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...

Abstract In a recent paper, Saxena et al.[1] developed the solutions of three generalized fractional kinetic equations in terms of the Mittag-Leffler functions. The object of the present paper is to further derive the solution of further generalized fractional kinetic equations. The results are obtained in a compact form in terms of generalized Mittag-Leffler functions. Their relation to fundam...

We present progress results of a new survey for bright QSOs (V < 14.5, R < 15.4, BJ < 15.2) covering the whole sky at high galactic latitudes, |b| > 30. The surface density of QSOs brighter than BJ = 14.8 turns out to be 2.9 ± 0.8 · 10deg. The optical Luminosity Function at 0.04 < z ≤ 0.3 shows significant departures from the standard pure luminosity evolution, providing new insights in the mod...