Características físico-químicas de amidos modificados com permanganato de potássio/ácido lático e hipoclorito de sódio/ácido lático

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Alternant and BCH codes over certain rings

Alternant codes over arbitrary finite commutative local rings with identity are constructed in terms of parity-check matrices. The derivation is based on the factorization of x s - 1 over the unit group of an appropriate extension of the finite ring. An efficient decoding procedure which makes use of the modified Berlekamp-Massey algorithm to correct errors and erasures is presented. Furthermore, we address the construction of BCH codes over Zm under Lee metric.

CYCLIC CODES THROUGH B[X], B[X; 1/kp Z(0)] and B[X; 1/p(k) Z(0)]: A COMPARISON

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

Quantization rules for bound states in quantum wells

An algebraic reformulation of the Bohr-Sommerfeld (BS) quantization rule is suggested and applied to the study of bound states in one-dimensional quantum wells. The energies obtained with the present quantization rule are compared to those obtained with the usual BS and WKB quantization rules and with the exact solution of the Schrodinger equation. We find that, in diverse cases of physical interest in molecular physics, the present quantization rule not only yields a good approximation to the exact solution of the Schrodinger equation, but yields more precise energies than those obtained with the usual BS and/or WKB quantization rules. Among the examples considered numerically are the Poeschl-Teller potential and several anharmonic oscillator potentials. which simulate molecular vibrational spectra and the problem of an isolated quantum well structure subject to an external electric field.

On negative flows of the AKNS hierarchy and a class of deformations of a bihamiltonian structure of hydrodynamic type

A deformation parameter of a bihamiltonian structure of hydrodynamic type is shown to parametrize different extensions of the AKNS hierarchy to include negative flows. This construction establishes a purely algebraic link between, on the one hand, two realizations of the first negative flow of the AKNS model and, on the other, two-component generalizations of Camassa-Holmand Dym-type equations. The two-component generalizations of Camassa-Holm- and Dym-type equations can be obtained from the negative-order Hamiltonians constructed from the Lenard relations recursively applied on the Casimir of the first Poisson bracket of hydrodynamic type. The positive-order Hamiltonians, which follow froth the Lenard scheme applied on the Casimir of the second Poisson bracket of hydrodynamic type, are shown to coincide with the Hamiltonians of the AKNS model. The AKNS Hamiltonians give rise to charges conserved with respect to equations of motion of two-component Camassa-Holm- and two-component Dym-type equations.

Lorentz-violating dilatations in momentum space and some extensions on nonlinear actions of Lorentz-algebra-preserving systems

We work on some general extensions of the formalism for theories which preserve the relativity of inertial frames with a nonlinear action of the Lorentz transformations on momentum space. Relativistic particle models invariant under the corresponding deformed symmetries are presented with particular emphasis on deformed dilatation transformations. The algebraic transformations relating the deformed symmetries with the usual (undeformed) ones are provided in order to preserve the Lorentz algebra. Two distinct cases are considered: a deformed dilatation transformation with a spacelike preferred direction and a very special relativity embedding with a lightlike preferred direction. In both analysis we consider the possibility of introducing quantum deformations of the corresponding symmetries such that the spacetime coordinates can be reconstructed and the particular form of the real space-momentum commutator remains covariant. Eventually feasible experiments, for which the nonlinear Lorentz dilatation effects here pointed out may be detectable, are suggested.

A possible way to relate the covariantization and the negative dimensional integration method in the light-cone gauge

Here we present a possible way to relate the method of covariantizing the gauge-dependent pole and the negative dimensional integration method for computing Feynman integrals pertinent to the light-cone gauge fields. Both techniques are applicable to the algebraic light-cone gauge and dispense with prescriptions to treat the characteristic poles.

T-duality in affine NA Toda models

The construction of non-Abelian affine Toda models is discussed in terms of its underlying Lie algebraic structure. It is shown that a subclass of such non-conformal two-dimensional integrable models naturally leads to the construction of a pair of actions, which share the same spectra and are related by canonical transformations.

Quantum V-algebras

The problem of the classification of the extensions of the Virasoro algebra is discussed. It is shown that all H-reduced G(r)-current algebras belong to one of the following basic algebraic structures: local quadratic W-algebras, rational U-algebras, nonlocal W-algebras, nonlocal quadratic WV-algebras and rational nonlocal UV-algebras. The main new features of the quantum Ir-algebras and their heighest weight representations are demonstrated on the example of the quantum V-3((1,1))-algebra.

