We show that the three body Calogero model with inverse square potentials can be interpreted as a maximally superintegrable and multiseparable system in Euclidean three-space. As such it is a special case of a family of systems involving one arbitrary function of one

We construct families of Hamiltonians extending the Calogero model and such that a finite number of eigenvectors can be computed algebraically.

Two biologically active Schiff bases, C13H10BrON (4), C13H9Br2O2N (5), were synthesized by the reaction of 2-aminophenol (1) with 3-bromobenzaldehyde (2) or 3,5-dibromo-4hydroxybenzaldehyde (3) in the presence of conc. H2SO4. The characterization of Schiff bases were carried out by using spectroscopic techniques including IR, H-NMR, FAB-MS along with elemental analyses. The Schiff bases were ch...

We justify the holomorphic perturbation for the 1particle Inozemtsev model from the trigonometric model and show the holomorphy of the eigenvalues and the eigenfuncions which are obtained by the series expansion. We investigate the relationship between the L 2 space and the nite dimensional space of certain elliptic functions, and determine the distribution of the \algebraic" eigenvalues on the...

We develop a theory for the Hermite-Krichever Ansatz on the Heun equation. As a byproduct, we find formulae which reduce hyperelliptic integrals to elliptic ones.

The review is based on the author’s papers since 1985 in which a new approach to the separation of variables (SoV) has being developed. It is argued that SoV, understood generally enough, could be the most universal tool to solve integrable models of the classical and quantum mechanics. It is shown that the standard construction of the action-angle variables from the poles of the Baker-Akhiezer...

We discuss the connection between the random matrix approach to disordered wires and the Calogero-Sutherland models. We show that different choices of random matrix ensembles correspond to different classes of CS models. In particular, the standard transfer matrix ensembles correspond to CS model with sinh-type interaction, constructed according to the Cn root lattice pattern. By exploiting thi...