The three space problem in topological groups

We study compact, countably compact, pseudocompact, and functionally bounded sets in extensions of topological groups. A property P is said to be a three space property if, for every topological group G and a closed invariant subgroup N of G, the fact that both groups N and G/N have P implies that G also has P. It is shown that if all compact (countably compact) subsets of the groups N and G/N are metrizable, then G has the same property. However, the result cannot be extended to pseudocompact subsets, a counterexample exists under p=c. Another example shows that extensions of groups do not preserve the classes of realcompact, Dieudonné complete and μ-spaces: one can find a pseudocompact, non-compact Abelian topological group G and an infinite, closed, realcompact subgroup N of G such that G/N is compact and all functionally bounded subsets of N are finite. Several examples given in the article destroy a number of tempting conjectures about extensions of topological groups.     

Bounded sets in topological groups and embeddings

We show that the existence of a non-metrizable compact subspace of a topological group G often implies that G contains an uncountable supersequence (a copy of the one-point compactification of an uncountable discrete space). The existence of uncountable supersequences in a topological group has a strong impact on bounded subsets of the group. For example, if a topological group G contains an uncountable supersequence and K is a closed bounded subset of G which does not contain uncountable supersequences, then any subset A of K is bounded in G?(K?A). We also show that every precompact Abelian topological group H can be embedded as a closed subgroup into a precompact Abelian topological group G such that H is bounded in G and all bounded subsets of the quotient group G/H are finite. This complements Ursul's result on closed embeddings of precompact groups to pseudocompact groups.     

On the effect of montmorillonite in the curing reaction of epoxy nanocomposites

The procedure for the fabrication of epoxy-based polymer layered silicate nanocomposites is important in respect of the nanostructure that is developed. To further our understanding of this, the influence of an organically modified clay (montmorillonite, MMT) on the curing kinetics of an epoxy resin has been studied by differential scanning calorimetry. Clay loadings of 10 and 20 mass% are used, and isothermal as well as dynamic cures have been investigated. For both cure schedules the effect of the MMT is to advance the reaction. Kinetic analysis yields values for the activation energy, but shows that the reaction cannot be described simply by the usual autocatalytic equation. The glass transition of the cured nanocomposites is lower than that for the cured neat resin, a result that is attributed to homopolymerisation taking place in addition to the epoxy–amine reaction.     

Multivariate resolution of NMR labile signals by means of hard- and soft-modelling methods

One of the difficulties frequently encountered when studying acid–base equilibria with NMR spectroscopy is the labile behaviour of the measured signal, which hinders the application of bilinear multivariate data analysis methods. In this work, a mathematical transformation is proposed for the conversion of NMR labile signals to inert signals, which make possible the application of multivariate data analysis methods, based on bilinear data models. The procedure has been applied to the analysis of NMR data corresponding to the acid–base equilibria of nucleotides dCMP and dGMP. Both hard-modelling (EQUISPEC) and soft-modelling (MCR-ALS) approaches have been applied for the analysis and resolution of transformed bilinear NMR data matrices.     

Syntheses and Structural Aspects of Cyclodextrin/Dialkylamine Inclusion Compounds

We report the syntheses and structural aspects of cyclodextrin host–guest inclusion compounds containing linear secondary alkylamines (dipropyl, dibutyl, dipentyl, dihexyl, and dioctyl) at 25 °C. Elemental analysis, ¹³C CP-MAS NMR spectroscopy, and powder X-ray diffraction analysis confirm the inclusion process. The basic host structure of the products is similar to that of typical cyclodextrin inclusion systems. ¹³C MAS NMR experiments show a different resonance pattern for the confined guest molecules with respect to the amine in the liquid phase. The presence of different resonance signals for the homologous carbon atoms of both dialkylamine branches is evidence for the non-symmetric location of the amine in the cyclodextrin channels.     

Preparation and Characterization of Compositions Based on PbO-MgO-Nb2O5 Using the Sol-Gel Method

Lead Magnesium Niobate, Pb(Mg_1/3Nb_2/3)O₃ (PMN), is an important relaxor ferroelectric material. A significant problem exists, however, in the preparation of this material: it is very difficult to prepare pure phase, without the presence of a pyrochlore impurity phase which degrades the dielectric properties. Depending on the processing conditions, the amount of pyrochlore phase varies.Considering the ternary diagram PbO-MgO-Nb₂O₅, different compositions have been prepared by a simple sol-gel method at room temperature using Pb(CH₃COO)₂, Mg(CH₃COO)₂, Nb(OC₂H₅)₅ as precursors. After the heat treatment, the samples obtained were analyzed by XRD and EPMA with the purpose of studying the compositions formed.From the analysis of these results, it seems to be that the appearance of pyrochlore can be related to the reactivity of the MgO and/or the presence of other phases of the binary system PbO-Nb₂O₅. An excess of Pb and Mg is necessary for compositions to be formed near the PMN. The control of the amount of these two elements is very important because an excess of MgO would lead to rich compositions in Mg as a secondary phase.     

Crystal structure oftrans-ethyl(1,5,6-trimethylbenzimidazole)-bis(dimethylglyoximato)cobalt(III). Relationships between structural and spectroscopic properties in compounds of the general formulae [Co(dmgH)2(R)(1,5,6-Me3Bzm)]

Summary The synthesis and x-ray crystal structure oftrans-[Co(dmgH)₂(Et)(1,5,6-Me₃Bzm)] where dmgH=dimethylglyoximate(–1), and 1,5,6-Me₃Bzm=1,5,6-trimethylbenzimidazole, is reported. The compound C₁₉H₂₆N₆O₄Co is monoclinic, space group P2₁/n;a=11.700(4);b=24.205(6);c=8.500(3) Å and =101.63(3)°. D(calcd) 1.299 g cm^–3; Z=4 and R=0.066 for 2359 independent reflections. Comparison of Co-N(axial ligand) bond lengths for compounds of general formulaetrans-[Co(dmgH)₂(R)(L)], with L=pyridine or 1,5,6-trimethylbenzimidazole and R=CH(CN)Cl, CH₂NO₂, Me, Et,i-Pr, cyclo-hexyl or adamantyl is made. The Co–N(1,5,6-Me₃Bzm) bond lengths of the trimethylbenzimidazole derivatives show a fairly linear relationship with the electronic parameter of the axial R group, derived from the¹³C-n.m.r. spectra of their pyridine analogues. The influence of steric effects on the properties of these Co^III compounds is discussed.