Invariant subsets of scattered trees and the tree alternative property of Bonato and Tardif

A tree is scattered if it does not contain a subdivision of the complete binary tree as a subtree. We show that every scattered tree contains a vertex, an edge, or a set of at most two ends preserved by every embedding of T. This extends results of Halin, Polat and Sabidussi. Calling two trees equimorphic if each embeds in the other, we then prove that either every tree that is equimorphic to a scattered tree T is isomorphic to T, or there are infinitely many pairwise non-isomorphic trees which are equimorphic to T. This proves the tree alternative conjecture of Bonato and Tardif for scattered trees, and a conjecture of Tyomkyn for locally finite scattered trees.     

Eléments finis stochastiques en élasticité linéaireA stochastic finite element method in linear mechanics

The stochastic finite element method presented in this Note consists in representing in a probabilistic form the response of a linear mechanical system whose material properties and loading are random. Each input random variable is expanded into a Hermite polynomial series in standard normal random variables. The response (e.g., the nodal displacement vector) is expanded onto the so-called polynomial chaos. The coefficients of the expansion are obtained by a Galerkin-type method in the space of probability. To cite this article: B. Sudret et al., C. R. Mecanique 332 (2004).     

Discrimination of bacteria from Jamaican bauxite soils using laser-induced breakdown spectroscopy

Soil bacteria are sensitive to ecological change and can be assessed to gauge anthropogenic influences and ecosystem health. In recent years, there has been a significant increase in the focus on new technologies that can be applied to the evaluation of soil quality. Laser-induced breakdown spectroscopy (LIBS) is a promising technique that has been used for the investigation and characterization of explosives, solids, liquids, gases, biological and environmental samples. In this study, bacteria from un-mined and a chronosequence of reclaimed bauxite soils were isolated on Luria–Bertani agar media. Polymerase chain reaction amplification of the bacterial 16S rDNA, sequencing, and phylogenetic analysis were applied to each isolated soil bacteria from the sample sites resulting in the identification and classification of the organisms. Femtosecond LIBS performed on the isolated bacteria showed atomic and ionic emission lines in the spectrum containing inorganic elements such as sodium (Na), magnesium (Mg), potassium (K), zinc (Zn), and calcium (Ca). Principal component analysis and partial least squares regression analysis were performed on the acquired bacterial spectra demonstrating that LIBS has the potential to differentiate and discriminate among bacteria in the un-mined and reclaimed chronosequence of bauxite soils.     

EPR and ENDOR study of the frozen ammoniated electron at low alkali-metal concentrations

Ammoniated electrons in dilute frozen solutions are examined using EPR spectroscopy under conditions where the formation of metallic nanoparticles is avoided. Two signals from two different species have been observed. One signal is metastable and decays irreversibly upon annealing. The metastable species saturates at a spin concentration of 10 nM. The annealing temperature for this species amounts to 60 K for frozen solutions of sodium in neat ammonia and is raised upon addition of metal iodide. The observed g value is smaller than the free electron g value and is compatible with a cluster-anion radical rather than with a cavity electron. The wave function of the unpaired electron contains about 6%-10% of 2p character at nitrogen. The observed g shift is fully compatible with previously reported theoretical calculations (Shkrob, I. A. J. Phys. Chem. A 2006, 110, 3967-3976). The second signal cannot be annealed in the frozen state. The line shape is homogeneous, and its width depends on the identity of the metal and at large metal concentrations on the metal concentration itself. Upon increasing alkali metal concentration above 0.15 MPM, the line shape changes from Lorentzian to Dysonian, indicating the presence of metal nanoparticles. A new ENDOR pulse sequence is introduced to investigate the presence of weakly coupled nuclear spins for homogeneous EPR lines. The observations are critically compared with available literature data.     

Towards the complete experiment: measurement of S((1)D2) polarization in correlation with single rotational states of CO(J) from the photodissociation of oriented OCS(v2 = 1|JlM = 111)

In this paper we report slice imaging polarization experiments on the state-to-state photodissociation at 42,594 cm(-1) of spatially oriented OCS(v(2) = 1|JlM = 111) → CO(J) + S((1)D(2)). Slice images were measured of the three-dimensional recoil distribution of the S((1)D(2)) photofragment for different polarization geometries of the photolysis and probe laser. The high resolution slice images show well separated velocity rings in the S((1)D(2)) velocity distribution. The velocity rings of the S((1)D(2)) photofragment correlate with individual rotational states of the CO(J) cofragment in the J(CO) = 57-65 region. The angular distribution of the S((1)D(2)) velocity rings are extracted and analyzed using two different polarization models. The first model assumes the nonaxial dynamics evolves after excitation to a single potential energy surface of an oriented OCS(v(2) = 1|JlM = 111) molecule. The second model assumes the excitation is to two potential energy surfaces, and the OCS molecule is randomly oriented. In the high J region (J(CO) = 62-65) it appears that both models fit the polarization very well, in the region J(CO) = 57-61 both models seem to fit the data less well. From the molecular frame alignment moments the m-state distribution of S((1)D(2)) is calculated as a function of the CO(J) channel. A comparison is made with the theoretical m-state distribution calculated from the long-range electrostatic dipole-dipole plus quadrupole interaction model. The S((1)D(2)) photofragment velocity distribution shows a very pronounced strong peak for S((1)D(2)) fragments born in coincidence with CO(J = 61).     

Intermolecular potential energy functions from gaseous viscosity data. Choice of the well depth

Dilute gas viscosity data may be inverted directly to give the intermolecular potential energy function if the well depth is known. The consequences of using different values of the well depth are studied, and it is concluded that the correct value may be distinguished by using second virial coefficient data.     

Scaled particle equation of state for hard non-spherical molecules

Applications of the method of anti-symmetrized product of strongly orthogonal geminals (APSG) to the boron hydrides B₂H₆, B₄H₄, B₄H₁₀, B₅H₉, B₅H₁₁ and B₆H₁₀ are described. Minimal basis sets of Slater-type orbitals are employed throughout. The APSG method is found to act as a localization process, with the B-H (terminal) and B-H (bridge)-B geminals well localized and transferable. Generation of several valence structures for B₅H₉, B₅H₁₁ and B₆H₁₀ suggests that the framework geminals of the preferred structure are of the closed three-centre type, although structures involving open BBB framework geminals are less stable by only a few kcal mol^-1. The principal natural orbital of each geminal is similar to the corresponding orbital produced by various localization criteria, while the weakly occupied natural orbitals are also localized and involve anti-bonding interactions between the component atoms of the bond.     

Untersuchung von Seifen

Ohne Zusammenfassung     

Les dimensions d'un ensemble abstrait

Sans résumé