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

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

Um modelo algébrico do quantificador da ubiquidade

Pós-graduação em Filosofia - FFC

Algumas generalizações do teorema clássico de Borsuk-Ulam

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

A BCH code and a sequence of cyclic codes

This study establishes that for a given binary BCH code C0 n of length n generated by a polynomial g(x) ∈ F2[x] of degree r there exists a family of binary cyclic codes {Cm 2m−1(n+1)n}m≥1 such that for each m ≥ 1, the binary cyclic code Cm 2m−1(n+1)n has length 2m−1(n + 1)n and is generated by a generalized polynomial g(x 1 2m ) ∈ F2[x, 1 2m Z≥0] of degree 2mr. Furthermore, C0 n is embedded in Cm 2m−1(n+1)n and Cm 2m−1(n+1)n is embedded in Cm+1 2m(n+1)n for each m ≥ 1. By a newly proposed algorithm, codewords of the binary BCH code C0 n can be transmitted with high code rate and decoded by the decoder of any member of the family {Cm 2m−1(n+1)n}m≥1 of binary cyclic codes, having the same code rate.

Construções euclidianas e o desfecho de problemas famosos da geometria

Construction techniques with ruler and the compasses, fundamental on Euclidean geometry, have been related to modern algebraic theories such as solving equations and extension of bodies from the works by Paolo Ruffini (1765-1822), Niels Henrik Abel (1802-1829) and Evariste Galois (1811-1832). This relation could provide an answer to some famous problems, from ancient Greece, such as doubling the cube, the trisection Angle, the Quadrature of the Circle and the construction of regular polygons, which remained unsolved for over two thousand years. Also important for our purposes are the notions of algebraic numbers, transcendental and the criteria for constructability, of those numbers. The objective of this study is to reconstruct relevant steps of geometric constructions with ruler (unmarked) and the compasses, from the elementary to the outcome buildings, in the nineteenth century, considering those mentioned problems.

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.

Goppa codes over certain semigroups

A Goppa code is described in terms of a polynomial, known as Goppa polynomial, and in contrast to cyclic codes, where it is difficult to estimate the minimum Hamming distance d from the generator polynomial. Furthermore, a Goppa code has the property that d ≥ deg(h(X))+1, where h(X) is a Goppa polynomial. In this paper, we present a decoding principle for Goppa codes constructed by generalized polynomials, which is based on modified Berlekamp-Massey algorithm.

A Note on Linear Codes over Semigroup Rings

In this paper, we introduced new construction techniques of BCH, alternant, Goppa, Srivastava codes through the semigroup ring B[X; 1 3Z0] instead of the polynomial ring B[X; Z0], where B is a finite commutative ring with identity, and for these constructions we improve the several results of [1]. After this, we present a decoding principle for BCH, alternant and Goppa codes which is based on modified Berlekamp-Massey algorithm. This algorithm corrects all errors up to the Hamming weight t ≤ r/2, i.e., whose minimum Hamming distance is r + 1.

A note about splittings of groups and commensurability under a cohomological point of view

Let G be a group, let S be a subgroup with infinite index in G and let FSG be a certain Z2G-module. In this paper, using the cohomological invariant E(G, S, FSG) or simply E˜(G, S) (defined in [2]), we analyze some results about splittings of group G over a commensurable with S subgroup which are related with the algebraic obstruction “singG(S)" defined by Kropholler and Roller ([8]. We conclude that E˜(G, S) can substitute the obstruction “singG(S)" in more general way. We also analyze splittings of groups in the case, when G and S satisfy certain duality conditions.

A dual homological invariant and some properties

Based on the cohomology theory of groups, Andrade and Fanti defined in [1] an algebraic invariant, denoted by E(G,S, M), where G is a group, S is a family of subgroups of G with infinite index and M is a Z2G-module. In this work, by using the homology theory of groups instead of cohomology theory, we define an invariant ``dual'' to E(G, S, M), which we denote by E*(G, S, M). The purpose of this paper is, through the invariant E*(G, S, M), to obtain some results and applications in the theory of duality groups and group pairs, similar to those shown in Andrade and Fanti [2], and thus, providing an alternative way to get applications and properties of this theory.

Schur-Szegö composition of entire functions

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

Tomografia da ionosfera a partir do GNSS e técnicas algébricas: estudo de caso para a região brasileira

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Transformações de Bäcklund para hierarquias integráveis abelianas

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Caracterização e redução das oscilações espúrias resultantes da representação de linhas de transmissão por meio de elementos discretos de circuitos

Pós-graduação em Engenharia Elétrica - FEIS

Identificação de forças de excitação em sistemas rotativos utilizando funções ortogonais

Pós-graduação em Engenharia Mecânica - FEIS