Selecciones Matemáticas

137-153

Authors: Osmar Alêssio

In this paper, we study the differential geometry of the transversal intersection curve of two surfaces in Minkowski 3-space, where each pair satisfies the following types spacelike-lightlike, timelike-lightlike and lightlike-lightlike. Surfaces are generally give by their parametric or implicit equations, then the surfacesurface intersection problem appear commonly as parametric-parametric, parametric-implicit and implicitimplicit. We derive the Frenet frame, Darboux frame, curvature, torsion, normal curvature and geodesic curvatures of transversal intersections for all types of intersection problems. We show the intersection curve may be spacelike (timelike, lightlike or pseudo null) curve. Finally, we show our methods by given several examples.

164-174

Authors: Frank Henry Acasiete Quispe

We studied the uniform stabilization of a class of Timoshenko systems with partial dissipation of the beam. Our main result is to prove that the semigroup associated to this model has polynomial decay. Moreover, we prove that the semigroup decays polynomially to zero. The system decays polynomially with rate depending on the coeficients of the problem. We also show the computational modeling of the system showing the results obtained theoretically.

193-203

Authors: C. E. Rubio-Mercedes

The FitzHugh-Nagumo system has a special type of solution called traveling wave, which has the form u(x, t) =f(x − μt) and w(x, t) =g(x − μt), which is a stable solution over time. Our interest is to numerically characterize the profile of a traveling wave (f-g) and its propagation speed μ(t). With a change of variables, we transform the problem of finding the solutions in original coordinates to a problem of finding the equilibria in a new coordinate system called mobile coordinates or non-local coordinate system. aa With numerical examples we will demonstrate that the solutions of the system of EDPs in non-local coordinates converge to a traveling wave of the original problem. The non-local coordinate system also allows to calculate the exact propagation speed.

212-229

Authors: Edwin O. S. Reyes

In [2], was obtained a characterization of the surfaces in R3 which are envelopes of a sphere congruence in R3, in which the other envelope is in R2. In this paper, we characterize the surfaces of H3 and S3 which are envelopes of a congruence of geodesic spheres in H3 and S3, respectively, in which the other envelope is contained in H2⊂H3 and S2⊂S3. We show that this characterization allows locally to obtain a parameterization of the surfaces contained in H3 and S3, this characterization extends the result obtained in [2]. Moreover, we provide sufficient conditions for these surfaces to be locally associated by a transformation of Ribaucour. Also, we present families of surfaces parameterized by lines of curvature in H3 and S3, which depend on a function of two variables which is solution of a differential equation. Finally, we characterize the surfaces of the spherical type ∑ in H3 and S3, as the surfaces where its radius function is the solution of the Helmholtz equation.

241 - 248

Authors: Edgar Vera Saravia

We offer a geometric introduction to the two-dimensional Euclidean Space E2 using both the geometric approach of the affine R-Space and the two-dimensional Geometric Algebra. These notes, intented for university proffessors of physics and mathematics, try to emulate the program developed by Felix Kline in the first decade of the 20th century.