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.     

Hydroxylation-induced modifications of the Al2O3/NiAl(0 0 1) surface at low water vapour pressure

STM, STS, LEED and XPS data for crystalline θ-Al₂O₃ and non-crystalline Al₂O₃ ultra-thin films grown on NiAl(0 0 1) at 1025 K and exposed to water vapour at low pressure (1 × 10⁻⁷-1 × 10⁻⁵ mbar) and room temperature are reported. Water dissociation is observed at low pressure. This reactivity is assigned to the presence of a high density of coordinatively unsaturated cationic sites at the surface of the oxide film. The hydroxyl/hydroxide groups cannot be directly identify by their XPS binding energy, which is interpreted as resulting from the high BE positions of the oxide anions (O_1s signal at 532.5-532.8 eV). However the XPS intensities give evidence of an uptake of oxygen accompanied by an increase of the surface coverage by Al³⁺ cations, and a decrease of the concentration in metallic Al at the alloy interface. A value of ∼2 for the oxygen to aluminium ions surface concentration ratio indicates the formation of an oxy-hydroxide (AlO_xOH_y with x + y ∼ 2) hydroxylation product. STM and LEED show the amorphisation and roughening of the oxide film. At P(H₂O) = 1 × 10⁻⁷ mbar, only the surface of the oxide film is modified, with formation of nodules of ∼2 nm lateral size covering homogeneously the surface. STS shows that essentially the valence band is modified with an increase of the density of states at the band edge. With increasing pressure, hydroxylation is amplified, leading to an increased coverage of the alloy by oxy-hydroxide products and to the formation of larger nodules (∼7 nm) of amorphous oxy-hydroxide. Roughening and loss of the nanostructure indicate a propagation of the reaction that modifies the bulk structure of the oxide film. Amorphisation can be reverted to crystallization by annealing under UHV at 1025 K when the surface of the oxide film has been modified, but not when the bulk structure has been modified.     

An adaptive scheme for the approximation of dissipative systems

We propose a new scheme for the long time approximation of a diffusion when the drift vector field is not globally Lipschitz. Under this assumption, a regular explicit Euler scheme–with constant or decreasing step–may explode and implicit Euler schemes are CPU-time expensive. The algorithm we introduce is explicit and we prove that any weak limit of the weighted empirical measures of this scheme is a stationary distribution of the stochastic differential equation. Several examples are presented including gradient dissipative systems and Hamiltonian dissipative systems.     

Peeling phylogenetic ‘oranges’

We investigate the combinatorics of a topological space that is generated by the set of edge-weighted finite trees. This space arises by multiplying the weights of edges on paths in trees and is closely connected to tree reconstruction problems involving finite state Markov processes. We show that this space is a contractible finite CW-complex whose face poset can be described via a partial order on semilabelled forests. We then describe some combinatorial properties of this poset, showing that, for example, it is pure, thin and contractible.     

Dehydrochlorination of monodisperse poly(vinylidene chloride) latex

The objective of the work described in this paper was to produce dispersions of small spherical carbon particles, having particle diameters in the region of 0.1 μm. To this end, the dehydrochlorination of poly(vinylidene chloride) (PVDC) latex particles was attempted. The PVDC latex was prepared by a dispersion polymerization route. Both chemical and thermal dehydrochlorination routes were attempted. Chemical dehydrochlorination, using a variety of base/solvent systems, led to nonporous, spherical black particles of the required size, but which contained only 60% carbon; most of the remainder was oxygen, introduced by nucleophilic substitution reactions. Thermal dehydrochlorination, at 700°C under a nitrogen atmosphere, using a fluidized bed arrangement, on the other hand, led to black particles, having 90% carbon and which retained their sphericity, but which were highly porous. Initial chemical dehydrochlorination, prior to thermal treatment, did not seem to reduce the porosity of the final carbons. Dispersions of the carbon particles in a variety of solvents were readily achieved.     

Vaporisation et dissociation thermique des sulfures de phosphore P4S3, P4S7 et P4S10 a l'etat gazeux

Résumé Nous avons montré par spectrométrie Raman à chaud et mesure des tensions de vapeur que P₄S₃ se vaporise de façon congruente tandis que P₄S₇ et P₄S₁₀ se dissocient dès le début de leur vaporisation. P₄S₇ donne réversiblement P₄S₃ et soufre. P₄S₁₀ se dissocie irréversiblement en P₄S₇ et soufre. A l'état de vapeur non saturante, P₄S₃ se dissocie au-dessus de 600° avec formation de phosphore, de soufre et d'autres espèces non identifiées.Nous avons mesuré expérimentalement la capacité calorifique de P₄S₃ liquide, calculé celle de P₄S₃ gazeux et son entropie standard. Nous avons aussi estimé l'enthalpie standard de vaporisation de P₄S₃ à l'aide des mesures des tensions de vapeur saturante. Nous en avons déduit l'entropie standard de P₄S₃ liquide et son point d'ébullition.

