Singular Value Decomposition and Ligand Binding Analysis

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Pure Spinors in AdS and Lie Algebra Cohomology

We show that the BRST cohomology of the massless sector of the Type IIB superstring on AdS(5) x S (5) can be described as the relative cohomology of an infinite-dimensional Lie superalgebra. We explain how the vertex operators of ghost number 1, which correspond to conserved currents, are described in this language. We also give some algebraic description of the ghost number 2 vertices, which appears to be new. We use this algebraic description to clarify the structure of the zero mode sector of the ghost number two states in flat space, and initiate the study of the vertices of the higher ghost number.

VSR symmetries in the DKP algebra: The interplay between Dirac and Elko spinor fields

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

INTEGRAL FUNCTIONALS ON C*-ALGEBRA OF VECTOR-VALUED REGULATED FUNCTIONS

In this paper we deal with the notion of regulated functions with values in a C*-algebra A and present examples using a special bi-dimensional C*-algebra of triangular matrices. We consider the Dushnik integral for these functions and shows that a convenient choice of the integrator function produces an integral homomorphism on the C*-algebra of all regulated functions ([a, b], A). Finally we construct a family of linear integral functionals on this C*-algebra.

Spectrum generating algebra for the pure spinor superstring

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

Higher spin constraints and the super (W∞/2 ⊕ W1+∞/2) algebra in the super eigenvalue model

We show that the partition function of the super eigenvalue model satisfies, for finite N (non-perturbatively), an infinite set of constraints with even spins s = 4, 6, . . . , ∞. These constraints are associated with half of the bosonic generators of the super (W∞/2 ⊕ W1+∞/2) algebra. The simplest constraint (s = 4) is shown to be reducible to the super Virasoro constraints, previously used to construct the model.

Dynamical algebra of quasi-exactly-solvable potentials

We show that by using second-order differential operators as a realization of the so(2,1) Lie algebra, we can extend the class of quasi-exactly-solvable potentials with dynamical symmetries. As an example, we dynamically generate a potential of tenth power, which has been treated in the literature using other approaches, and discuss its relation with other potentials of lowest orders. The question of solvability is also studied. © 1991 The American Physical Society.

Flattening of the resonance spectrum of hadrons from κ-deformed Poincaré algebra

Recently Lukierski et al. [1] defined a κ-deformed Poincaré algebra which is characterized by having the energy-momentum and angular momentum sub-algebras not deformed. Further Biedenharn et al. [2] showed that on gauging the κ-deformed electron with the electromagnetic field, one can set a limit on the allowed value of the deformation parameter ∈ ≡ 1/κ < 1 fm. We show that one gets Regge like angular excitations, J, of the mesons, non-strange and strange baryons, with a value of ∈ ∼ 0.082 fm and predict a flattening with J of the corresponding trajectories. The Regge fit improves on including deformation, particularly for the baryon spectrum.

O uso de elementos da criptografia como estímulo matemático na sala de aula

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Class Notes for Math 901/902: Abstract Algebra, Instructor Tom Marley

Topics include: Free groups and presentations; Automorphism groups; Semidirect products; Classification of groups of small order; Normal series: composition, derived, and solvable series; Algebraic field extensions, splitting fields, algebraic closures; Separable algebraic extensions, the Primitive Element Theorem; Inseparability, purely inseparable extensions; Finite fields; Cyclotomic field extensions; Galois theory; Norm and trace maps of an algebraic field extension; Solvability by radicals, Galois' theorem; Transcendence degree; Rings and modules: Examples and basic properties; Exact sequences, split short exact sequences; Free modules, projective modules; Localization of (commutative) rings and modules; The prime spectrum of a ring; Nakayama's lemma; Basic category theory; The Hom functors; Tensor products, adjointness; Left/right Noetherian and Artinian modules; Composition series, the Jordan-Holder Theorem; Semisimple rings; The Artin-Wedderburn Theorem; The Density Theorem; The Jacobson radical; Artinian rings; von Neumann regular rings; Wedderburn's theorem on finite division rings; Group representations, character theory; Integral ring extensions; Burnside's paqb Theorem; Injective modules.

Class Notes for Math 905: Commutative Algebra, Instructor Sylvia Wiegand

Topics include: Rings, ideals, algebraic sets and affine varieties, modules, localizations, tensor products, intersection multiplicities, primary decomposition, the Nullstellensatz

O uso de elementos da criptografia como estímulo matemático na sala de aula

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

ON THE RADICAL OF A FREE MALCEV ALGEBRA

We prove that the prime radical rad M of the free Malcev algebra M of rank more than two over a field of characteristic not equal 2 coincides with the set of all universally Engelian elements of M. Moreover, let T(M) be the ideal of M consisting of all stable identities of the split simple 7-dimensional Malcev algebra M over F. It is proved that rad M = J(M) boolean AND T(M), where J(M) is the Jacobian ideal of M. Similar results were proved by I. Shestakov and E. Zelmanov for free alternative and free Jordan algebras.

A model and an algebra for semi-structured and full-text queries

The need for a convergence between semi-structured data management and Information Retrieval techniques is manifest to the scientific community. In order to fulfil this growing request, W3C has recently proposed XQuery Full Text, an IR-oriented extension of XQuery. However, the issue of query optimization requires the study of important properties like query equivalence and containment; to this aim, a formal representation of document and queries is needed. The goal of this thesis is to establish such formal background. We define a data model for XML documents and propose an algebra able to represent most of XQuery Full-Text expressions. We show how an XQuery Full-Text expression can be translated into an algebraic expression and how an algebraic expression can be optimized.