In the Randall-Sundrum scenario we analize the dynamics of a spherically symmetric 3-brane when matter fields propagate in the bulk. For a well defined class of conformal fields of weight -4 we determine a new set of exact 5-dimensional solutions which localize gravity in the vicinity of the brane and are stable under radion field perturbations. Geometries which describe the dynamics of inhomog...

We review the recent progress on the construction of the determinant representations of the correlation functions for the integrable supersymmetric fermion models. The factorizing F -matrices (or the so-called F -basis) play an important role in the construction. In the F -basis, the creation (and the annihilation) operators and the Bethe states of the integrable models are given in completely ...

We exhibit counterexamples to a Conjecture of Nesin, since we build a connected solvable group with finite center and of finite Morley rank in which no normal nilpotent subgroup has a nilpotent complement. The main result says that each centerless connected solvable group G of finite Morley has a normal nilpotent subgroup U and an abelian subgroup T such that G = U o T , if and only if, for any...

A way to compose a matrix P and a finite dimensional representation ρ of C via a map h into a new matrix P ∗h ρ is defined. Several results about the spectrum, eigenvectors, kernel and rank of P ∗h ρ are proved.

Working in the F-basis provided by the factorizing F-matrix, the scalar products of Bethe states for the supersymmetric t-J model are represented by determinants. By means of these results, we obtain the determinant representations of the correlation functions of the model.

In this paper a closed form solution of a fractional integro-differential equation of Volterra type involving Mittag-Leffler function has been obtained using straight forward technique of Sumudu transform. Some particular cases have also been considered.

This paper is mostly a survey, with a few new results. The first part deals with functional equations for q-exponentials, q-binomials and q-logarithms in q-commuting variables and more generally under q-Heisenberg relations. The second part discusses translation invariance of Jackson integrals, q-Fourier transforms and the braided line. Last modified: August 26, 1996 Note: Report No. 1, Institu...