Affine Lie algebraic origin of constrained KP hierarchies

An affine sl(n + 1) algebraic construction of the basic constrained KP hierarchy is presented. This hierarchy is analyzed using two approaches, namely linear matrix eigenvalue problem on hermitian symmetric space and constrained KP Lax formulation and it is shown that these approaches are equivalent. The model is recognized to be the generalized non-linear Schrödinger (GNLS) hierarchy and it is used as a building block for a new class of constrained KP hierarchies. These constrained KP hierarchies are connected via similarity-Bäcklund transformations and interpolate between GNLS and multi-boson KP-Toda hierarchies. Our construction uncovers the origin of the Toda lattice structure behind the latter hierarchy. © 1995 American Institute of Physics.

Lattice constellations and codes from quadratic number fields

We propose new classes of linear codes over integer rings of quadratic extensions of Q, the field of rational numbers. The codes are considered with respect to a Mannheim metric, which is a Manhattan metric modulo a two-dimensional (2-D) grid. In particular, codes over Gaussian integers and Eisenstein-Jacobi integers are extensively studied. Decoding algorithms are proposed for these codes when up to two coordinates of a transmitted code vector are affected by errors of arbitrary Mannheim weight. Moreover, we show that the proposed codes are maximum-distance separable (MDS), with respect to the Hamming distance. The practical interest in such Mannheim-metric codes is their use in coded modulation schemes based on quadrature amplitude modulation (QAM)-type constellations, for which neither the Hamming nor the Lee metric is appropriate.

Algebraic approach to optimal clone selection applied in metagenomic projects

Due to the wide diversity of unknown organisms in the environment, 99% of them cannot be grown in traditional culture medium in laboratories. Therefore, metagenomics projects are proposed to study microbial communities present in the environment, from molecular techniques, especially the sequencing. Thereby, for the coming years it is expected an accumulation of sequences produced by these projects. Thus, the sequences produced by genomics and metagenomics projects present several challenges for the treatment, storing and analysis such as: the search for clones containing genes of interest. This work presents the OCI Metagenomics, which allows defines and manages dynamically the rules of clone selection in metagenomic libraries, thought an algebraic approach based on process algebra. Furthermore, a web interface was developed to allow researchers to easily create and execute their own rules to select clones in genomic sequence database. This software has been tested in metagenomic cosmid library and it was able to select clones containing genes of interest. Copyright 2010 ACM.

Unfolding physics from the algebraic classification of spinor fields

After reviewing the Lounesto spinor field classification, according to the bilinear covariants associated to a spinor field, we call attention and unravel some prominent features involving unexpected properties about spinor fields under such classification. In particular, we pithily focus on the new aspects - as well as current concrete possibilities. They mainly arise when we deal with some non-standard spinor fields concerning, in particular, their applications in physics. © 2012 Elsevier B.V.

The algebraic structure behind the derivative nonlinear Schrödinger equation

The Kaup-Newell (KN) hierarchy contains the derivative nonlinear Schrödinger equation (DNLSE) amongst others interesting and important nonlinear integrable equations. In this paper, a general higher grading affine algebraic construction of integrable hierarchies is proposed and the KN hierarchy is established in terms of an Ŝℓ2Kac-Moody algebra and principal gradation. In this form, our spectral problem is linear in the spectral parameter. The positive and negative flows are derived, showing that some interesting physical models arise from the same algebraic structure. For instance, the DNLSE is obtained as the second positive, while the Mikhailov model as the first negative flows. The equivalence between the latter and the massive Thirring model is also explicitly demonstrated. The algebraic dressing method is employed to construct soliton solutions in a systematic manner for all members of the hierarchy. Finally, the equivalence of the spectral problem introduced in this paper with the usual one, which is quadratic in the spectral parameter, is achieved by setting a particular automorphism of the affine algebra, which maps the homogeneous into principal gradation. © 2013 IOP Publishing Ltd.

Teorema de Riemann-Roch, morfismos de Frobenius e a hipótese de Riemann

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

Constructions of ideal lattices with full diversity

In this paper, we present new constructions of ideal lattices for the Rayleigh fading channel in Euclidean spaces with full diversity. These constructions are through totally real subfields of cyclotomic fields, obtained by endowing their ring of integers. With this method we reproduce rotated versions of algebraic lattices where the performance in terms of minimum product distance is related with the field determinant.

Anéis de inteiros de corpos de números e aplicações

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Algebraic constructions of densest lattices

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Algebraic solution of an anisotropic nonquadratic potential

We show that an anisotropic nonquadratic potential, for which a path integral treatment has been recently discussed in the literature, possesses the SO(2, 1) ⊗SO(2, 1) ⊗SO(2, 1) dynamical symmetry, and construct its Green function algebraically. A particular case which generates new eigenvalues and eigenfunctions is also discussed. © 1990.

Algebraic solution of an anisotropic ring-shaped oscillator

Using an algebraic technique related to the SO (2, 1) group we construct the Green function for the potential ar2 + b(r sin θ)-2 + c(r cos θ)-2 + dr2 sin2θ + er2 cos2θ. The energy spectrum and the normalized wave functions are also obtained. © 1990.

Clássicos versus Keynes: a abordagem formal de David Champernowne

Este texto tem por objetivo ressaltar um aspecto que não tem sido tratado com a devida profundidade na literatura que estuda a formalização da Teoria Geral do Emprego, dos Juros e da Moeda de John Maynard Keynes (1936). Mais precisamente, o texto destaca a estratégia de formalização adotada por David G. Champernowne em seu artigo intitulado Unemployment, Basic and Monetary: the classical analysis and the keynesian, publicado em 1935-36 na Review of Economic Studies. Chamamos a atenção para o fato dele distinguir a teoria clássica da teoria de Keynes não apenas pelos pressupostos adotados por cada teoria, mas principalmente pela construção de subsistemas a partir de um sistema geral, com características recursivas (relações de causalidade) distintas. As explicações em prosa, a descrição algébrica das funções comportamentais e condições de equilíbrio e a ilustração por meio de diagramas, além da escolha de conjuntos específicos de variáveis para representar cada uma das teorias e suas diferentes versões são aspectos deste artigo de Champernowne que merecem uma análise mais minuciosa.

The Quasi-lattice of Indiscernible Elements

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

Structural aspects of the fermion-boson mapping in two-dimensional gauge and anomalous gauge theories with massive fermions

Using a synthesis of the functional integral and operator approaches we discuss the fermion-buson mapping and the role played by the Bose field algebra in the Hilbert space of two-dimensional gauge and anomalous gauge field theories with massive fermions. In QED, with quartic self-interaction among massive fermions, the use of an auxiliary vector field introduces a redundant Bose field algebra that should not be considered as an element of the intrinsic algebraic structure defining the model. In anomalous chiral QED, with massive fermions the effect of the chiral anomaly leads to the appearance in the mass operator of a spurious Bose field combination. This phase factor carries no fermion selection rule and the expected absence of Theta-vacuum in the anomalous model is displayed from the operator solution. Even in the anomalous model with massive Fermi fields, the introduction of the Wess-Zumino field replicates the theory, changing neither its algebraic content nor its physical content. (C) 2002 Elsevier B.V. (USA).