Sistema Regional de Información
en línea para Revistas Científicas de América Latina,
el Caribe, España y Portugal

In the present work, we describe some results about the K-theory of Z-graded algebras. First, in the context of C* algebras, we begin with the Pimsner-Voiculescu sequence for crossed products and its generalizations. We will see that there are results analog to these in the context of locally convex algebras and we conclude with results for generalized Weyl algebras.

Interrelationships between two species are a basic theme in Population Dynamics, particularly the interaction between predators and their prey. This importance is due to the fact that it allows a deeper understanding of the behavior of complex food webs. In this paper we extend the analysis of a modified Leslie-Gower predator-prey model by assuming that the functional response is sigmoid or Holling type III and the predator have an alternative food. We show that the system representing the model has up to three positive equilibrium points; we establish conditions to determine the nature of each equilibrium point. In addition, we show the existence of different types of bifurcations, including those of Hopf and the homoclinic. The analytical results are discussed from an ecological perspective.

This work is intended to provide basic information and numerical experimentation of biological models focusing on how computation can be used to generate results via software R. In addition, this work enriches the scientific literature in Spanish that links mathematics and computational biology. It also provides detailed information on the analysis of Predator-prey, Toxoplasma gondii, and Common influency models. For the development of this article we will speak in the first instance of the dynamics of the predator-prey model. In the last two models, it is solved numerically for a range of values of a given parameter. This in order to show deductions that contribute to a deeper investigation of the data involved, and even to the analysis of a professional specialized in the model.

In this work, the ecologically well-posedness of a predator-prey model is demonstrated by showing that a region of the first quadrant is a positively invariant attracting set for the solutions of that model. The predator-prey model considers logistic-type growth in both populations and a non-differentiable functional response that generalizes previous ones. Due to non-differentiability, there is no uniqueness of solutions, and the standard methodology cannot be applied directly. Topological equivalences, geometrical arguments, and the Poincare-Bendixson theorem are used to obtain our result.

In several previous works, different predation models have been modified by considering the use of prey refuges, for which a partial analysis of their dynamics is done. In some of them, it is stated that the use of refuge has a stabilizing effect on the predator-prey interaction. One of the purposes of this paper is to show that some of these new systems, derived from the Lotka-Volterra model, this assertion is not fulfilled. In this work, several of the models studied have more than one positive equilibrium point, and the behavior of the solutions is highly dependent on the initial conditions

In this work we establishe relations between modules over a ring and vector spaces, we show results of linear algebra that can be extended to modules and we present counterexamples to those ones that cannot be extended. By identify abelian groups with Z-modules we classify every the finitely generated abelian groups and we show a decomposition in direct sum of ciclic subgroups. Finally, we apply the results about finitely generated abelian groups to determine the rational canonical form of an endomorphis of finitely generated K[t]-modules and simplify the computer of associated numbers to the endomorphism, for example: therank and the determinant.

We discuss a sharpened Hausdorff–Young inequality for n-dimensional Hermite expansions.

In this brief note we give an overview of Hardy spaces Hp and bounded mean oscillation spaces, BMO, two classic spaces that have played an important role in investigations of central branches in harmonic analysis. The given bibliography opens paths to follow in this field.

In this work, we study the geometry of 2x2 order matrix curves with real coefficients. We use the Gram-Schmidt orthogonalization process to generate a convenient moving benchmark. Thus, we obtain the Frenet-Serret formulas. We present a version of the fundamental theorem of 2x2 matrix curves.

The objetive of these notes is to give a brief overview of wavelet theory, both of the fundamental mathematical arguments and of the ideas it contains. In addition, the theory is suitable for multidisciplinary work.