Linear Form of 3-scale Relativity Algebra and the Relevance of Stability

We show that the algebra of the recently proposed Triply Special Relativity can be brought to a linear (ie, Lie) form by a correct identification of its generators. The resulting Lie algebra is the stable form proposed by Vilela Mendes a decade ago, itself a reapparition of Yang's algebra, dating from 1947. As a corollary we assure that, within the Lie algebra framework, there is no Quadruply Special Relativity.Comment: 5 page

Soft singularity and the fundamental length

It is shown that some regular solutions in 5D Kaluza-Klein gravity may have interesting properties if one from the parameters is in the Planck region. In this case the Kretschman metric invariant runs up to a maximal reachable value in nature, i.e. practically the metric becomes singular. This observation allows us to suppose that in this situation the problems with such soft singularity will be much easier resolved in the future quantum gravity then by the situation with the ordinary hard singularity (Reissner-Nordstr\"om singularity, for example). It is supposed that the analogous consideration can be applied for the avoiding the hard singularities connected with the gauge charges.Comment: 5 page

A stochastic approach to the solution of magnetohydrodynamic equations

The construction of stochastic solutions is a powerful method to obtain localized solutions in configuration or Fourier space and for parallel computation with domain decomposition. Here a stochastic solution is obtained for the magnetohydrodynamics equations. Some details are given concerning the numerical implementation of the solution which is illustrated by an example of generation of long-range magnetic fields by a velocity source.Comment: 21 pages Latex, 5 figure

Validação de seqüência didática sobre o aquecimento global a partir de uma análise das atividades e ações propostas

Este trabalho procurou realizar a validação de uma seqüência didática (SD) sobre aquecimento global, proposta a partir de uma situação-problema que foi desenvolvida com alunos do ensino médio de uma escola pública. A SD foi construída articulando os fundamentos da teoria da atividade de Leontiev (1985) e da teoria de assimilação de ações mentais de Galperin (1986). Na análise da seqüência, verificamos que a maior parte das atividades propostas atingiu os seus objetivos e as ações realizadas pelos alunos promoveram aprendizagens significativas no âmbito conceitual e atitudinal. Dessa forma, podemos considerar que a seqüência aplicada alcançou um resultado de aprendizagem satisfatório

On the nonlinearity interpretation of q- and f-deformation and some applications

q-oscillators are associated to the simplest non-commutative example of Hopf algebra and may be considered to be the basic building blocks for the symmetry algebras of completely integrable theories. They may also be interpreted as a special type of spectral nonlinearity, which may be generalized to a wider class of f-oscillator algebras. In the framework of this nonlinear interpretation, we discuss the structure of the stochastic process associated to q-deformation, the role of the q-oscillator as a spectrum-generating algebra for fast growing point spectrum, the deformation of fermion operators in solid-state models and the charge-dependent mass of excitations in f-deformed relativistic quantum fields.Comment: 11 pages Late