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Revista Matemática Complutense Nº 20

Nombre de la Revista: Revista Matemática Complutense
Número de Sumario: 20
Fecha de Publicación: 2007/1

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     

Palabras Clave: Order statistics; Permanents; Log-concavity; Outliers; Single-outlier model; Multiple-outlier model; Recurrence relations; Robust estimators; Sensitivity; Bias; Mean square error; Location-outlier; Scale-outlier; Censoring; Progressive Type-II censoring;
In this paper, we consider order statistics and outlier models, and focus primarily on multiple-outlier models and associated robustness issues. We first synthesise recent developments on order statistics arising from independent and non-identically 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.
Palabras Clave: Smallest prime divisor; Largest prime divisor.

The Asymptotic Dimension of the First Grigorchuk Group Is Infinity    
SMITH, Justin
Palabras Clave: Asymptotic dimension.
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 3-Manifolds with Boundary   
SUZUKI, Shin’ichi
Palabras Clave: 3-manifolds with boundary; Heegaard splittings.
The purpose of this paper is to relate several generalizations of the notion of the Heegaard splitting of a closed 3-manifold to compact, orientable 3-manifolds with nonempty boundary.  

Semi-group Conditions for Affine Algebraic Plane Curves with More than One Place at Infinity     
WIGHTWICK, Penelope G.
Palabras Clave: Affine algebraic curves; Classification; Link at infinity.
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 Abhyankar-Moh 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 Abhyankar-Moh 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
Palabras Clave: Polynomials; Cubes.
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. 

Div-Curl Young Measures and Optimal Design in Any Dimension   
Palabras Clave: High-dimensional conductivity; Cost depending on the field; Relaxed formulation.
We explicitly introduce and exploit div-curl 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 div-curl Young measures, we make the treatment dimension-independent.

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