Selecciones Matemáticas

1 - 13

Authors: Erick Manuel Delgado Moya, Aymee Marrero Severo

The Zika Virus (ZIKV) is a virus transmitted by Aedes aegypti mosquitoes (same as the one transmitting dengue and chikungunya fever). The main way of contagion by the ZIKV is caused by the bite of a mosquito that, after feeding from someone contaminated, can transport the virus throughout its life, transmitting the disease to a population that does not have the immunity. It can also be transmitted through a person’s sexual relationship with ZIKV to their partners, even if the infected person does not have the symptoms of the disease. In this work, we present two mathematical models for the Zika epidemic by using (1) ordinary differential equations and, (2) ordinary differential equations with temporal delay (discrete), which is the time it takes mosquitoes to develop the virus. We make a comparison between the two modeling variants. Computational simulations are performed for Suriname and El Salvador, which are countries that are prone to develop the epidemic in an endemic manner.

19 - 25

Authors: Carlos M. C. Riveros

In this paper we introduce the generalized Helmholtz equation and present explicit solutions to this generalized Helmholtz equation, these solutions depend on three holomorphic functions. As an application we present explicit solutions to the Helmholtz equation. We note that these solutions are not necessarily limited to certain domains of the complex plane C.

31-34

Authors: Alberto Torchinsky

We solve the Cauchy problem for the n-dimensional wave equation using elementary properties of the Bessel functions

41 - 48

Authors: Jorge Eliecer Hernádez Hernández

This article presents some fractional integral inequalities of the Hermite-Hadamard and Minkowski type using the fractional integral operator defined by R.K. Raina (2016) in [1], which generalize some previous results found by L. Bougoffa [5] and S.S. Dragomir [7].

66 - 76

Authors: Neisser Pino Romero

In the present work, the existence of Uniformly Bound Solutions of a SI Mathematical Model with vital dynamics, with logistic growth for the Susceptibles, developed by Delay Differential Equations is constructed, and the behavior of the solutions will be studied (qualitative analysis) for the Infection-Free Point where the necessary conditions for its asymptotic stability will be determined; and furthermore, that the Uniformly Bounded Solution of the Model tends to the steady state of the Infection-Free Point. In addition, it will be simulated computationally (approximate solutions) with initial populations and epidemiological rates of the model. The simulation will complement the qualitative analysis (behavior of solutions) to conclude trends of behaviors of the transmission of the disease over time.

84 - 97

Authors: Carolina A. Silva

This paper presents a regression model for discrete time data with cure fraction. For this purpose, we considered a mixture model, in which times are modeled through the discrete Weibull distribution and the cure probability modeled with covariates by using the logit link function. Considering that the model is a mixture, the estimation of the parameters was performed by EM algorithm. The behavior of the estimating algorithm was tested with Monte Carlo simulation experiments and an application for real data was added.

108 - 118

Authors: Franco Rubio López

In this paper we obtain some upper bounds for the minimum of the Weber function on a strongly convex ball in a Riemannian manifold with positive sectional curvature; where the minimum is reached on the weighted geometric median of “m” given points in the strongly convex.

128 - 139

Authors: Segundo B. Correa Erazo

In this article we generate graphs of fractal curves, which are determined as fixed points of a contractive operator. To do this, we consider five points P1; P2; P3; P4 y P5 in the plane and two affine transformations w1;w2, the same ones that will constitute a system of iterated functions (IFS) with only two contractive transformations. for the visualization of the graphs a program in mathematica 11.0 called fractalfunction has been created and we choose as the starting point of the iterative process the set [P1; P5].

121-136

Authors: Juan Montealegre

In this paper we study the local well-posedness of the initial value problem for a Nutku-Oguz-Burgers system with time dependent coefficients, formed by two Korteweg-de Vries equations coupled through the non-linear terms. The system appears as a model of wave propagation in a shallow channel with variable bottom surface, in which both nonlinear and dispersive effects are relevant. The proof of existence and uniqueness of local solution and the continuous dependence on the initial data of the local solution in Sobolev spaces Hs(R)xHs(R), s > 3/2, are based on the works [9] and [17].

