condition of Hutchinson.

     

On two--block--factor sequences and one--dependence

The distributions of two--block--factors arising from i.i.d. sequences are observed to coincide with the distributions of the superdiagonals of jointly exchangeable and dissociated arrays . An inequality for superdiagonal probabilities of the arrays is presented. It provides, together with the observation, a simple proof of the fact that a special one--dependent Markov sequence of Aaronson, Gilat and Keane (1992) is not a two--block factor.

     

Whitehead test modules

A (right -) module is said to be a Whitehead test module for projectivity (shortly: a p-test module) provided for each module , implies is projective. Dually, i-test modules are defined. For example, is a p-test abelian group iff each Whitehead group is free. Our first main result says that if is a right hereditary non-right perfect ring, then the existence of p-test modules is independent of ZFC + GCH. On the other hand, for any ring , there is a proper class of i-test modules. Dually, there is a proper class of p-test modules over any right perfect ring.

A non-semisimple ring is said to be fully saturated (-saturated) provided that all non-projective (-generated non-projective) modules are i-test. We show that classification of saturated rings can be reduced to the indecomposable ones. Indecomposable 1-saturated rings fall into two classes: type I, where all simple modules are isomorphic, and type II, the others. Our second main result gives a complete characterization of rings of type II as certain generalized upper triangular matrix rings, . The four parameters involved here are skew-fields and , and natural numbers . For rings of type I, we have several partial results: e.g. using a generalization of Bongartz Lemma, we show that it is consistent that each fully saturated ring of type I is a full matrix ring over a local quasi-Frobenius ring. In several recent papers, our results have been applied to Tilting Theory and to the Theory of -modules.

     

Abstract functions with continuous differences and Namioka spaces

Let be a semigroup and a topological space. Let be an Abelian topological group. The right differences of a function are defined by for . Let be continuous at the identity of for all in a neighbourhood of . We give conditions on or range under which is continuous for any topological space . We also seek conditions on under which we conclude that is continuous at for arbitrary . This led us to introduce new classes of semigroups containing all complete metric and locally countably compact quasitopological groups. In this paper we study these classes and explore their relation with Namioka spaces.

     

环的弱理想（Ⅰ）

通过对环的子环所满足的条件进行加强,推广了环的思想概念,引入了弱理想的概念,讨论了弱理想的基本性质,并证明了：（１）环Ｒ的理想类是Ｒ的弱理想类的真子集。（２）一个含有单位元的交换环Ｒ是除环的充分必要条件是Ｒ没有真弱理想。     

粘弹基上受压粘弹杆的稳定性

由纤维复合等材料研制的各种结构的广泛应用,使得其力学性能的研究日趋重要。由于这类材料具有明显的时间效应,因而,必须采用粘弹性理论研究其与时间相关的各种性质。利用动力学的观点和方法,研究了粘弹性基础上两端受压粘弹性直杆的动力稳定性。考虑杆的线性变形,将问题化为等价的四阶常微分方程,分析了方程不动点的稳定性,由此得到杆的蠕变及瞬时临界载荷,讨论了杆失稳的临界时间,并数值计算了杆的动力响应,得到了相应的     

多维OU型Markov过程的弱对偶半群及其无穷小算子

研究多维ＯＵ型Ｍａｒｋｏｖ过程的不变测度、参考测度、弱对偶半群及其无穷小算子．说明了ＯＵ型Ｍａｒｋｏｖ过程不变概率测度和弱对偶半群的存在唯一性,Ｌéｖｙ过程Ａｔ的不变测度不一定是由它产生的ＯＵ型Ｍａｒｋｏｖ过程的不变测度,以及Ｌｅｂｅｓｇｕｅ测度ｍ和极限分布ξ在ｓｕｐｐξ＝Ｒｄ的条件下都是ＯＵ型Ｍａｒｋｏｖ过程的参考测度．     

交联聚苯乙烯强－弱碱树脂的合成及脱色性能研究

交联聚苯乙烯氯甲基化后，分别与甲胺（或二甲胺）、三甲胺（或α－甲基吡啶、二甲基乙醇胺）混合胺化试剂进行亲核取代反应，合成了一系列同时带有强－弱碱功能基的交联聚苯乙烯树脂，并表征了这些树脂的结构，测定了树脂对甜菊甙的脱色性能，结果表明，这些树脂功能基碱性适中，脱色容量较高，甜菊甙损失较少，再生效率高。     

Crystal Structures of 1,5,9,18,22,26-Hexaaza[11.11]-p-cyclophane Adducts; Two-dimensional Supramolecular Networks

Two newly identified supramolecular structures arise from self-assembly of the macrocyclic 1,5,9,18,22,26- hexaaza[11.11]-p-cyclophane salts with o-nitrophenol (C₂₈H₅₀N₆)⁴⁺·4(C₆H₄NO₂O)⁻ (1) and with HCl (C₂₈H₅₂N₆)⁶⁺·6Cl^-·4H₂O (2). In both cases two-dimensional supramolecular sheets are formed.     

Self‐Assembly of Dialkyltin Moieties and Mercaptobenzoic Acid into Macrocyclic Complexes with Hydrophobic “Pseudo‐Cage” or Double‐Cavity Structures: Supramolecular Infrastructures Involving Intermolecular C?H⋅⋅⋅S Weak Hydrogen Bonds and π–π Interactions

Four novel organotin complexes of two types—[R₂Sn(o‐SC₆H₄CO₂)]₆ (R=Me, 1 ?H₂O; nBu, 2 ) and {[R₂Sn(m‐CO₂C₆H₄S)R₂Sn(m‐SC₆H₄CO₂)SnR₂]O}₂ (R=Me, 3 ; nBu, 4 )—have been prepared by treatment of o‐ or m‐mercaptobenzoic acid and the corresponding R₂SnCl₂ (R=Me, nBu) with sodium ethoxide in ethanol (95 %). All the complexes were characterized by elemental analysis, FT‐IR and NMR (¹H, ¹³C, ¹¹⁹Sn) spectroscopy, TGA, and X‐ray crystallography diffraction analysis. The molecular structure analyses reveal that both 1 and 2 are hexanuclear macrocycles with hydrophobic “pseudo‐cage” structures, while 3 and 4 are hexanuclear macrocycles with double‐cavity structures. Furthermore, the supramolecular structure analyses show that looser and more intriguing supramolecular infrastructures were also found in complexes 1 – 4 , which exist either as one‐dimensional chains of rings or as two‐dimensional networks assembled from the organometallic subunits through intermolecular C? H???S weak hydrogen bonds (WHBs) and π–π interactions.