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.     

Equivalence of u–p and ζ–ψ formulations of the time-dependent Navier–Stokes equations

This paper deals with the non-stationary incompressible Navier--Stokes equations for two-dimensional flows expressed in terms of the velocity and pressure and of the vorticity and streamfunction. The equivalence of the two formulations is demonstrated, both formally and rigorously, by virtue of a condition of compatibility between the boundary and initial values of the normal component of velocity. This condition is shown to be the only compatibility condition necessary to allow for solutions of a minimal regularity, namely H¹ for the velocity, as in most current numerical schemes relying on spatial discretizations of local type.     

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.     

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.     

A systematic formula for the asymptotic expansion of singular integrals

Asymptotic theories like the lifting-line, the slender body or the slender ship lead to lineintegrals with singular kernels. Sometimes these integrals are improper, that is to say that they are defined only by their Finite Part. To find asymptotic expansions of these integrals, the Matched Asymptotic Expansion Method is widely used along with other more specific methods depending on the kernel type. The first method is laborious and not systematic, and the other methods are sometimes too much specific to treat general cases. Moreover, all of them are not well adapted to deal with Finite Part integrals.Here, a new method is proposed to avoid the previous difficulties. This method is systematic for homogeneous kernels and gives approximations up to any order, as long as the derivative of the weight function exists at this given order. Moreover the occurrence of logarithmic terms in the expansion is explained and easily predictable. An elliptic integral and the classical lifting-line theory are treated to illustrate the ease of this method.

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Résumé Les théories asymptotiques telles que la ligne portante, le corps élancé ou le navire de grand allongement conduisent à des intégrales curvilignes à noyaux singuliers. Parfois, ces intégrales sont impropres c'est à dire qu'elles sont définies en Parties Finies. Différentes méthodes ont été mises au point pour trouver les développements asymptotiques de ces intégrales. Généralement elles dépendent fortement de la nature du noyau, et c'est finalement la méthode des développements raccordés qui est utilisées quand le noyau est trop compliqué. Cependant, cette méthode est laborieuse et comme les précèdentes non adaptée aux intégrales défines par leur Partie Finie.Une nouvelle méthode est proposée pour surmonter ces difficultés. Cette méthode est systématique pour les noyaux homogènes et donne les approximations à tout ordre pourvu que les dérivées de la fonction poids existent jusqu'à cet ordre. De plus la présence de termes logarithmiques dans le développement est expliquée et aisément prédictible.Une intégrale elliptique, ainsi que la fameuse théorie de la ligne portante sont traités pour illustrer les possibilités de la méthode.

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Nomenclature D domain of integration - f(x) weight function - FP Finite Part - h(x) weight function - I ,I _o bounded intervals - j, J integers - K(x, ) singular kernel - L, L integers - M integer defining the approximation order - P _k (x) Legendre polynomial - R set of real numbers - R(ß) equals 1 if is an integer and 0 if not - R _{f, J} ,R _{K, L} remainders of Taylor developments - S () equals either 1 or the sign function:sgn() - t, u, v, x variable of integration - , real numbers - homogeneity order of the kernel - F () Euler's integral (gamma function) - small parameter - [.] integer part of     

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.     

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.     

Photosensitization of DNA damage by a new cationic pyropheophorbide derivative: sequence-specific formation of a frank scission

Pyropheophorbides are red-absorbing porphyrin-like photosensitizers that may interact with DNA either by intercalation or by external binding with self-stacking according to the value of the nucleotide to chromophore molar ratio (N/C). This article reports on the nature and sequence selectivity of the DNA damage photoinduced by a water-soluble chlorhydrate of aminopyropheophorbide. First, this pyropheophorbide is shown to induce on irradiation the cleavage of phiX174 DNA by both Type-I and -II mechanisms, suggested by scavengers and D2O effects. These conclusions are then improved by sequencing experiments performed on a 20-mer oligodeoxynucleotide (ODN) irradiated at wavelengths >345 nm in the presence of the dye, N/C varying from 2.5 to 0.5. Oxidation of all guanine residues to the same extent is observed after piperidine treatment on both single- and double-stranded ODN. Moreover, unexpectedly, a remarkable sequence-selective cleavage occurring at a 5'-CG-3' site is detected before alkali treatment. This frank break is clearly predominant for a low nucleotide to chromophore molar ratio, corresponding to a self-stacking of the dye along the DNA helix. The electrophoretic properties of the band suggest that this lesion results from a sugar oxidation, which leads via a base release to a ribonolactone residue. The proposal is supported by high-performance liquid chromatography-matrix-assisted laser desorption-ionization mass spectrometry experiments that also reveal other sequence-selective frank scissions of lower intensity at 5'-GC-3' or other 5'-CG-3' sites. This sequence selectivity is discussed with regard to the binding selectivity of cationic porphyrins.     

Self-Assembly of Gold Nanoclusters on Molecularly Modified GaAs

The elaboration of closed-packed monolayers of Au₅₅(PPh₃)₁₂Cl₆ clusters on oxidized and non-oxidized GaAs surfaces is reported. The first part of this work describes the use of silanethiol modified GaAs oxide surfaces to trap 18 nm gold colloids and Au₅₅(PPh₃)₁₂Cl₆ clusters. The surfaces characterized by AFM measurements present high-quality coverage on a quite long range for both metallic species. The second part is devoted to the elaboration of Au₅₅(PPh₃)₁₂Cl₆ cluster monolayers on non-oxidized p-type GaAs substrates, functionalized with dithiol molecules. AFM measurements demonstrate the presence of closed-packed two-dimensional arrangements of Au₅₅ clusters.     

Influence of steric symmetry and electronic dissymmetry on the enantioselectivity in palladium-catalyzed allylic substitutions

Chiral P,N-ligands with pseudo-C2 and pseudo-Cs symmetry based on chiral pyrrolidine and phospholane rings or on dinaphthatodihydroazepino and dinaphthatodihydrophosphepino moieties were prepared and assessed in the palladium-catalyzed allylic substitutions of allylic acetates. Higher selectivity was achieved with pseudo-C2-symmetric ligands based on the binaphthyl skeleton than with the analogous C2-symmetric P,P- and N,N-analogues. Pseudo-C2-type ligands had properties superior to those of pseudo-meso-type ligands when 1,3-diphenyl-2-propenyl acetate was used as a substrate, whereas the reverse situation was found for 3-cyclohexenyl acetate. Chirally flexible ligands, prepared by substitution of one of the rigid binaphthyl skeletons for a flexible biphenyl system, were found to induce chirality to the same extent as a 1:1 mixture of the rigid ligands.