154-163

Authors: Raúl Sánchez A.

We study the existence of weak solution for a non-linear problem with fractional p-Laplacian operator for the case where the order of the fractional derivative is 1/p

175-192

Authors: Jhelly Reynaluz Pérez Núñez

In epidemiological mathematics, the SIR model is well known, as well as the diseases that can be simulated with this model. In the present work starting from a SIR model with vital dynamics, a host-vector model is elaborated, where the transmission of the disease is no longer given by interaction of individuals of the same species, but is carried out by interaction of the susceptible individuals with the infected individuals, of both populations. Two host-vector models (MVH) with vital dynamics are also developed, initially maintaining the population constant, then with variable population and death due to disease.

204-211

Authors: Nelson Omar Aragonés Salazar

This article presents some properties of the casisupermodular function and demonstrates principles of discarding to solve the problem of minimization and maximization of this type of function defined in the family of subsets of a given finite set (finite boolean lattice); these principles are generalized, in the case of minimization, to a relatively complemented finite lattice. This work extends some results obtained by V.R. Khachaturov and R.V. Khachaturov for the case of supermodular functions.

230 - 240

Authors: Rina Roxana Paucar Rojas

The aim of this work is to study and describe the resolution or desingularization of irreducible quasi ordinary surfaces, following Lipman’s approach ( [6], [7]). To achieve our goal, we define the quasi ordinary surfaces and describe their parametrization by quasi ordinary branches, we also define the quasi ordinary rings, local rings of the quasi ordinary irreducible surfaces, then we study the relationship that exists between the tangent cone and singular locus of a quasi ordinary ring and the distinguished pairs of a quasi ordinary normalized branch that represents this ring. Also, we define the special transforms of a quasi ordinary ring and show that they are again quasi ordinary.

249 - 264

Authors: Obidio Rubio

We describe a model that interprets the circulation of the tropical ocean in the periods when the meteorological phenomenon known as ”El Ni˜no” appears; A study area is defined as being the equatorial pacific, the ocean current is described by the primitive equations, which consists of the equations of motion and temperature transport which are strongly coupled. As boundary conditions, the wind stresses on the surface of the ocean is fundamental for the warming of waters, which due to its high variability we consider it random and described by a multiplicative white noise, generating the so-called stochastic primitive equations for the circulation of the tropical ocean. The variational formulation of the problem is presented and some estimates that allow verifying the existence of solutions of these equations.

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.

4

Authors: Gerard Jhon Alva Morales

Estudiamos la inestabilidad en el sentido de Lyapunov de un punto de equilibrio de un sistema hamiltoniano con n grados de libertad para una clase amplia de energias potenciales. Mostraremos aquí que, esta clase de energias potenciales determinan condiciones suficientes para la inestabilidad de este punto de equilibrio.

6

Authors: Willy Zubiaga Vera

Sea E un espacio de Banach separable con norma |.|. En el presente trabajo, se tiene como objetivo construir una norma |.|1 que sea equivalente a |.|en E, tal que |.|1 sea estrictamente convexa. Además se demuestra que su norma dual conjugada es también estrictamente convexa.

7

Authors: Jorge Horna Mercedes

En este artículo presentamos algunas aplicaciones de dinámica simbolica en el campo de los sistemas dinámicos mediante la discretización del espacio.

19

Authors: Jenny Rojas Jerónimo

En este artículo presentamos la teoría que nos garantiza la convexificación de una función estrictamente monótona. Se demuestra un teorema y dos corolarios para la convexificación de funciones estrictamente monótonas dos veces continuamente diferenciables, luego se generaliza estos resultados para la convexificación de funciones estrictamente monótonas no diferenciables. Ambos casos son ejemplificados. Estos resultados se usan en optimización de funciones monótonas no diferenciables.