Revista Matemática Complutense

Servicio de Publicaciones de la Universidad Complutense de Madrid

- Volumen 19, n° 2  (2006) - 

Más información/Texto completo en http://revistas.ucm.es/portal/ ....

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Fundamental Groups of Some Special Quadric Arrangements    
AMRAM, Meirav | TEICHER, Mina
259 
Palabras Clave: Fundamental groups; Complement of curve; Conic arrangement.
 
Resumen: Continuing our work on the fundamental groups of conic-line arrangements [3], we obtain presentations of fundamental groups of the complements of three families of quadric arrangements in P2. The first arrangement is a union of n conics, which are tangent to each other at two common points. The second arrangement is composed of n quadrics which are tangent to each other at one common point. The third arrangement is composed of n quadrics, n−1 of them are tangent to the nth one and each one of the n − 1 quadrics is transversal to the other n − 2 ones.
 

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Stabilization of a Coupled Multidimensional System    
NICAISE, Serge | SENE, Abdoulaye
277 
Palabras Clave: Multidimensional structures; Stabilization; Exponential decay.
 
Resumen: We introduce a model of a vibrating multidimensional structure made of a n-dimensional body and a one dimensional rod. We actually consider the anisotropic elastodynamic system in the n-dimensional body and the Euler-Bernouilli beam in the one-dimensional rod. These equations are coupled via their boundaries. Using appropriate feedbacks on a part of the boundary we show the exponential decay of the energy of the system.
 

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Anisotropic Besov Spaces and Approximation Numbers of Traces on Related Fractal Sets     
TAMÁSI, Erika
297 

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Inf-Convolution and Regularization of Convex Functions on Riemannian Manifolds of Nonpositive Curvature     
AZAGRA, Daniel | FERRERA, Juan
323 
Palabras Clave: Inf-convolution; Convex function; Regularization; Riemannian manifold.
 
Resumen: We show how an operation of inf-convolution can be used to approximate convex functions with C1 smooth convex functions on Riemannian manifolds with nonpositive curvature (in a manner that not only is explicit but also preserves some other properties of the original functions, such as ordering, symmetries, infima and sets of minimizers), and we give some applications.
 

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Extension of Lipschitz Functions Defined on Metric Subspaces of Homogeneous Type     
BRUDNYI, Alexander | BRUDNYI, Yuri
347 
Palabras Clave: Metric space of homogeneous type; Lipschitz function; Linear extension.

Resumen: If a metric subspace Mo of an arbitrary metric space M carries a doubling measure µ, then there is a simultaneous linear extension of all Lipschitz functions on Mo ranged in a Banach space to those on M. Moreover, the norm of this linear operator is controlled by logarithm of the doubling constant of µ.
 

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Applications of Contractive-like Mapping Principles to Fuzzy Equations     
NIETO, Juan J. | RODRÍGUEZ LÓPEZ, Rosana
361 
Palabras Clave: Fixed points; Fuzzy sets; Fuzzy equations; Fuzzy differential equations; Upper and lower solutions; Existence and uniqueness of solution.
 
Resumen: We recall a recent extension of the classical Banach fixed point theorem to partially ordered sets and justify its applicability to the study of the existence and uniqueness of solution for fuzzy and fuzzy differential equations. To this purpose, we analyze the validity of some properties relative to sequences of fuzzy sets and fuzzy functions.
 

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Berezin and Berezin-Toeplitz Quantizations for General Function Spaces     
ENGLIS, Miroslav
385 
Palabras Clave: Berezin quantization; Berezin-Toeplitz quantization; Star product; Harmonic Bergman space; Sobolev-Bergman space; Reproducing kernel.
 
Resumen: The standard Berezin and Berezin-Toeplitz quantizations on a K¨ahler manifold are based on operator symbols and on Toeplitz operators, respectively, on weighted L2-spaces of holomorphic functions (weighted Bergman spaces). In both cases, the construction basically uses only the fact that these spaces have a reproducing kernel. We explore the possibilities of using other function spaces with reproducing kernels instead, such as L2-spaces of harmonic functions, Sobolev spaces, Sobolev spaces of holomorphic functions, and so on. Both positive and negative results are obtained.
 

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Singular Poisson Reduction of Cotangent Bundles    
HOCHGERNER, Simon | RAINER, Armin
431 

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Structure of the Hardy Operator Related to Laguerre Polynomials and the Euler Differential Equation     
KRUGLYAK, Natan | MALIGRANDA, Lech | PERSSON, Lars-Erik
467 

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Interpolation of the Measure of Non Compactness between Quasi-Banach Spaces     
FERNÁNDEZ MARTÍNEZ, Pedro
477 
Palabras Clave: Measure of non-compactness; Interpolation theory; Quasi-Banach spaces.
 
Resumen: We study the behavior of the ball measure of non-compactness under several interpolation methods. First we deal with methods that interpolate couples of spaces, and then we proceed to extend the results to methods that interpolate finite families of spaces. We will need an approximation hypothesis on the target family of spaces.
 

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