Sumario:
Revista Matemática Complutense
Servicio de Publicaciones de la Universidad Complutense de Madrid
Volumen 20  Número 1 (2007)
Más información/Texto completo en http://revistas.ucm.es/portal/ ....

1. Contenidos/Contents
 Permanents, Order Statistics, Outliers, and Robustness BALAKRISHNAN, N. 7 Palabras Clave: Order statistics; Permanents; Logconcavity; Outliers; Singleoutlier model; Multipleoutlier model; Recurrence relations; Robust estimators; Sensitivity; Bias; Mean square error; Locationoutlier; Scaleoutlier; Censoring; Progressive TypeII censoring; Resumen: In this paper, we consider order statistics and outlier models, and focus primarily on multipleoutlier models and associated robustness issues. We first synthesise recent developments on order statistics arising from independent and nonidentically distributed random variables based primarily on the theory of permanents. We then highlight various applications of these results in evaluating the robustness properties of several linear estimators when multiple outliers are possibly present in the sample.
 On Rough and Smooth Neighbors BANKS, William D.  LUCA, Florian  SHPARLINSKI, Igor E. 109 Palabras Clave: Smallest prime divisor; Largest prime divisor.
 The Asymptotic Dimension of the First Grigorchuk Group Is Infinity SMITH, Justin 119 Palabras Clave: Asymptotic dimension. Resumen: We describe a sufficient condition for a finitely generated group to have infinite asymptotic dimension. As an application, we conclude that the first Grigorchuk group has infinite asymptotic dimension.
 Handlebody Splittings of Compact 3Manifolds with Boundary SUZUKI, Shin’ichi 123 Palabras Clave: 3manifolds with boundary; Heegaard splittings. Resumen: The purpose of this paper is to relate several generalizations of the notion of the Heegaard splitting of a closed 3manifold to compact, orientable 3manifolds with nonempty boundary.
 Semigroup Conditions for Affine Algebraic Plane Curves with More than One Place at Infinity WIGHTWICK, Penelope G. 139 Palabras Clave: Affine algebraic curves; Classification; Link at infinity. Resumen: An interesting and open question is the classification of affine algebraic plane curves. Abhyankar and Moh [1] completely described the possible links at infinity for those curves where the link has just one component, a knot. Such curves are said to have one place at infinity. The AbhyankarMoh result has been of great assistance in classifying those polynomials which define a connected curve with one place at infinity. This paper provides a new proof of the AbhyankarMoh result which is then used to find a description for the case where the polynomial defines a curve with one point at infinity.
 On Polynomials That Are Sums of Two Cubes HOOLEY, Christopher 207 Palabras Clave: Polynomials; Cubes. Resumen: It is proved that, if F(x) be a cubic polynomial with integral coefficients having the property that F(n) is equal to a sum of two positive integral cubes for all sufficiently large integers n, then F(x) is identically the sum of two cubes of linear polynomials with integer coefficients that are positive for sufficiently large x. A similar result is proved in the case where F(n) is merely assumed to be a sum of two integral cubes of either sign. It is deduced that analogous propositions are true for cubic polynomials F(x0, . . . , xr) in more than one indeterminate.
 DivCurl Young Measures and Optimal Design in Any Dimension PEDREGAL, Pablo 239 Palabras Clave: Highdimensional conductivity; Cost depending on the field; Relaxed formulation. Resumen: We explicitly introduce and exploit divcurl Young measures to examine optimal design problems governed by a linear state law in divergence form. The cost is allowed to depend explicitly on the gradient of the state. By means of this family of measures, we can formulate a suitable relaxed version of the problem, and, in a subsequent step, put it in a similar form as the original optimal design problem with an appropriate set of designs and generalized state law. Many of the issues involved has been analyzed elsewhere. The emphasis here is placed on the fact that, by using divcurl Young measures, we make the treatment dimensionindependent.
