El sentimiento estético de los matemáticos : acercamiento a la belleza matemática

Fil: Amster, Pablo. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina.Es posible hablar de belleza en una disciplina como la Matemática, habitualmente clasificada entre\nlas ciencias "duras"? En este artículo se propone un breve recorrido informal por algunos de sus\nvariados temas, desde las clásicas construcciones de la geometría hasta otros resultados un tanto\nmás inquietantes, que revelan en ella un carácter inesperado... casi podría decirse, un carácter\nromántico

Symmetry breaking for an elliptic equation involving the fractional Laplacian.

We study the symmetry breaking phenomenon for an elliptic equation involving the fractional Laplacian in a large ball. Our main tool is an extension of the Strauss radial lemma involving the fractional Laplacian, which might be of independent interest; and from which we derive compact embedding theorems for a Sobolev-type space of radial functions with power weights.Fil: Amster, Pablo Gustavo. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló". Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; Argentina. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentin

On a Dirichlet boundary value problem for an Ermakov-Painlevé I equation : a Hamiltonian EPI system

Here, a proto-type Ermakov–Painlevé I equation is introduced and a homogeneous Dirichlet-type boundary value problem analysed. In addition, a novel Ermakov– Painlevé I system is set down which is reducible by an involutory transformation to the autonomous Ermakov–Ray–Reid system augmented by a single component Ermakov– Painlevé I equation. Hamiltonian such systems are delimited

An iterative method for a second order problem with nonlinear two-point boundary conditions.

A semi-linear second order ODE under a nonlinear two-point boundary condition is considered. Under appropriate conditions on the nonlinear term of the equation, we define a two-dimensional shooting argument which allows to obtain solutions for some specific situations by the use of Poincar´e-Miranda’s theorem. Finally, we apply this result combined with the method of upper and lower solutions and develop an iterative sequence that converges to a solution of the problem

An iterative method for a second order problem with nonlinear two-point boundary conditions

A semi-linear second order ODE under a nonlinear two-point boundary condition is considered. Under appropriate conditions on the nonlinear term of the equation, we define a two-dimensional shooting argument which allows to obtain solutions for some specific situations by the use of Poincaré-Miranda?s theorem. Finally, we apply this result combined with the method of upper and lower solutions and develop an iterative sequence that converges to a solution of the problem.Fil: Amster, Pablo Gustavo. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; ArgentinaFil: Cárdenas Alzate, Pedro Pablo. Universidad Tecnológica de Pereira; Colombi