Diffraction of neutral helium clusters: evidence for "magic numbers"

The size distributions of neutral 4He clusters in cryogenic jet beams, analyzed by diffraction from a 100 nm period transmission grating, reveal magic numbers at N=10-11, 14, 22, 26-27, and 44 atoms. Whereas magic numbers in nuclei and clusters are attributed to enhanced stabilities, this is not expected for quantum fluid He clusters on the basis of numerous calculations. These magic numbers occur at threshold sizes for which the quantized excitations calculated with the diffusion Monte Carlo method are stabilized, thereby providing the first experimental confirmation for the energy levels of 4He clusters.     

Some Long-Range Dependence Processes Arising from Fluctuations of Particle Systems

Several long-range dependence, self-similar Gaussian processes arise from asymptotics of some classes of spatially distributed particle systems and superprocesses. The simplest examples are fractional Brownian motion and sub-fractional fractional Brownian motion, the latter being intermediate between Brownian motion and fractional Brownian motion. In this paper we focus mainly on long-range dependence processes that arise from occupation time fluctuations of immigration particle systems with or without branching, and we study their properties. Some long-range dependence non-Gaussian processes that appear in a similar way are also mentioned. Mathematics Subject Classifications (2000) Primary 60G15, 60G18; secondary 60F17, 60G20, 60J80.Research partially supported by CONACyT grant 37130-E (Mexico).     

A general method for the Suzuki-Miyaura cross-coupling of sterically hindered aryl chlorides: synthesis of di- and tri-ortho-substituted biaryls in 2-propanol at room temperature

The catalytic formation of di- and trisubstituted ortho biaryl junctions has been achieved using a palladacylce pre-catalyst bearing a N-heterocyclic carbene ligand. This transformation is performed at room temperature in technical grade 2-propanol.     

Number of Sylow subgroups in -solvable groups

If is a finite group and is a prime number, let be the number of Sylow -subgroups of . If is a subgroup of a -solvable group , we prove that divides .

     

New proof of two Berstein-Hilton theorems

With arguments of Homotopy Theory and without the assumption of finite type, we give short proofs of two classic theorems which deal with the co--type of a suspension and the homotopy class of a suspension map.

     

A conjecture on the number of conjugacy classes in ap-solvable group

IfG is ap-solvable group, it is conjectured that k(G/O _P (G) ≤ |G| _p ′. The conjecture is easily obtained for solvable groups as a consequence of R. Knörr’s work on the k(GV) problem. Also, a related result is obtained: k(G/F(G)) is bounded by the index of a nilpotent injector ofG.     

The first order of the hyperspherical harmonic expansion method

The hyperspherical harmonic expansion method is studied in this work. Our attention is focused on the properties of the L_m-approximation in which only the hyperspherical harmonics of minimal order are taken into account. Exact solutions of the Schrödinger equation for a few simple hyperspherical potentials are given. Recipes for constructing antisymmetric hyperspherical harmonics for fermions are investigated, and various procedures to derive the effective potential in the L_m-approximation are discussed. The method is applied to the calculation of ground state and hyperradial excited states (which are identified as the breathing modes) of doubly-magic nuclei. Finally, the energy per particle is derived in the L_m-approximation with Skyrme like forces for an infinitely heavy self-conjugate nucleus.     

Hyperspherical calculations with skyrme-like forces

The first approximation of the hyperspherical harmonic method is used to describe in a unified way the ground state and the breathing mode of several doubly-magic nuclei with Skyrme-like forces. A comparison is made with other methods.