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.
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.
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.
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.
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. 相似文献
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. 相似文献
High level ab initio and density functional theory calculations have been carried out to investigate the relative stability of the different conformers of hyponitrous acid and its mono- and dithio-derivatives. Geometries and vibrational frequencies were obtained at the B3LYP/6-311+G(d,p) level and final energies through B3LYP/6-311++G(3df,2pd) single point calculations. The reliability of this theoretical scheme has been assessed by comparing these DFT results with those obtained at the G3 level of theory, for some suitable cases. The cis conformers of hyponitrous acid and its mono- and dithio-derivatives are systematically more stable than the
trans ones because in the cis conformation a dative interaction between the nitrogen-lone pairs and the σNX^* antibonding orbital is significantly favored. Quite interestingly, in general, the conformers presenting an intramolecular hydrogen bond (IHB) are not the global minima of the corresponding potential energy surfaces and only for hyponitrous acid the conformer with a OH ⋅s O IHB is slightly more stable than the cis conformer without IHB. The low stability of the tautomers with IHB is closely related with another weak intramolecular interaction which involves the lone-pairs of the chalcogen atoms and the πNN* antibondig orbital, and which is significantly perturbed when the IHB is formed. 相似文献
Diphenyl oxalate was synthesized from transesterification of dimethyl oxalate with phenol over TS-1(2.5 wt% Ti)catalyst.TS-1 catalyst,as a beterogeneous catalyst,showed excellent selectivity of diphenyl oxalate and methylphenyl oxalate compared with other homogeneous catalysts.Lewis acid sites on TS-1 catalyst were the active sites for transesterification of dimethyl oxalate with phenol.the high selectivity was closely related to the weak acid sites over TS-1. 相似文献
We have studied the basicity of 2-phenyl-5-R-1,3,4-oxadiazoles (R = H, Me, CH2Ph, t-Bu, CH2Cl, CCl3, CF3) in aqueous sulfuric acid solutions. These compounds are weak organic bases (pKBH+ is −1.8 to −5.2). The values of pKBH+ determined on the H0 and X acidity function scales agree well with each other. The substituent at the 5 position has a substantial effect on the
basicity of the 1,3,4-oxadiazole ring.
__________
Translated from Khimiya Geterotsiklicheskikh Soedinenii, No. 5, pp. 748–756, May, 2006. 相似文献