Gray code for derangements

We give a Gray code and constant average time generating algorithm for derangements, i.e., permutations with no fixed points. In our Gray code, each derangement is transformed into its successor either via one or two transpositions or a rotation of three elements. We generalize these results to permutations with number of fixed points bounded between two constants.     

On the construction of 2-substituted 1,4-diacetoxybutadiene moiety: application to the synthesis of (±)-caulerpenyne

The synthesis of 2-substituted 1,4-diacetoxybutadiene derivatives with a partial control of stereochemistry is described from two potentially precursor enals by a judicious choice of experimental conditions (Ac₂O/DMAP in Et₃N). These conditions have been successfully applied in the first total synthesis of caulerpenyne.     

UV curing of a novel resin derived from poly(ethylene terephthalate)

The synthesis and characterization of photopolymerizable unsaturated polyester resins based on PET waste are described. The resins came from a depolymerization process based on the glycolysis of PET by diethylene glycol (DEG). Different molecular weights of glycolysates were synthesized. Then, the latter was functionalized by a methyl hemiester of maleic acid to obtain unsatured α,ω‐bismaleate PET oligomers. In the presence of an electron donor monomer, such as triethylene glycol divinyl ether, these electron acceptor oligomers were copolymerized by way of charge‐transfer complexes under UV irradiation. The reaction was monitored in situ by real‐time IR spectroscopy to study the kinetics of photopolymerization. This one was studied in relation with the physical and chemical characteristics of oligoesters and the composition of mixtures containing divinyl ethers. © 2007 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 45: 1324–1335, 2007     

Une nouvelle définition de l'entropie dynamique des systèmes non commutatifs

An alternative definition of entropy for non-commutative systems, equivalent to the one by A. Connes, H. Narnhofer, and W. Thirring, is given. It is based on the concepts of conditional entropy, and stationary couplings with classical systems. It allows to prove that any quantum dynamical system with singular spectrum has zero entropy.     

Stochastic Arithmetic: s-spaces and Some Applications

It has been recently shown that computation with stochastic numbers as regard to addition and multiplication by scalars can be reduced to computation in familiar vector spaces. In this work we show how this can be used for the algebraic solution of linear systems of equations with stochastic right-hand sides. On several examples we compare the algebraic solution with the simulated solution using the CADNA package.     

New access to H-phosphonates via metal-catalyzed phosphorus-oxygen bond formation

A novel approach to H-phosphonates from hypophosphorous acid using a transfer hydrogenation process was developed. This method is atom-economical, environmentally friendly, catalytic, and efficient, leading easily to H-phosphonate monoesters or ammonium salt in moderate to good yields.     

Studies in mass spectrometry. IV—Fragmentation of aryltriflates. Substituent effects on [ArO]+ ion abundances: Looking for a best suited electron energy in the steady state approach. Experimental evidence for the ‘through bond’ stabilization of aryl cations by meta electron donor Substituents

The fragmentation patterns of 24 substituted phenyltrifluoromethanesulfonates has been determined by exact mass and metastable transition measurements. The influence of the ring substituent(s) on the abundance of the [ArO]+ ions has been investigated at low energies and a new standard parameter for plotting against Hammett's ó constants is proposed. The direct loss of CF₃SO₃ from the molecular ion of 3,5-(diisopropyl)-phenyl-, 3,5-(dicyclopropyl)phenyl- and 3,5-di(α-methylcyclopropyl)-phenyl-methanesulfonate, and further observations on the fragmentation processes of these compounds are consistent with M.O. calculations on the ‘through bond’ stabilization of the [Ar]+ σ state by meta electron donor substituents.     

Two-photon absorption in quadrupolar pi-conjugated molecules: influence of the nature of the conjugated bridge and the donor-acceptor separation

Quadrupolar-type substitution of pi-conjugated chromophores with donor and acceptor groups has been shown to increase their two-photon absorption (TPA) response by up to two orders of magnitude. Here, we apply highly correlated quantum-chemical calculations to evaluate the impact of the nature of conjugated bridge and the charge-transfer distance on that enhancement. We compare chromophores with phenylenevinylene-, thienylenevinylene-, polyene-, and indenofluorene-type backbones substituted by dimethylamino and cyano groups. In all compounds, we find a strongly TPA-active A(g) state (either 2A(g) or 3A(g)) in the low-energy region, as well as a higher lying TPA-active state (mA(g)) at close to twice the energy of the lowest lying one-photon allowed state; the smaller energy detuning in the mA(g) states results in very large TPA cross sections delta. We also investigate the influence of the degree of ground-state polarization on TPA. Independent of the nature of the backbone and the donor-acceptor separation, delta displays the same qualitative evolution with a maximum before the cyanine-like limit; the highest TPA cross sections are calculated for distirylbenzene- and polyene-based systems.     

Origin of high second- and third-order nonlinear optical response in ammonio/borato diphenylpolyene zwitterions: the remarkable role of polarized aromatic groups

We present a quantum-chemical analysis of the molecular structure and second- and third-order polarizabilities in a series of promising nonlinear optical (NLO) chromophores, the zwitterionic ammonio/borato diphenylpolyenes, R3N+Ph(C=C)nPhB-R3, whose synthesis has been reported recently. The molecular geometries are obtained via MP2/6-31G optimization, while the NLO properties are calculated with the INDO Hamiltonian using the sum-over-states and finite-field real-space methods. The real-space approach allows the direct evaluation of the NLO-active segments of the molecules, while the sum-over-states results illustrate the virtual excitations and charge-transfer pathways that are essential in the NLO response. Both methods highlight the remarkable and unexpected result that it is the strongly polarized phenylene groups that play the key role in generating a high NLO response.     

Photooxidation of ABS of long-wavelengths

The evolution of the photochemical degradation of ABS has been studied in conditions of long wavelength irradiation (λ's> 300 nm). The main photoproducts involved in the oxidative evolution have been identified by using FTIR spectroscopy and chemical titrations. A particular attention has been devoted to α–β unsaturated ketones that appear as secondary photoproducts. Those ketones present a low photochemical stability when exposed in the range 300–400 nm. Conditions for their formation have been experimentally studied. Formation of oxidation photoproducts has been also studied at the macroscopic level and it has been shown that their repartition in the polymer is heterogeneous. The origins of the heterogenities have been studied.