Three Electrons in a Two-Dimensional Parabolic Trap: The Relative Motion Solution

In agreement with the Kohn theorem the relative motion (rel) of three electrons in a two-dimensional parabolic trap separates from the centre-of-mass (CM) motion. By introducing new coordinates the Hamiltonian for relative motion in the approximation of non-interacting electrons can be taken to the normal form. The eigenstates of the normalized Hamiltonian are products of the Fock-Darwin states for normal modes. The energy levels for relative motion are obtained by diagonalizing the exact Hamiltonian in the eigenbasis for the non-interacting case. In this basis the interaction matrix elements can be obtained in the analytical form. Since the rank of the Hamiltonian matrix is significantly reduced, the calculations are faster and more accurate than those for the full (CM + rel) motion. This advantage is especially important for the calculations of excited states and the analysis of energy spectra.     

Sur le degré dynamique des transformations de Cremona du plan qui stabilisent une courbe irrationnelle non-elliptique

We show that the first dynamical degree of a Cremona transformation stabilizing an irrational non elliptic curve is 1. Moreover, among these transformations, we characterize those which have finite order. To cite this article: I. Pan, C. R. Acad. Sci. Paris, Ser. I 341 (2005).     

Testing the mechanism of QGP-Induced energy loss

We present an analytic model of jet quenching, based on the (D)GLV energy loss formalism, to describe the system size dependence of QGP-induced parton absorption in relativistic heavy ion collisions. Numerical simulations of the transverse momentum dependence of jet quenching are given for central Au+Au and Cu+Cu reactions. Low p _Tdijet correlations are shown to be sensitive to the reappearance of the lost energy as soft hadrons. At high p _Twe find that the attenuation of dihadrons is similar to that of single inclusive particles. Comparison to recent data from PHENIX and STAR is given as a test of the jet quenching theory.     

Quadratic distances for capacity and bi-capacity approximation and identification

The application of multi-attribute utility theory based on the Choquet integral requires the prior identification of a capacity if the utility scale is unipolar, or of a bi-capacity if the utility scale is bipolar. In order to implement a minimum distance principle for capacity or bi-capacity approximation or identification, quadratic distances between capacities and bi-capacities are studied. The proposed approach, consisting in solving a strictly convex quadratic program, has been implemented within the GNU R kappalab package for capacity and nonadditive integral manipulation. Its application is illustrated on two examples.      

Self-consistent modelling of argon microwave discharge sustained by electromagnetic wave in dipole mode

Microwave discharges produced by travelling/standing electromagnetic waves have drawn considerable attention in recent years due to their wide application in microelectronic industry. Here are presented the axial distributions of the electrons and ions as well as those of excited atoms in an argon microwave discharge at a low gas pressure (400 mTorr) sustained by a 2.45 GHz travelling dipolar electromagnetic wave. The numerical calculations are based on a self-consistent kinetic-electrodynamic model and the results obtained are in a good agreement with the experimental data. The model yields also the magnitude of the wave power sustaining the discharge and the axial profiles of all electromagnetic-wave characteristics and the axial distribution of the neutral gas temperature.     

Lattice valued intuitionistic fuzzy sets

In this paper a new definition of a lattice valued intuitionistic fuzzy set (LIFS) is introduced, in an attempt to overcome the disadvantages of earlier definitions. Some properties of this kind of fuzzy sets and their basic operations are given. The theorem of synthesis is proved: For every two families of subsets of a set satisfying certain conditions, there is an lattice valued intuitionistic fuzzy set for which these are families of level sets. The research supported by Serbian Ministry of Science and Technology, Grant No. 1227.