The spectrum of an open vertex model based on the U(q)[SU(2)] algebra at roots of unity

We study the exact solution of an N-state vertex model based on the representation of the U(q)[SU(2)] algebra at roots of unity with diagonal open boundaries. We find that the respective reflection equation provides us one general class of diagonal K-matrices having one free-parameter. We determine the eigenvalues of the double-row transfer matrix and the respective Bethe ansatz equation within the algebraic Bethe ansatz framework. The structure of the Bethe ansatz equation combine a pseudomomenta function depending on a free-parameter with scattering phase-shifts that are fixed by the roots of unity and boundary variables. (C) 2010 Elsevier B.V. All rights reserved.

Memory and hypertext: a reflection on relational knowledge

This paper analyzes the changes the ways of organizing memory have undergone since ancient times, turning them into the current artificial memory systems. It aims to draw a parallel between the art of memory (which associates images to specific texts) and the hypertext (which also uses associations, but in a non-linear way). Our methodology consisted of a qualitative approach, involving the collection of texts about the art of memory and hypertext; this enables us to salvage the historical-cultural changes which have modified form and use of the art of memory and allowed the creation of hypertext. It also analyzes the similarities among artificial memory systems created by different cultures in order to prevent loss of knowledge produced by society.

Dirac equation in noncommutative space for hydrogen atom

We consider the energy levels of a hydrogen-like atom in the framework of theta-modified, due to space noncommutativity, Dirac equation with Coulomb field. It is shown that on the noncommutative (NC) space the degeneracy of the levels 2S(1/2), 2P(1/2) and 2P(3/2) is lifted completely, such that new transition channels are allowed. (C) 2009 Elsevier B.V. All rights reserved.

Lie algebra methods for the applications to the statistical theory of turbulence

Approximate Lie symmetries of the Navier-Stokes equations are used for the applications to scaling phenomenon arising in turbulence. In particular, we show that the Lie symmetries of the Euler equations are inherited by the Navier-Stokes equations in the form of approximate symmetries that allows to involve the Reynolds number dependence into scaling laws. Moreover, the optimal systems of all finite-dimensional Lie subalgebras of the approximate symmetry transformations of the Navier-Stokes are constructed. We show how the scaling groups obtained can be used to introduce the Reynolds number dependence into scaling laws explicitly for stationary parallel turbulent shear flows. This is demonstrated in the framework of a new approach to derive scaling laws based on symmetry analysis [11]-[13].

Generalized solutions of a nonlinear parabolic equation with generalized functions as initial data

In [H. Brezis, A. Friedman, Nonlinear parabolic equations involving measures as initial conditions, J. Math. Pure Appl. (9) (1983) 73-97.] Brezis and Friedman prove that certain nonlinear parabolic equations, with the delta-measure as initial data, have no solution. However in [J.F. Colombeau, M. Langlais, Generalized solutions of nonlinear parabolic equations with distributions as initial conditions, J. Math. Anal. Appl (1990) 186-196.] Colombeau and Langlais prove that these equations have a unique solution even if the delta-measure is substituted by any Colombeau generalized function of compact support. Here we generalize Colombeau and Langlais` result proving that we may take any generalized function as the initial data. Our approach relies on recent algebraic and topological developments of the theory of Colombeau generalized functions and results from [J. Aragona, Colombeau generalized functions on quasi-regular sets, Publ. Math. Debrecen (2006) 371-399.]. (C) 2009 Elsevier Ltd. All rights reserved.