K-theory for the leaf space of foliations by Reeb components

The K-theory of the C¹-algebra $\text{C}{}^1\text{(V, F)}$ associated to C^∞-foliations (V, F) of a manifold V in the simplest non-trivial case, i.e., dim V = 2, is studied. Since the case of the Kronecker foliation was settled by Pimsner and Voiculescu (J. Operator Theory4 (1980), 93–118), the remaining problem deals with foliations by Reeb components. The K-theory of $\text{C}{}^1\text{(V, F)}$ for the Reeb foliation of S³ is also computed. In these cases the C¹-algebra $\text{C}{}^1\text{(V, F)}$ is obtained from simpler C¹-algebras by means of pullback diagrams and short exact sequences. The K-groups $\text{K}{}_1\text{(C}{}^1\text{(V, F))}$ are computed using the associated Mayer-Vietoris and six-term exact sequences. The results characterize the C¹-algebra of the Reeb foliation of $\text{T}$² uniquely as an extension of C(S¹) by C(S¹). For the foliations of $\text{T}$² it is found that the K-groups count the number of Reeb components separated by stable compact leaves. A C^∞-foliation of $\text{T}$² such that K₁(C¹($\text{T}$², F)) has infinite rank is also constructed. Finally it is proved, by explicit calculation using (M. Penington, “K-Theory and C¹-Algebras of Lie Groups and Foliations,” D. Phil. thesis, Oxford, 1983), that the natural map $\text{μ: K}{}_1\text{,}{}_{\mathrm{\tau }}\text{(BG) → K}{}_1\text{(C}{}^1\text{(V, F))}$ is an isomorphism for foliations by Reeb components of $\text{T}$² and S³. In particular this proves the Baum-Connes conjecture (P. Baum and A. Connes, Geometric K-theory for Lie groups, preprint, 1982; A. Connes, Proc. Symp. Pure Math.38 (1982), 521–628) when V = $\text{T}$².     

Lewis acid catalyzed addition of 2,2,2-trifluorodiazoethane to unactivated aldehydes

Condensations of 2,2,2-trifluorodiazoethane with pentanal, cyclohexancarboxaldehyde and benzaldehyde have been performed in presence of antimony pentachloride or boron trifiuoride. These reactions lead mainly to homologated aldehydes or ketones α substituted by a trifluoromethyl group.     

Synthesis and chemical transformations of perfluoroalkylimidoyl iodides

The addition of perfluoroalkyliodes CF₃(CF₂)_nl (n= 3, 5, 7) to isocyanides 2 produces perfluoroalkylimidoyl iodides 3 under thermal conditions when the isocyanide nitrogen substituent is n-butyl or cyclohexyl, but fails when it is t-butyl or 2,6-dimethylphenyl. The same reaction can be induced at room temperature by the addition of decimolar quantity of copper powder. This type of metal-catalyzed condensation is general for all perfluoroalkyliodides and isocyanides studied. The perfluoroalkylimidoyl-iodides 3 have been transformed into a variety of perfluorocarboxylic acid derivatives (amides, amidines. imidates, imidoylfluorides) and perfluoroalkylamines.     

Condensation du complexe hexafluoroacetone - fluorure de potassium sur les cetones alpha - halogenees

During its condensation with α-halo ketones, the hexafluoro- acetone-potassium fluoride complex behaves as a weak nucleophile and a strong base. Nucleophilic substitution produces α-perfluoroalkoxy ketones. Abstraction of a proton α to the carbonyl function leads to the formation of ether-ketones substituted by the group C(CF₃)₂. In some cases, hydrogen halide elimination can occur.     

Solid-state binding of dimethyl sulphoxide involving carboxylic host molecules. X-ray crystal structures of four inclusion species

The crystal structures of four dimethyl sulphoxide (DMSO) inclusion compounds with different carboxylic acid hosts,1–4, have been studied by single crystal X-ray analysis. Crystals of thetrans-9,10-dihydro-9,10-ethanoanthracene-11,12-dicarboxylic acid inclusion compound (1a), [1 · DMSO (1: 1)] show monoclinic (P2₁/n) symmetry with the unit cell dimensionsa = 11.522(4),b = 18.658(2),c = 8.709(1) Å and = 98.92(2)°. The clathrate of the 9,10-dihydro-9,10-ethanoanthracene-11,12-dicarboxylic acid (2a), [2 · DMSO (1: 2)] is triclinic (P) with the cell dimensionsa = 15.043(7),b =9.657(4),c = 8.118(7) Å, = 101.81(5), = 96.05(4) and = 100.04(4)°. Triclinic (P) symmetry is shown also by the inclusion compound of 9,10-dihydro-9,10-ethanoanthracene-11-monocarboxylic acid (3a) [3 · DMSO (1:1)] with the cell dimensionsa=6.3132(1),b=7.9846(2),c=17.5314(4) Å, = 96.46(2), = 87.08(2) and = 106.02(2)°. The 9,9-bianthryl-2-monocarboxylic acid clathrate (4a) [4 · DMSO (1:1)] is monoclinic (P2₁/n) and the cell dimensions area = 19.625(18),b = 8.817(1),c = 14.076(8) Å and = 97.92(6)°. In all these structures, the hosts show the same basic recognition pattern for the DMSO guest, involving a strong O-H ... O bond from the COON to the S=O group, and a possible C-H ... O type interaction between the carbonyl O atom of the host and a CH₃ group of the guest. The crystals consist of discrete host-guest aggregates which are mainly held together by weak intermolecular interactions of the Van der Waals' type. The stoichiometries of the aggregates are, however, different.     

New gem-dicyanocyclobutane-containing hydroxyesters

Six new gem-dicyanocyclobutanes containing carbomethoxy and hydroxyl/acetoxy functions were synthesized by cycloaddition of the appropriate vinyl ethers or alkoxystyrenes to methyl β,β-dicyanoacrylate. They proved to be too thermally labile to allow polycondensation to potentially piezoelectric linear polyesters.     

Cu K-edge EXAFS characterisation of copper(I) arenethiolate complexes in both the solid and liquid state: detection of Cu-Cu coordination

Herein we describe a structural characterisation with EXAFS of copper(I) arenethiolate complexes in both the solid and liquid state. Previously noted difficulties in the detection of the Cu-Cu interaction have been attributed to anti-phase behaviour of different Cu-Cu neighbour contributions. A data analysis procedure solely based on EXAFS parameters is presented which resolves these problems. A careful analysis of the individual coordination shells and the use of different k-weightings during the data analysis are shown to be an absolute necessity to obtain reliable results. During R-space fitting, the difference file technique is used to separate, examine and compare the individual contributions. Using this technique their statistical significance and correctness can be determined. Anti-phase behaviour can be detected and accounted for in this way. An additional mixed organocopper aggregate [Cu4(SAr)2(Mes)2] with different Cu sites is analysed, which proves the value of the analysis procedure described above. Moreover, this newly developed EXAFS data analysis procedure is applicable to any other EXAFS spectrum obtained. The structural analysis of these organocopper complexes with EXAFS provides information about their actual structure and dynamic behaviour in solution. The technique can now be used to obtain insights into the reactivity of these complexes and the way in which they form catalytic reaction intermediates.     

Pervaporative transport modelling in a ternary system: ethyltertiarybutylether/ethanol/polyurethaneimide

The study deals with the analysis of diffusion and mass transfer modelling during pervaporation in a true ternary system involving a polar liquid mixture (ETBE/EtOH) and a polar block copolymer (polyurethaneimide or PUI). A survey of methods of pervaporative transfer modelling in ternary systems is first developed. From differential permeation experiments carried out with both pure liquids, it appears that both permeants obey a Fickian law. Moreover, the diffusional behaviour is consistent with Long's model, which has thus been assumed for the related ternary system. An extension of the Brun's model is then derived, which takes into account the diffusion coupling as well the significant deviation from sorption ideality. From a practical point of view, the calculated values of fluxes show generally good agreement with the experimental results, although a small deviation occurs for mixtures of low ethanol content. Diffusion coefficients of both pure solvents corresponding to transient or steady state are compared. A very good agreement is found for the aprotic permeant (ETBE). whereas the diffusion coefficient of ethanol in transient state is only the quarter of the value corresponding to steady state. The results are discussed in comparison with related investigations in the literature, involving specific liquid-polymer interactions.     

A study of method robustness for arsenic speciation in drinking water samples by anion exchange HPLC-ICP-MS

Regulating arsenic species in drinking waters is a reasonable objective, since the various species have different toxicological impacts. However, developing robust and sensitive speciation methods is mandatory prior to any such regulations. Numerous arsenic speciation publications exist, but the question of robustness or ruggedness for a regulatory method has not been fully explored. The present work illustrates the use of anion exchange chromatography coupled to ICP-MS with a commercially available "speciation kit" option. The mobile phase containing 2 mM NaH(2)PO(4) and 0.2 mM EDTA at pH 6 allowed adequate separation of four As species (As(III), As(V), MMAA, DMAA) in less than 10 min. The analytical performance characteristics studied, including method detection limits (lower than 100 ng L(-1) for all the species evaluated), proved the suitability of the method to fulfill the current regulation. Other parameters evaluated such as laboratory fortified blanks, spiked recoveries, and reproducibility over a certain period of time produced adequate results. The samples analyzed were taken from water utilities in different areas of the United States and were provided by the U.S. EPA. The data suggests the speciation setup performs to U.S. EPA specifications but sample treatment and chemistry are also important factors for achieving good recoveries for samples spiked with As(III) as arsenite and As(V) as arsenate.     

Electrochemical behavior of ellipticine derivatives: Part III. Reduction of 2-methyl-ellipticinium cations and their conjugated bases

In neutral DMF, ellipticinium cations 9 R—E⁺H—2 CH₃ undergo a reversible 1 e addition (standard potential ca. ?1.35 V) to yield a neutral radical which rapidly dimerizes (dimerization rate constant ca. 10⁷ mol^?1 1 s^?1). In basic DMF or in the presence of superoxide anion, the corresponding conjugated bases undergo a reversible 1 e addition accompanied by a fast and reversible proton addition (standard potential at pH_DMF 0 ca. ?0.52 V) to yield the same neutral radical. R being H, OCH₃ or OH, there is no effect of the substituent at the C-9 position on the electrochemical process.