The vibration-rotation spectrum of methinophosphide: l-Type doubling, l-type resonance and the ν2, 2ν2, and 3ν2 bands of H12CP; The ν1 and ν2 bands of H13CP

The vibration-rotation bands ν₂, 2ν₂, and several “hot” bands of H¹²CP have been recorded and assigned. The states with v₂ = 2, perturbed by l-type resonance and l-type doubling effects have been analyzed on the basis of the existing theory. The energy difference between the 02²0 and the 02⁰0 states was found to be 17.5095 (19) cm^?1. Because of insufficient data, the states with v₂ = 3 could not be corrected for l-type resonance interaction and therefore only an effective l-type doubling constant was obtained. The ν₁ and ν₂ bands of the H¹³CP isotopic molecule (present at natural concentration) were also identified and their spectroscopic constants obtained. The value of I_e for H¹²CP is found to be 25.18793 (26) amu Ų.     

Spaces of Tilings, Finite Telescopic Approximations and Gap-Labeling

The continuous Hull of a repetitive tiling T in ℝ^d with the Finite Pattern Condition (FPC) inherits a minimal ℝ^d-lamination structure with flat leaves and a transversal which is a Cantor set. This class of tiling includes the Penrose & the Amman Benkker ones in 2D, as well as the icosahedral tilings in 3D. We show that the continuous Hull, with its canonical ℝ^d-action, can be seen as the projective limit of a suitable sequence of branched, oriented and flat compact d-manifolds. As a consequence, the longitudinal cohomology and the K-theory of the corresponding C*-algebra are obtained as direct limits of cohomology and K-theory of ordinary manifolds. Moreover, the space of invariant finite positive measures can be identified with a cone in the d^th homology group canonically associated with the orientation of ℝ^d. At last, the gap labeling theorem holds: given an invariant ergodic probability measure μ on the Hull the corresponding Integrated Density of States (IDS) of any selfadjoint operators affiliated to takes on values on spectral gaps in the ℤ-module generated by the occurrence probabilities of finite patches in the tiling. Accepted in Revised Form: 7 May 2005     

Sorption thermodynamics of CO2, CH4, and their mixtures in the ITQ-1 zeolite as revealed by molecular simulations

The thermodynamic properties and siting of carbon dioxide and methane sorbed in the siliceous form of zeolite MCM-22, ITQ-1, were studied by means of grand canonical Monte Carlo simulation. ITQ-1 comprises two independent pore systems of different geometry. It was found to be CO(2)-selective toward CO(2)/CH(4) gas mixtures, its equilibrium selectivity being distinctly higher in its sinusoidal channel pore system than in the large cavity system over a wide range of pressures starting from the Henry law regime, at the three temperatures considered. A maximum in selectivity is observed at low temperature, high pressure, and methane-rich gas-phase composition.     

On the clarification of the IR stretching vibration assignment of adsorbed N2 on Rh0 and Rhdelta+ surface atoms of supported Rh crystallites

The low-temperature adsorption of N(2) on Rh/SiO(2) samples of various particle-size distributions was followed by FTIR. The addition of O(2) pulses on Rh(0) surfaces saturated with chemisorbed N(2) allowed us to reassign stretching frequencies attributed originally to N(2)-Rh(0) to N(2)-Rh(delta+). The formation of the latter oxidized Rh species is assumed to be induced by an electron withdrawal from adsorbed oxygen species on Rh surface centers neighboring those onto which N(2) species are chemisorbed. The present work, thus, enables us to delimit ranges of frequencies for which the adsorption of N(2) can be considered to occur on either Rh(0) or Rh(delta+) centers for nu(N2) lower or higher than 2243 cm(-1), respectively. The N(2)-FTIR experiments performed on the studied catalysts also suggest a lattice plane selectivity for N(2) adsorption on metallic Rh planes of different natures which, to our knowledge, has not been reported yet for Rh.     

Finite element approximation of the Neumann eigenvalue problem in domains with multiple cracks

^** Email: belhach{at}poncelet.univ-metz.fr^*** Email: bucur{at}math.univ-metz.fr^**** Email: jmse{at}math.univ-metz.fr We study the Neumann–Laplacian eigenvalue problem in domainswith multiple cracks. We derive a mixed variational formulationwhich holds on the whole geometric domain (including the cracks)and implements efficient finite-element discretizations forthe computation of eigenvalues. Optimal error estimates aregiven and several numerical examples are presented, confirmingthe efficiency of the method. As applications, we numericallyinvestigate the behaviour of the low eigenvalues in domainswith a large number of cracks.     

Real-space observation of spectral degeneracy breaking in a waveguide-coupled disk microresonator

We report on the real-space observation of resonant frequency splitting in a high-Q waveguide-coupled silicon-on-insulator microdisk resonator. Phase sensitive near-field analysis reveals the stationary nature of the two resonant states, and spectral investigations clearly show their orthogonality. These measurements emphasize the role of the coupling waveguide in this splitting phenomenon. The symmetry of the two stationary whispering gallery modes is clearly observed and is found to follow the axial symmetry of the waveguide-coupled microdisk as it has been reported by earlier theoretical predictions.     

Maximal surfaces and the universal Teichmüller space

We show that any element of the universal Teichmüller space is realized by a unique minimal Lagrangian diffeomorphism from the hyperbolic plane to itself. The proof uses maximal surfaces in the 3-dimensional anti-de Sitter space. We show that, in AdS _n+1, any subset E of the boundary at infinity which is the boundary at infinity of a space-like hypersurface bounds a maximal space-like hypersurface. In AdS₃, if E is the graph of a quasi-symmetric homeomorphism, then this maximal surface is unique, and it has negative sectional curvature. As a by-product, we find a simple characterization of quasi-symmetric homeomorphisms of the circle in terms of 3-dimensional projective geometry.     

A general ultrasound-assisted access to room-temperature ionic liquids

The replacement of common organic solvents by room-temperature ionic liquids (RTILs) is a topical subject in both academia and industry. In the last decades, the number of applications for RTILs has followed an exponential curve and spilled over the boundaries of chemistry. Still, one of the main drawbacks of these compounds is their difficult access. The present ultrasound-assisted method affords a general and easy access to a large variety of room-temperature ionic liquids.