Classification of Triadic Chord Inversions Using Kohonen Self-organizing Maps

In this paper we discuss the application of the Kohonen Selforganizing Maps to the classification of triadic chords in inversions and root positions. Our motivation started in the validation of Schönberg´s hypotheses of the harmonic features of each chord inversion. We employed the Kohonen network, which has been generally known as an optimum pattern classification tool in several areas, including music, to verify that hypothesis. The outcomes of our experiment refuse the Schönberg´s assumption in two aspects: structural and perceptual/functional

The cluster of galaxies Abell 376

We present a dynamical analysis of the galaxy cluster Abell 376 based on a set of 73 velocities, most of them measured at Pic du Midi and Haute-Provence observatories and completed with data from the literature. Data on individual galaxies are presented and the accuracy of the determined velocities is discussed as well as some properties of the cluster. We obtained an improved mean redshift value z=0.0478^{+0.005}_{-0.006} and velocity dispersion sigma=852^{+120}_{-76}km/s. Our analysis indicates that inside a radius of 900h_{70}^{-1}kpc (15 arcmin) the cluster is well relaxed without any remarkable feature and the X-ray emission traces fairly well the galaxy distribution. A possible substructure is seen at 20 arcmin from the centre towards the Southwest direction, but is not confirmed by the velocity field. This SW clump is, however, kinematically bound to the main structure of Abell 376. A dense condensation of galaxies is detected at 46 arcmin (projected distance 2.6h_{70}^{-1}Mpc) from the centre towards the Northwest and analysis of the apparent luminosity distribution of its galaxies suggests that this clump is part of the large scale structure of Abell 376. X-ray spectroscopic analysis of ASCA data resulted in a temperature kT = 4.3+/-0.4 keV and metal abundance Z = 0.32+/-0.08 Z_solar. The velocity dispersion corresponding to this temperature using the T_X-sigma scaling relation is in agreement with the measured galaxies velocities.Comment: 11 pages, 10 figures, accepted for publication in A&

On the algebraic Bethe ansatz: Periodic boundary conditions

In this paper, the algebraic Bethe ansatz with periodic boundary conditions is used to investigate trigonometric vertex models associated with the fundamental representations of the non-exceptional Lie algebras. This formulation allow us to present explicit expressions for the eigenvectors and eigenvalues of the respective transfer matrices.Comment: 36 pages, LaTex, Minor Revisio