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.     

Hamiltonian Gromov-Witten invariants

In this paper we introduce invariants of semi-free Hamiltonian actions of S¹ on compact symplectic manifolds using the space of solutions to certain gauge theoretical equations. These equations generalise both the vortex equations and the holomorphicity equation used in Gromov-Witten theory. In the definition of the invariants we combine ideas coming from gauge theory and the ideas underlying the construction of Gromov-Witten invariants.     

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.     

Laser-induced charge transfer in the LiH3+ quasi-molecule

The laser-induced charge-transfer cross section for Li³⁺ + H collisions is calculated using the perturbation approach of Copelang and Tang, and is compared to the collision-induced cross section. The validity of perturbation theory and the use of simple criteria based on the Landau-Zener formula to extend the usefulness of the theory are examined.     

Synthesis and properties of perchlorobi-9-fluorenylidene,An exceptionally twisted ethylene

The synthesis and properties of perchlorobi-9-fluorenylidene, a highly twisted ethylene, are reported. It is a diamagnetic chlorocarbon.     

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.     

New synthetic routes to cationic rhenium tricarbonyl bipyridine complexes with labile ligands

Triflate abstraction from the complex [Re(OTf)(CO)(3)(bipy)] (1) using the salt NaBAr'(4) (Ar' = 3,5-bis(trifluoromethyl)phenyl) in dichloromethane solution in the presence of L = PPh(3), NCMe, NCPh, imines, ketones, Et(2)O, THF, MeOH, and MeI affords cationic complexes [Re(L)(CO)(3)(bipy)](+) as their BAr'(4)(-) salts. The new complexes have been characterized spectroscopically and, for [Re(eta(1)-O=C(Me)R)(CO)(3)(bipy)]BAr'(4) (R = CH(3), 6a; R = Ph, 6b), and [Re(THF)(CO)(3)(bipy)]BAr'(4) (9), also by single-crystal X-ray diffraction. Compared with conventional methodologies, the route reported here allows the coordination of a broader range of weakly coordinating ligands and requires considerably milder conditions. On the other hand, the reactions of lithium acetylides with [Re(THF)(CO)(3)(bipy)]BAr'(4) (9) can be used for the high-yield syntheses of rhenium alkynyls [Re(Ctbd1;CR)(CO)(3)(bipy)] (R = Ph, 12; R = SiMe(3), 13). Complex 9 was found to catalyze the aziridination of benzylideneaniline with ethyl diazoacetate.