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.     

Representation of Cubic Lattices by Symmetric Implication Algebras

In this paper a cubic lattice L(S) is endowed with a symmetric implication structure and it is proved that L(S) \ {0} is a power of the three-element simple symmetric implication algebra. The Metropolis–Rota’s symmetries are obtained as partial terms in the language of symmetric implication algebras.     

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.     

The effect of microwave annealing on the electrical characteristics of lanthanum doped bismuth titanate films obtained by the polymeric precursor method

Lanthanum doped bismuth titanate thin films (Bi_3.25La_0.75Ti₃O₁₂ - BLT) were produced by the polymeric precursor method and crystallized in a domestic microwave oven and in conventional furnace. Using platinum coated silicon substrates configuration, ferroelectric properties of the films were determined with remanent polarization P_r and a coercive field E_c of 3.9 μC/cm² and 70 kV/cm for the film annealed in the microwave oven and 20 μC/cm² and 52 kV/cm for the film annealed in conventional furnace, respectively. The films annealed in conventional furnace exhibited excellent retention-free characteristics at low infant periods indicating that BLT thin films can be a promise material for use in non-volatile memories. On the other hand, the pinning of domains wall causes a strong decay at low infant periods for the films annealed in the microwave furnace which makes undesireable the application for future FeRAMS memories.     

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.     

Structural Analysis of Ti And Pb Citrate Using NMR and FT-Raman Signals and Quantum Mechanics Simulations

Titanium citrate and lead and titanium citrate were prepared by polymeric precursor method in aqueous solution. This citrate was analyzed by ¹H, ¹³C NMR and gHMBC–NMR (Hetero-nuclear multiple-bond correlation) to investigate the formation of the citrate complexs and influence of the Pb²⁺ ion in this complex. These complexs were characterized by interaction between Ti⁴⁺ ion and citric acid carboxyls. Quantum mechanic simulations in level ab initio were used to study the electronic structure and natural charges (NBO) to both the complexs. Such techniques indicated the formation of an octahedral complex with an arrangement similar to Ti atom in the crystalline structure of the PbTiO₃. A study using the technique FT-Raman made possible the confirmation of the interaction among the Ti⁴⁺ and Pb²⁺ ions with the citric acid carboxyls.     

Pseudorotational analysis of 4-thiohexofuranose derivatives from H-H coupling constants

On the basis of Altona's empirical generalization of the Karplus equation, an expression of ³J_H,H as function of pseudorotation parameters for five-membered rings, was deduced. The resulting equation was parametrized by means of molecular mechanics calculations for tetrahydrofuran and tetrahydrothiophene. Estimation of ³J_H,H for the full pseudorotational itinerary was made. From the best fit between calculated and measured ³J_H,H values the preferred conformation of those rings may be established. The procedure was applied for the conformational analysis of 4-thiohexofuranose derivatives, having and β, -galacto and D- manno, and - -talo configurations.     

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.