Plethysms and interacting boson models

A short review of the plethysm technique aiming to its application in finding branching rules for the reduction of an irreducible representation of a group under the restriction to one of its subgroups is given. The algebraic structure of the interacting boson model and some of its extensions is given together with the branching rules needed to classify their basis states, obtained by the use of plethysms. (C) 2003 American Institute of Physics.

Discretizing the deformation parameter in the su(q)(2) quantum algebra

Inspired in recent works of Biedenham [1, 2] on the realization of the q-algebra su(q)(2), We show in this note that the condition [2j + 1](q) = N-q(j) = integer, implies the discretization of the deformation parameter alpha, where q = e(alpha). This discretization replaces the continuum associated to ct by an infinite sequence alpha(1), alpha(2), alpha(3),..., obtained for the values of j, which label the irreps of su(q)(2). The algebraic properties of N-q(j) are discussed in some detail, including its role as a trace, which conducts to the Clebsch-Gordan series for the direct product of irreps. The consequences of this process of discretization are discussed and its possible applications are pointed out. Although not a necessary one, the present prescription is valuable due to its algebraic simplicity especially in the regime of appreciable values of alpha.

Conformal structures and twistors in the paravector model of spacetime

Some properties of the Clifford algebras Cl-3,Cl-0, Cl-1,Cl-3, Cl-4,Cl-1 similar or equal to C circle times Cl-1,Cl-3 and Cl-2,Cl-4 are presented, and three isomorphisms between the Dirac-Clifford algebra C circle times Cl-1,Cl-3 and Cl-4,Cl-1 are exhibited, in order to construct conformal maps and twistors, using the paravector model of spacetime. The isomorphism between the twistor space inner product isometry group SU( 2,2) and the group $pin(+)(2,4) is also investigated, in the light of a suitable isomorphism between C circle times Cl-1,Cl-3 and Cl-4,Cl-1. After reviewing the conformal spacetime structure, conformal maps are described in Minkowski spacetime as the twisted adjoint representation of $ pin(+)(2,4), acting on paravectors. Twistors are then presented via the paravector model of Clifford algebras and related to conformal maps in the Clifford algebra over the Lorentzian R-4,(1) spacetime.We construct twistors in Minkowski spacetime as algebraic spinors associated with the Dirac-Clifford algebra C circle times Cl-1,Cl-3 using one lower spacetime dimension than standard Clifford algebra formulations, since for this purpose, the Clifford algebra over R-4,R-1 is also used to describe conformal maps, instead of R-2,(4). Our formalism sheds some new light on the use of the paravector model and generalizations.

Soliton-cuspon interaction for the Camassa-Holm equation

The interaction of different kinds of solitary waves of the Camassa-Holm equation is investigated. We consider soliton-soliton, soliton-cuspon and cuspon-cuspon interactions. The description of these solutions had previously been shown to be reducible to the solution of an algebraic equation. Here we give explicit examples, numerically solving these algebraic equations and plotting the corresponding solutions. Further, we show that the interaction is elastic and leads to a shift in the position of the solitons or cuspons. We give the analytical expressions for this shift and represent graphically the coupled soliton-cuspon, soliton-soliton and cuspon-cuspon interactions.

Supersymmetry for integrable hierarchies on loop superalgebras

An algebraic approach is employed to formulate N = 2 supersymmetry transformations in the context of integrable systems based on loop superalgebras sl(p + 1, p), p >= 1, with homogeneous gradation. We work with extended integrable hierarchies, which contain supersymmetric AKNS and Lund-Regge sectors. We derive the one-soliton solution for p = 1 which solves positive and negative evolution equations of the N = 2 supersyrnmetric model.

Algorithm for probing the unitarity of topologically massive models

An uncomplicated and easy handling prescription that converts the task of checking the unitarity of massive, topologically massive, models into a straightforward algebraic exercise, is developed. The algorithm is used to test the unitarity of both topologically massive higher-derivative electromagnetism (TMHDE) and topologically massive higher-derivative gravity (TMHDG). The novel and amazing features of these effective field models are also discussed.