A highly simple, rapid, sensitive and selective method is developed for spectrophotometric determination of gabapentin in pure form as well as in pharmaceutical formulations. The method is based on the formation of a yellow Schiff base derived from the condensation of gabapentin drug (1-amino methyl) cyclo hexane acetic acid and 2,5-dihydroxybenzaldehyde (DHBA) exhibiting a maximum absorbance a...

A new integrable spin chain of the Haldane-Shastry type is introduced. It is interpreted as the inverse-square interacting spin chain with a reflecting end. The lattice points of this model consist of the square of the zeros of the Laguerre polynomial. Using the “exchange operator formalism”, the integrals of motion for the model are explicitly constructed. Typeset using REVTEX ∗E-mail address ...

We introduce spin Calogero-Moser systems associated with root systems of simple Lie algebras and give the associated Lax representations (with spectral parameter) and fundamental Poisson bracket relations. Our analysis is based on a group-theoretic framework similar in spirit to the standard classical r-matrix theory for constant r-matrices. Systèmes de Calogero Moser à spins associés aux algèb...

Integrable equations in (1 + 1) dimensions have their own higher order integrable equations, like the KdV, mKdV and NLS hierarchies etc. In this paper we consider whether integrable equations in (2 + 1) dimensions have also the analogous hierarchies to those in (1 + 1) dimensions. Explicitly is discussed the Bogoyavlenskii-Schiff(BS) equation. For the BS hierarchy, there appears an ambiguity in...

The radial distribution function of liquid sodium has been studied by considering the integral equation Perturbation Theory of Madden and Fitts for the reference part and the optimised cluster theory for the attractive part of the pair potential. Calculations were carried out for the long range oscillatory potential of Schiff. The calculated results are compared with the molecular dynamics calc...

We show that the quasiparticle kinetic theory for quantum and classical Calogero models reduces to free-streaming Boltzmann equation. reconcile this simple emergent behaviour with strongly interacting character of model by developing a Bethe-Lax correspondence in case. This demonstrates explicitly freely propagating degrees freedom are not bare particles, but rather quasiparticles corresponding...

We apply a recently introduced reduction procedure based on the embedding of non-crystallographic Coxeter groups into crystallographic ones to Calogero-Moser systems. For rational potentials the familiar generalized Calogero Hamiltonian is recovered. For the Hamiltonians of trigonometric, hyperbolic and elliptic type, we obtain novel integrable dynamical systems with a second potential term whi...

We introduce spin Calogero-Moser systems associated with root systems of simple Lie algebras and give the associated Lax representations (with spectral parameter) and fundamental Poisson bracket relations. The associated integrable models (called integrable spin CalogeroMoser systems in the paper) and their Lax pairs are then obtained via Poisson reduction and gauge transformations. For Lie alg...

Exact coherent states in the Calogero-Sutherland models (of time-dependent parameters) which describe identical harmonic oscillators interacting through inversesquare potentials are constructed, in terms of the classical solutions of a harmonic oscillator. For quasi-periodic coherent states of the time-periodic systems, geometric phases are evaluated. For the AN−1 Calogero-Sutherland model, the...

We introduce osp(m|n) spin Calogero–Sutherland models and find that the have symmetry of half-loop algebra or Yangian if only coupling constant model equals to .