Selecciones Matemáticas

2

Authors: Nelson Aragonés Salazar

En este trabajo se presentan dos principios de descarte para solucionar el problema de la minimización de una función supermodular definida en un ret´ıculo finito relativamente complementado. Este resultado generaliza el presentado en [1] para el caso de una función supermodular definida en la clase de subconjuntos de un conjunto finito dado.

9

Authors: Irla Mantilla

En el presente trabajo se estudia una Ecuación Diferencial Parcial Hiperbólica con término fuente no homogéneo de segundo orden, su forma canónica, su resolución mediante la fórmula de D’Alembert y el Teorema de Green. Para la resolución de este problema solo se requiere las condiciones iniciales mixtas. Existen diversos problemas físicos que conducen a este tipo de modelo matemático, por lo cual esta técnica de resolución contribuye al conocimiento de encontrar soluciones explícitas de problemas como por ejemplo tipo onda bidimensional sometidos a fuerzas exteriores. Dentro de los resultados se genera la solución explícita de tres casos: respecto a la homogeneidad y no homogeneidad de las condiciones iniciales y del término fuente, desde el punto de vista de solución analítica para funciones de clase C2.

10

Authors: Carlos Carrión Riveros

In this work, we present explicit parameterizations of hypersurfaces parameterized by lines of curvature with prescribed Gauss map and we characterize the hypersurfaces with planar curvature lines. As an application we obtain a classification of isothermic surfaces with respect to the third fundamental form with two planar curvature lines. Also, we present a class of surfaces with one family of planar curvature lines and generalize these results to present classes of hypersurfaces with families of planar curvature lines.

10

Authors: Luis J. Caucha

We simulated the dynamics of CO2 transport in the alveolar sacs of the human lung. Using Arbitrary Lagrangian Eulerian (ALE) framework, we control the movement domain for a normal and fast maneuver. The fluid of room air inspired and CO2 concentrations were approximated by Navier-Stokes and convection diffusion equations; the stress-stretch in the wall for different volumes were quantified in equal time of respiration. The expansion for a normal and forced maneuver were represented as 9 and 90% to the initial geometry. The difference of the CO2 was 73x10

13

Authors: Márcio Rostirolla Adames

This article consider the classical problem of linear non-homogeneous second order Initial Value Problems with analytic coefficients. It classifies the possible kinds of analytic solutions, giving criteria for the nonexistence of analytical solutions and for the existence of multiple analytic solutions. An alternative proof for the convergence of the power series method is given and it applies for some singular irregular points.

15

Authors: Maruja Gavilán Gonzales

El objetivo del presente trabajo es estudiar algunas propiedades y aplicaciones de la función Gamma, denotada por

5

Authors: Nélida Medina García

We consider the ring of polynomials R = K[x1, dots,xn] in the variables x1, dots,xn and complex coefficients. The permutation group of 1, dots,n acts sore R by permuting the variables. The set of invariants by this action forms a ring generated by elementary symmetric polynomials. Emmy Noether proves that if a finite group of inverse matrices G subsetGL(n;k) acts on R, then the ring of invariants is generated by a finite number of invariant homogeneous and defines an operator in G to obtain invariant polynomials. There are algebraic relationships between the generators of the invariant ring and the orbits of Cn/G. In 1963, Masayoshi Nagata demonstrated that the ring of the invariants of geomagically reductive groups is finitely generated. We analice the existence of a quotient variety X/G where G is an algebraic group acting on an algebraic variety X.

8

Authors: César Torres Ledesma

In this paper we consider the fractional Hamiltonian system given by (0.2) −tDα T(0Dα t u(t)) = ∇F(t,u(t)), a.e t ∈ [0,T] u(0) = u(T) = 0. where α ∈ (1/2,1), t ∈ [0,T],u∈Rn, F : [0,T]×Rn →R is a given function and ∇F(t,u) is the gradient of F at u. The novelty of this paper is that, using a modified version of mountain pass theorem for functional bounded from below we prove the existence of at least three solutions for (0.2).

10

Authors: Obidio Rubio

In this paper we present an estimate of the posterior error of finite element-constructed finite element meshes and finite element discontinuous over time for the transport equation of CO2 in the bags Alveolar cells of the human lung, using the dual weighted residual method (DWR).

12

Authors: Liliana Puchuri Medina

The classic Lotka-Volterra model belongs to a family of differential equations known as “Generalized Lotka-Volterra”, which is part of a classification of four models of quadratic fields with center. These models have been studied to address the Hilbert infinitesimal problem, which consists in determine the number of limit cycles of a perturbed hamiltonian system with center. In this work, we first present an alternative proof of the existence of centers in Lotka-Volterra predator-prey models. This new approach is based in algebraic equations given by Kapteyn, which arose to answer Poincar´e’s problem for quadratic fields. In addition, using Hopf Bifurcation theorem, we proof that more realistic models, obtained by a non-linear perturbation of a classic Lotka-Volterra model, also possess limit cycles.

13

Authors: Yuri Sampaio Maluf

This paper discusses the Hawkes process to modeling of the offering book, especially the ETF it iShare Ibovespa index fund. The study aimed to investigate the dynamics of the influences of the offers in relation to the past orders. We study too to the interaction of the order rates of the opposing sides of the Book. Another point addressed is the verification of the operating strategy that captures the dynamics studied. At the first moment, the univariate approach was performed and in the second moment the multivariate of the Hawkes process. The results show that in both cases the Hawkes process it fits well to the data. The fit model indicates that agents have similar behaviors when they act as buyers or sellers of assets. As for the strategy, it was not possible to establish spare gains from changes in bid rates. However, these results are due to the it bid-ask spread more that the predictive capacity of the functions.

20

Authors: Julio Becerra Saucedo

This article presents an analytical study on the local and global existence of the solution of diffusion - reaction problem. We show that if the solution exists locally then, it blows up in finite time. This result covers the case that the solution exists globally. We concluded that the maximum time of existence of the solution depends on the domain, the term representing the reaction in the equation and a test function defined in this job. Likewise we propose the possibility of extending the local existence to the global one using the proper solution framework.