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.

     

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.     

Weak Interactions and 2D Layer Structure of a New Ion-pair Complex Bis(1-benzyl-4-methylquinolinium)-bis(maleonitriledithiolato)nickel(Ⅱ)

A new ion-pair complex,[BzMeQl]2[Ni(mnt)2] 1 ([BzMeQl]+=1-benzyl-4-methylquino-linium,mnt2-= maleonitriledithiolate) has been synthesized and structurally characterized by IR,ESI-MS and X-ray diffraction methods. Complex 1 is of triclinic,space group P1,with a=9.079(2),b=10.154(2),c=11.243(2),α=81.58(1),β=69.63(1),γ=68.02(1)°,V=940.1(3)3,Dc=1.427 g/cm3,Z=1,F(000)=418 and R=0.0442. A 2D layer structure is formed via the cation-cation π…π and C–H…π interactions observed in the solid state of the complex.     

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.     

The Role of Intramolecular Hydrogen Bonds vs. Other Weak Interactions on the Conformation of Hyponitrous Acid and Its Mono- and Dithio-Derivatives

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 σ_NX^* 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 π_NN^* antibondig orbital, and which is significantly perturbed when the IHB is formed.     

Preparation of Diphenyl Oxalate from Transesterification of Dimethyl Oxalate with Phenol over TS—1 Catalyst

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.     

Basicity of 2-phenyl-5-R-1,3,4-oxadiazoles

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 (pK_BH ⁺ is −1.8 to −5.2). The values of pK_BH ⁺ 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.