Invariant measures for the horocycle flow on periodic hyperbolic surfaces

We classify the ergodic invariant Radon measures for the horocycle flow on geometrically infinite regular covers of compact hyperbolic surfaces. The method is to establish a bijection between these measures and the positive minimal eigenfunctions of the Laplacian of the surface. Two consequences arise: if the group of deck transformations G is of polynomial growth, then these measures are classified by the homomorphisms from G ₀ to ℝ where G ₀ ≤ G is a nilpotent subgroup of finite index; if the group is of exponential growth, then there may be more than one Radon measure which is invariant under the geodesic flow and the horocycle flow. We also treat regular covers of finite volume surfaces. The first author was supported by NSF grant 0500630. The second author was supported by NSF grant 0400687.     

A biased random-key genetic algorithm with forward-backward improvement for the resource constrained project scheduling problem

This paper presents a biased random-key genetic algorithm for the resource constrained project scheduling problem. The chromosome representation of the problem is based on random keys. Active schedules are constructed using a priority-rule heuristic in which the priorities of the activities are defined by the genetic algorithm. A forward-backward improvement procedure is applied to all solutions. The chromosomes supplied by the genetic algorithm are adjusted to reflect the solutions obtained by the improvement procedure. The heuristic is tested on a set of standard problems taken from the literature and compared with other approaches. The computational results validate the effectiveness of the proposed algorithm.     

124Sn target residues in the interaction of heavy ions at intermediate energies

Cross sections, recoil energy distributions for residues produced by¹⁴N,²⁰Ne,⁴⁰Ar on¹²⁴Sn targets have been measured in the 10–70 MeV/u intermediate energy range. As the projectile energy increases, processes as complete fusion-evaporation, incomplete fusion-evaporation and intranuclear cascade-evaporation participate progressively in the nuclear collisions. Peculiar residues corresponding to a gain of 4, 5 or even 6 protons for the¹²⁴Sn target have been observed in the 30–50 MeV energy range.     

The vacuum uv emission spectrum of the 15N22+ molecular ion

The vacuum uv emission of the ¹⁵N₂²⁺ ion has been recorded for the first time. Rotational analysis of two bands, analogous to those already observed in the case of the natural isotope, confirm their assignment to the D¹Σ_u⁺-X¹Σ_g⁺ (0, 0) and (1, 1) bands. More precise data are also obtained for the ³Σ_g^? state which perturbs ground state vibrational levels.     

Molecular structure, spectroscopic properties and DFT calculations of 2-(methylthio)nicotinic acid

The analyses of possible conformations, molecular structures, vibrational and electronic properties of 2-(methylthio)nicotinic acid molecule, C₇H₇NO₂S, with the synonym 2-(methylsulfanyl)nicotinic acid have been first presented theoretically. At the same time, FT-IR and micro-Raman spectra of 2-(methylthio)nicotinic acid were recorded in the regions 400–4000 cm^?1 and 100–4000 cm^?1, respectively. In our calculations, the DFTB3LYP method with 6–311G(d, p) basis set was used to have the structural and spectroscopic data about the mentioned molecule in the ground state and the results obtained were compared with experimental values. Furthermore, gauge invariant atomic orbital (GIAO) ¹H and ¹³C NMR chemical shifts in different solvents, UV-vis TD-DFT calculations, the highest occupied molecular orbitals (HOMO-2, HOMO-1, HOMO), lowest unoccupied molecular orbital (LUMO), molecular electrostatic potantial (MEP) surface, atomic charges and thermodynamic properties of molecule have been theoretically verified and simulated at the mentioned level. The energetic behavior of title molecule in different solvent media was investigated by using DFT/B3LYP method with 6–311G(d, p) basis set in terms of integral equation formalism polarizable continuum model (IEFPCM). In addition, the calculated infrared intensities, Raman activities, reduce masses and force constants of the compound under study have been also reported.     

On the transfer matrix of a MIMO system

We develop a deterministic ab initio model for the input–output relationship of a multiple‐input multiple‐output (MIMO) wireless channel, starting from the Maxwell equations combined with Ohm's law. The main technical tools are scattering and geometric perturbation theories. The derived relationship can lead us to a deep understanding of how the propagation conditions and the coupling effects between the elements of multiple‐element arrays affect the properties of an MIMO channel, e.g. its capacity and its number of degrees of freedom. Copyright © 2011 John Wiley & Sons, Ltd.     

The CRT is the scaling limit of unordered binary trees

We prove that a uniform, rooted unordered binary tree (also known as rooted, binary Pólya tree) with n leaves has the Brownian continuum random tree as its scaling limit for the Gromov‐Hausdorff topology. The limit is thus, up to a constant factor, the same as that of uniform plane trees or labeled trees. Our analysis rests on a combinatorial and probabilistic study of appropriate trimming procedures of trees. © 2011 Wiley Periodicals, Inc. Random Struct. Alg., 38, 467–501, 2011     

Homology of proof-nets

This work defines homology groups for proof-structures in multiplicative linear logic (see [Gir1], [Gir2], [Dan]). We will show that these groups characterize proof-nets among arbitrary proof-structures, thus obtaining a new correctness criterion and of course a new polynomial algorithm for testing correctness. This homology also bears information on sequentialization. An unexpected geometrical interpretation of the linear connectives is given in the last section. This paper exclusively focuses onabstract proof-structures, i.e. paired-graphs. The relation with actual proofs is investigated in [Gir1], [Gir2], [Dan], [Ret] and [Tro].     

Characterization of Trimmed NURBS Surface Boundaries Using Topological Criteria

This paper presents an approach based on topology for the determination of characteristics and properties of curves used in the trimming of NURBS surfaces. Through discrete subdivision and topological criteria, a method is presented to determine characteristics of the boundary; such as whether the set of trimming curves forms a set of closed loops, whether trimming curves contain singularities or self intersections, and whether the boundary is simply connected. A surface mesh partitionning the parameter space is used, formed of isoparametric lines in both parametric directions. Topological properties of the cells of this mesh and their intersections with the trimming curves allow to localize the boundary. Topological treatment of this localization allows to define the interior and exterior of the face, and to refine the boundary localization. Singularities and self intersections of the boundary as well as voids in the face are investigated through the study of topological properties of neighbors. As an application, an algorithm for point localization is presented that very rapidly allows to determine whether a given point in parameter space lies inside, on the boundary or outside of the trimmed surface.     

Des équations de Dirac et de Schrödinger pour la transformation de Fourier

Dyson has associated with the Fredholm determinants of the even (resp. odd) Dirichlet kernels a Schrödinger equation on the half-axis and has used, in tandem, the Gel'fand–Levitan and Marchenko methods of inverse scattering theory to study the asymptotics of these determinants. We have proposed following our unearthing of the conductor operator to seek to realize the Fourier transform itself as a scattering, and we obtain here to this end two Dirac systems on the entire real axis which are intrinsically associated, respectively, to the cosine and to the sine transforms. To cite this article: J.-F. Burnol, C. R. Acad. Sci. Paris, Ser. I 336 (2003).