Revista Matemática Complutense

Servicio de Publicaciones de la Universidad Complutense de Madrid

Vol 21  Nº 1   (2008)

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

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3.  Contenidos / Contents  

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The Nonlinear Geometry of Banach Spaces.  
KALTON, Nigel J.
7 
Palabras Clave: Banach space; Nonlinear; Lipschitz; Uniform homeomorphism; Coarse embedding.
 
Resumen: We survey some of the recent developments in the nonlinear theory of Banach spaces, with emphasis on problems of Lipschitz and uniform homeomorphism and uniform and coarse embeddings of metric spaces.  

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Identifiability and Stability of Boundaries in a Supercritical Free Surface Flow.     
TENIOU, Djamel- Eddine | AIT-YAHIA, Rachida | HERNANE, Dahbia
61 
Palabras Clave: Inverse problem; Free boundary; Identifiability; Stability.
 
Resumen: In this paper, we have studied a problem of identifiability of boundaries and stability of the solutions for the direct and the inverse problem concerning a supercritical and irrotational ow of an inviscid uid over an obstacle which lies on the bottom of a channel. The identifiability of the solution means its uniqueness when it exists. The stability is studied in the sense that for the direct problem and the inverse one, we study the variation of the obtained geometry for a little perturbation of the bottom or of the free surface. The proofs of the theorems are based on Holmgren theorem and the mean value theorem. The stability obtained is linear.  

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A New Proof of the Jawerth-Franke Embedding.  
VYBÍRAL, Jan
75 
Palabras Clave: Besov spaces; Triebel-Lizorkin spaces; Sobolev embedding; Jawerth-Franke embedding.
 
Resumen: We present an alternative proof of the Jawerth embedding (...) The original proof given in [3] uses interpolation theory. Our proof relies on wavelet decompositions and transfers the problem from function spaces to sequence spaces. Using similar techniques, we also recover the embedding of Franke [2].  

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On Conjugacy of p-gonal Automorphisms of Riemann Surfaces.  
GROMADZKI, Grzegorz
83 
Palabras Clave: Automorphisms of Riemann surfaces; