k-spaces and Borel filters on the set of integers

We say that a countable, Hausdorff, topological space with one and only one accumulation point is a point-space. For such a space, we give several properties which are equivalent to the property of being a k-space. We study some free filters on the set of integers and we determine if the associated point-spaces are k-spaces or not. We show that the filters of Lutzer-van Mill-Pol are k-filters. We deduce that, for each countable ordinal , there exists a free filter of true additive class (Baire's classification) and a free filter of true multiplicative class for which the associated point-spaces are k-spaces but not , the existence being true in the additive case for . In particular, we answer negatively a question raised in J. Calbrix, C. R. Acad. Sci. Paris 305 (1987), 109--111.

     

Some geometric aspects of the calculus of fractions

We give necessary and sufficient conditions on class S of maps of a category C so that a good calculus of fractions is possible in C[S ^-1], and a geometric characterization of the communitative diagrams in the category of fractions. These conditions are also described simply in terms of Grothendiek topologies.We characterize the categories which arise in this manner by the fact that the functor C C[S ^-1] is uniformly flat and give some applications of this result.     

The Boolean Prime Ideal Theorem Plus Countable Choice Do Not Imply Dependent Choice

Two Fraenkel-Mostowski models are constructed in which the Boolean Prime Ideal Theorem is true. In both models, AC for countable sets is true, but AC for sets of cardinality 2 and the 2m = m principle are both false. The Principle of Dependent Choices is true in the first model, but false in the second. Mathematics Subject Classification: 03E25, 03E35, 04A25.     

Cocycle d'Euler etK2

In this paper we construct a canonical 2-cocycle on the groupP SL(2,k) with values in the Witt groupW(k) of the fieldk. This allows us to produce anatural homomorphism :H ₂(SL(2,k); Z)I ²(k), whereI ²(k) is the square of the fundamental ideal. We prove that this homomorphism is in fact a lift of Milnor's symbol.

     

Analysis of chlorinated, sulfochlorinated and sulfonamide derivatives of n-tetradecane by gas chromatography/mass spectrometry

The photosulfochlorination of n-tetradecane by sulfuryl chloride leads to a reaction mixture containing unreacted n-tetradecane, chloro n-tetradecanes and n-tetradecanesulfonyl chlorides. Direct and simultaneous GC analysis of the mixture of the sulfochlorinated and chlorinated isomers is followed by mass spectrometry identification of all the components either by electron impact (EI-MS) and by negative and positive chemical ionisation (NCI-MS and PCI-MS). With the goal of performing an accurate quantitative GC analysis, and as n-tetradecanesulfonyl chlorides prone to degrade partially into the corresponding chlorides, the former are converted to N,N-diethylsufonamides, more stable thermally, and then analysed by GC/EI-MS and GC/PCI-MS. The chloro n-tetradecanes, sulfonylchlorides and sulfonamides spectra present strong similarities. However, some differences between terminal and internal isomers are noticed and the peculiar behaviour of sulfonamides is emphasized.     

Chemo- and regioselective synthesis of 2-alkylidenetetrahydrofurans bearing a chiral sulfur atom by domino reactions of sulfoximines

The addition of the dianion of Johnson’s sulfoximine to α,ω-halogenoesters evolves by an intramolecular heterocyclization to provide a direct access to 2-alkylidenetetrahydrofurans bearing a chiral sulfur atom via domino addition-elimination/S_N reactions.     

A simplified method for molecular correlation energy calculations by separation into internal and non-internal parts. Application to multiconfigurational zeroth-order wavefunctions

A simplified method of determining the molecular correlation energy by two separate calculations, one for the internal and one for the non-internal correlation energies, is extended to multiconfigurational zeroth-order wavefunctions. This extension offers the possibility of deriving correlated potential energy curves or surfaces for processes involving configurational changes. The internal correlation energy is shown to be correctly determined by an MC/CI procedure combining the use of minimal and extended basis sets. An original semi-empirical “atoms-in-molecules” method based on the L.C.A.O. expansion of the molecular wavefunction is proposed for the non-internal correlation energy calculations. This method is shown to be able to overcome some of the shortcomings of a previous populations analysis approach. Test calculations concern potential curve parameters (D _e ,T _e ,R _e ,W _e ) of the ground and some excited states of the NH, C₂, HCN and CN molecules. The results are found to be in good agreement with corresponding experimental and large CI results. Aspirant du Fonds National Belge de la Recherche Scientifique Boursier I.R.S.I.A.     

Design and synthesis of push-pull chromophores for second-order nonlinear optics derived from rigidified thiophene-based pi-conjugating spacers.

Two series of push-pull chromophores built around thiophene-based pi-conjugating spacers rigidified either by covalent bonds or by noncovalent intramolecular interactions have been synthesized and characterized by UV-vis spectroscopy, electric field induced second harmonic generation (EFISH) and differential scanning calorimetry. Comparison of the linear and second-order nonlinear optical properties of chromophores based on a covalently bridged dithienylethylene (DTE) spacer with those of their analogues based on open chain DTE shows that the rigidification of the spacer produces a considerable bathochromic shift of the absorption maximum together with a dramatic enhancement of the molecular quadratic hyperpolarizability (mu beta) which reaches values among the highest reported so far. A second series of NLO-phores has been derived from a 2,2'-bi(3,4-ethylenedioxythiophene) (BEDOT) pi-conjugating spacer. As indicated by X-ray and UV-vis data, rigidification of the spacer originates in that case, from noncovalent intramolecular interactions between sulfur and oxygen atoms. Again, comparison with the parent compounds based on an unsubstituted bithiophene spacer reveals a marked red shift of the absorption maximum and a large enhancement of mu beta. In an attempt to distinguish the contribution of the electronic and geometrical effects of the ethylenedioxy group, a third series of NLO-phores based on 3,4-ethylenedioxythiophene (EDOT) and 3,4-dihexyloxythiophene spacers has been synthesized. Comparison with compounds based on unsubstituted thiophene shows that, despite a red shift of lambda(max), introduction of alkoxy groups leads to a decrease of mu beta. Theoretical calculations indicate that this effect results from a decrease of the dipole moment (mu) caused by the auxiliary electron-donor alkoxy groups on the thiophene ring. In contrast, replacement of BT by BEDOT produces an increase of mu, which associated with the noncovalent rigidification of the BT system accounts for the observed enhancement of mu beta.     

Very general formation of tetrahydropterin cation radicals during reaction of iron porphyrins with tetrahydropterins: model for the corresponding NO-synthase reaction

Electron transfer from tetrahydropterins to iron porphyrins, with formation of intermediate tetrahydropterin cation radicals, is a very general reaction that was shown to occur not only with tetrahydrobiopterin, as originally found in NO-synthases, but also with another important biological cofactor, tetrahydrofolate, and various iron porphyrins, either in their ferric state, or in the Fe(II)O(2) state, as in the first model of the corresponding NO-synthase reaction described in this paper.     

Supercapacitive admittance tomoscopy

A sensor for measuring adsorption on a substrate has been designed including a contactless detection scheme, called supercapacitive admittance tomoscopy (SCAT). The sensor comprises a thin dielectric layer with two parallel band electrodes on the one side and a chemically modified surface on the other onto which the adsorption of molecules occurs. Upon application of a high frequency ac voltage between the two electrodes, a capacitive coupling is established across the dielectric layer, and the admittance measured depends on the surface state of the chemically modified interface. On the basis of this principle, a flow sensor has been developed to measure sensorgrams to follow the dynamics of the adsorption and has been tested for the adsorption of IgG on the modified surface.