The construction of a q-deformed N=2 superconformal algebra is proposed in terms of level 1 currents of U q ( su(2)) quantum affine Lie algebra and a single real Fermi field. In particular, it suggests the expression for the q-deformed Energy-Momentum tensor in the Sugawara form. Its constituents generate two isomorphic quadratic algebraic structures. The generalization to U q ( su(N + 1)) is also proposed.

In this paper we employ the construction of Dirac bracket for the remaining current of sl(2) q deformed Kac-Moody algebra when constraints similar to those connecting the sl(2)-WZW model and the Liouville theory are imposed and show that it satisfy the q-Virasoro algebra proposed by Frenkel and Reshetikhin. The crucial assumption considered in our calculation is the existence of a classical Poisson bracket algebra induced, in a consistent manner by the correspondence principle, mapping the quantum generators into commuting objects of classical nature preserving their algebra.

The Reynolds' transport theorem deals with the rate of change of an extensive property, N, of a fluid in a control volume. Its purpose is to provide a link between the concepts associated to the control volumesand those associated to systems. The Reynolds' transport theorem is something extremely important in the formulation of the basic laws of fluid dynamics, which are the mass conservation equation, momentum conservation equationsand the energy conservation equation. This paper aims to propose an approach of the Reynolds' Transport Theorem for finite control volume equations for mass, momentum and energy.

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