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It is shown by Raman spectroscopy at high temperature and by vapor tensimetric measurements that the vaporisation of P₄S₃ is congruent, whereas P₄S₇ and P₄S₁₀ dissociate at the beginning of vaporisation. P₄S₇ gives P₄S₃ and sulfur reversibly. The dissociation of P₄S₁₀ into P₄S₇ and sulfur is irreversible. Above 600°, in non-saturated vapour the dissociation of P₄S₃ gives phosphorus, sulfur and some unidentified gaseous species. The heat capacity of liquid P₄S₃ has been measured. That of gaseous P₄S₃ and its standard entropy have been calculated. The vaporisation standard enthalpy of P₄S₃ has been estimated from the experimental results on the saturated vapour pressures. The standard entropy of liquid P₄S₃ and its boiling point have been derived from these data.

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Zusammenfassung Mittels Raman-Spektrometrie bei erhöhter Temperatur und durch Messung der Dampfdrucke wurde festgestellt, daß sich P₄S₃ verflüchtigt, während P₄S₇ und P₄S₁₀ mit Beginn der Verflüchtigung dissoziieren. P₄S₇ ergibt reversibel P₄S₃ und Schwefel. Im Zustand ungesättigten Dampfes dissoziiert P₄S₃ oberhalb von 600° unter Bildung von Phosphor, Schwefel und anderer nicht identifizierter Substanzen.Die Wärmekapazität von flüssigem P₄S₃ wurde gemessen, während die vom gasförmigem P₄S₃ sowie seine Standard-Entropie berechnet wurden. Die Standard-Enthalpie der Verflüchtigung des P₄S₃ wurde durch Messungen der Sättigungs-Dampfdrucke ermittelt. Daraus wurden die Standard-Entropie des flüssigen P₄S₃ sowie sein Siedepunkt berechnet.

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- - , P₄S₃ , P₄S₇ P₄S₁₀ . P₄S₇ P₄S₃ , P₄S₁₀ P₄S₇ . 600° P₄S₃ , . P₄S₃, P₄S₃ . P₄S₃. P₄S₃ .

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Nous remercions Monsieur Letoffe du laboratoire du Professeur J. Bousquet, INSA de Lyon, 20 Avenue Albert Einstein 401, 69621 Villeurbanne, qui a r6alis6 pour nous les déterminations expérimentales des capacités calorifiques de P₄S₈ liquide.     

A facility for the production of iodine-123 by spallation of caesium

A facility for the continuous production of iodine-123 by spallation of elemental caesium by 482 MeV protons has been in operation at a TRIUMF beam dump for about 2 years. Radioxenon from the target is efficiently trapped on alumina which is subsequently used to remove the¹²¹Te decay product. The yield is 100 mCi/h from a 20 gm/cm² target at 10 μA. Impurities are¹²⁵I<2% and¹²¹Te<0.2% at 27 hours after end of production. The¹²³I consists mainly of iodide along with significant iodate impurity. The product is used extensively in Canadian clinics for thyroid analyses and for labelling radiopharmaceuticals.     

Exact exponent for the number of persistent spins in the zero-temperature dynamics of the one-dimensional Potts model

For the zero-temperature Glauber dynamics of theq-state Potts model, the fractionr(q, t) of spins which never flip up to timet decays like a power lawr(q, t)t ^–(q) when the initial condition is random. By mapping the problem onto an exactly soluble one-species coagulation model (A+AA) or alternatively by transforming the problem into a free-fermion model, we obtain the exact expression of (q) for all values ofq. The exponent (q) is in general irrational, (3)=0.53795082..., (4)=0.63151575..., ..., with the exception ofq=2 andq=, for which (2)=3/8 and ()=1.     

The thermodynamic properties of acetals+heptane mixtures at 298.15 K

Excess enthalpies and excess volumes were determined at 298.15 K for: dimethoxymethane+heptane, diethoxymethane+heptane, 1,1-dimethoxyethane+heptane, 1,1-diethoxyethane+heptane, 2,2-dimethoxypropane+heptane and 1,1-diethoxypropane+heptane.