Utilizando una información compleja y cualitativa (la escritura de los dos primeros nombres) se presenta un método que permite cuantificar adecuadamente las diferencias entre catorce lenguas europeas construyendo una matriz de distancias. Para realizar el estudio comparativo se emplean dos técnicas de análisis multivariante: el análisis de proximidades ("multidimensional scaling") y el análisis jerárquico de conglomerados ("hierarchical cluster analysis").
Given a set of points in the complex plane, an incomplete polynomial is defined as the one which has these points as zeros except one of them. The classical result known as Gauss-Lucas theorem on the location of zeros of polynomials and their derivatives is extended to convex linear combinations of incomplete polynomials. An integral representation of convex linear combinations of incomplete polynomials is also given.
We study one-parameter families of diffeomorphisms unfolding heterodimensional cycles (i.e. cycles containing periodic points of different indices). We construct an open set of such arcs such that, for a subset of the parameter space with positive relative density at the bifurcation value, the resulting nonwandering set is the disjoint union of two hyperbolic basic sets of different indices and a strong partially hyperbolic set which is robustly transitive. The dynamics of the diffeomorphisms we...
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