Closed expressions for Lie algebra invariants and finite transformations

A simple procedure to obtain complete, closed expressions for Lie algebra invariants is presented. The invariants are ultimately polynomials in the group parameters. The construction of finite group elements requires the use of projectors, whose coefficients are invariant polynomials. The detailed general forms of these projectors are given. Closed expressions for finite Lorentz transformations, both homogeneous and inhomogeneous, as well as for Galilei transformations, are found as examples.

Point transformations are canonical transformations

It is shown that point transformations are also canonical transformations. © 1999 IOP Publishing Ltd.

Phase transformations in the Cu-Al alloy with Ag addition

The effect of Ag addition on the phase transformations that occur in the Cu-10% Al alloy was studied using differential thermal analysis, scanning electron and optical microscopies and energy dispersive X-ray analysis. The results indicated that Ag addition is responsible for the separation of the reverse martensitic transformation in two stages, and for the refinement of the α-phase grains. The relative amount of the β1 martensitic phase, retained on slow cooling (above 2 K min-1 of cooling rate), and the relative fraction of phase α2 are increased. The solubility limit of Ag in the matrix is close to 6 mass% and at this concentration the maximum stability of the β-phase is reached. © 2005 Akadémiai Kiadó, Budapest.

Physical parameters and basis transformations in the two-Higgs-doublet model

A direct connection between physical parameters of general two-Higgs-doublet model (2HDM) potentials after electroweak symmetry breaking (EWSB) and the parameters that define the potentials before EWSB is established. These physical parameters, such as the mass matrix of the neutral Higgs bosons, have well-defined transformation properties under basis transformations transposed to the fields after EWSB. The relations are also explicitly written in a basis covariant form. Violation of these relations may indicate models beyond 2HDMs. In certain cases the whole potential can be defined in terms of the physical parameters. The distinction between basis transformations and reparametrizations is pointed out. Some physical implications are discussed. © 2008 The American Physical Society.

Darboux-Bäcklund transformations and rational solutions of the painlevé IV equation

Rational solutions of the Painlevé IV equation are constructed in the setting of pseudo-differential Lax formalism describing AKNS hierarchy subject to the additional non-isospectral Virasoro symmetry constraint. Convenient Wronskian representations for rational solutions are obtained by successive actions of the Darboux-Bäcklund transformations. ©2010 American Institute of Physics.

Szego{double acute} and para-orthogonal polynomials on the real line: Zeros and canonical spectral transformations

We study polynomials which satisfy the same recurrence relation as the Szego{double acute} polynomials, however, with the restriction that the (reflection) coefficients in the recurrence are larger than one in modulus. Para-orthogonal polynomials that follow from these Szego{double acute} polynomials are also considered. With positive values for the reflection coefficients, zeros of the Szego{double acute} polynomials, para-orthogonal polynomials and associated quadrature rules are also studied. Finally, again with positive values for the reflection coefficients, interlacing properties of the Szego{double acute} polynomials and polynomials arising from canonical spectral transformations are obtained. © 2012 American Mathematical Society.

On the Bäcklund and Darboux transformations for the Tzitzéica model

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

DE SITTER TRANSITIVITY, CONFORMAL TRANSFORMATIONS AND CONSERVATION LAWS

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Microbial transformations of Aryltetralone and Aryltetralin Lignans by Cunninghamella echinulata and Beauveria bassiana

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)