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.     

The O(N) vector model in the large-N limit revisited: multicritical points and double scaling limit

The multicritical points of the O(N)-invariant N vector model in the large-N limit are re-examined. Of particular interest are the subtleties involved in the stability of the phase structure at critical dimensions. In the limit N → ∞ while the coupling g → g_c in a correlated manner (the double scaling limit) a massless bound state O(N) singlet is formed and powers of 1/N are compensated by IR singularities. The persistence of the N → ∞ results beyond the leading order is then studied with particular interest in the possible existence of a phase with propagating small mass vector fields and a massless singlet bound state. We point out that under certain conditions the double scaled theory of the singlet field is non-interacting in critical dimensions.     

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.

     

Shape-tunable polymer nodules grown from liposomes via ring-opening metathesis polymerization

A new inisurf (acting as surfactant and initiator) molecule for ring-opening metathesis polymerization (ROMP) was synthesized and used in aqueous solution in order to control the size and shape of polymer nodules grown from liposomes. Nodules were observed to grow in size with conversion of monomer, and depending on the monomer used, they adopted either a spherical or comet-like shape. Here, we investigate polymer production from a liposome surface. We use a hydrophobic derivative of the Grubbs catalyst positioned at the liposome surface to allow for ROMP of monomers dissolved in the aqueous outer phase. We obtain nodules of polymer that can grow up to tens of micrometers, unveiling new efficient possibilities of polymerization from a membrane in an aqueous solution.     

Development of a tandem cyclization mediated by samarium(II) iodide: sequential intramolecular conjugate addition/nucleophilic acyl substitution

The development of a one-pot tandem intramolecular conjugate addition/nucleophilic acyl substitution using samarium(II) iodide is reported. The reaction relies on the reagent’s unique ability to mediate both radical and anionic pathways, which are likely integral to the mechanism of this transformation. The tricyclic hemiacetal product was formed in good yield, with excellent diastereoselectivity, and its structure was verified by X-ray crystallographic analysis.     

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.