ar X iv : m at h - ph / 0 10 50 19 v 1 1 5 M ay 2 00 1 Extension of a Spectral Bounding Method to Complex Rotated Hamiltonians , with Application to p 2 −

ar X iv : m at h - ph / 0 00 50 19 v 1 1 6 M ay 2 00 0 2 and 3 - dimensional Hamiltonians with Shape Invariance Symmetry

Via a special dimensional reduction, that is, Fourier transforming over one of the coordinates of Casimir operator of su(2) Lie algebra and 4-oscillator Hamiltonian, we have obtained 2 and 3 dimensional Hamiltonian with shape invariance symmetry. Using this symmetry we have obtained their eigenspectrum. In the mean time we show equivalence of shape invariance symmetry and Lie algebraic symmetry...

ar X iv : m at h / 00 12 25 1 v 2 [ m at h . A G ] 3 0 M ay 2 00 1 Euler Characteristics of Theta Divisors of Jacobians for Spectral Curves

We show how to calculate the Euler characteristic of an affine Jacobi variety of a spectral curve from its defining equations. 0 Membre du CNRS 1 Laboratoire associé au CNRS.

ar X iv : h ep - p h / 04 02 19 0 v 2 2 6 M ay 2 00 4 1 Pentaquarks in the 10 F - and 10 F - plets

ar X iv : m at h - ph / 0 50 80 68 v 1 3 1 A ug 2 00 5 LAMÉ EQUATION , QUANTUM TOP AND ELLIPTIC BERNOULLI POLYNOMIALS

A generalisation of the odd Bernoulli polynomials related to the quantum Euler top is introduced and investigated. This is applied to compute the coefficients of the spectral polynomials for the classical Lamé operator.

ar X iv : 0 90 5 . 20 47 v 1 [ m at h . A T ] 1 3 M ay 2 00 9 KNASTER ’ S PROBLEM FOR ALMOST ( Z p ) k - ORBITS

In this paper some new cases of Knaster's problem on continuous maps from spheres are established. In particular, we consider an almost orbit of a p-torus X on the sphere, a continuous map f from the sphere to the real line or real plane, and show that X can be rotated so that f becomes constant on X.