Efeito do 1,3/1,6 beta-glucano no sistema imune de cadelas submetidas a ovário-histerectomia

Pós-graduação em Medicina Veterinária - FCAV

A note on units of finite local rings in an ascending chain

In this paper we present matrices over unitary finite commutative local rings connected through an ascending chain of containments, whose elements are units of the corresponding rings in the chain such that the McCoy ranks are the largest ones.

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.

The cohomological invariant E'(G,W) and some properties

Let G be a group, W a nonempty G-set and M a Z2G-module. Consider the restriction map resG W : H1(G,M) → Pi wi∈E H1(Gwi,M), [f] → (resGG wi [f])i∈I , where E = {wi, i ∈ I} is a set of orbit representatives in W and Gwi = {g ∈ G | gwi = wi} is the G-stabilizer subgroup (or isotropy subgroup) of wi, for each wi ∈ E. In this work we analyze some results presented in Andrade et al [5] about splittings and duality of groups, using the point of view of Dicks and Dunwoody [10] and the invariant E'(G,W) := 1+dimkerresG W, defined when Gwi is a subgroup of infinite index in G for all wi in E, andM = Z2 (where dim = dimZ2). We observe that the theory of splittings of groups (amalgamated free product and HNN-groups) is inserted in the combinatory theory of groups which has many applications in graph theory (see, for example, Serre [12] and Dicks and Dunwoody [10]).

Some considerations about cohomology of finite groups

In this work we present some considerations about cohomology of finite groups. In the first part we use the restriction map in cohomology to obtain some results about subgroups of finite index in a group. In the second part, we use Tate cohomology to present an application of the theory of groups with periodic cohomology in topology.

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.

Quaternion orders over quadratic integer rings from arithmetic fuchsian groups

In this paper we show that the quaternion orders OZ[ √ 2] ≃ ( √ 2, −1)Z[ √ 2] and OZ[ √ 3] ≃ (3 + 2√ 3, −1)Z[ √ 3], appearing in problems related to the coding theory [4], [3], are not maximal orders in the quaternion algebras AQ( √ 2) ≃ ( √ 2, −1)Q( √ 2) and AQ( √ 3) ≃ (3 + 2√ 3, −1)Q( √ 3), respectively. Furthermore, we identify the maximal orders containing these orders.

Bit-parallel coprocessor for standard ECC-GF(2m) on FPGA

This paper presents the design of a high-speed coprocessor for Elliptic Curve Cryptography over binary Galois Field (ECC- GF(2m)). The purpose of our coprocessor is to accelerate the scalar multiplication performed over elliptic curve points represented by affine coordinates in polynomial basis. Our method consists of using elliptic curve parameters over GF(2163) in accordance with international security requirements to implement a bit-parallel coprocessor on field-programmable gate-array (FPGA). Our coprocessor performs modular inversion by using a process based on the Stein's algorithm. Results are presented and compared to results of other related works. We conclude that our coprocessor is suitable for comparing with any other ECC-hardware proposal, since its speed is comparable to projective coordinate designs.

Fourier series for quaternions and the square of the error theorem

In this paper we introduce a type of Hypercomplex Fourier Series based on Quaternions, and discuss on a Hypercomplex version of the Square of the Error Theorem. Since their discovery by Hamilton (Sinegre [1]), quaternions have provided beautifully insights either on the structure of different areas of Mathematics or in the connections of Mathematics with other fields. For instance: I) Pauli spin matrices used in Physics can be easily explained through quaternions analysis (Lan [2]); II) Fundamental theorem of Algebra (Eilenberg [3]), which asserts that the polynomial analysis in quaternions maps into itself the four dimensional sphere of all real quaternions, with the point infinity added, and the degree of this map is n. Motivated on earlier works by two of us on Power Series (Pendeza et al. [4]), and in a recent paper on Liouville’s Theorem (Borges and Mar˜o [5]), we obtain an Hypercomplex version of the Fourier Series, which hopefully can be used for the treatment of hypergeometric partial differential equations such as the dumped harmonic oscillation.

A note on pairs of regular foliations on the solid torus

We discuss the geometry of the pair of foliations on a solid torus given by the Reeb foliation together with discs transverse to the boundary of the torus.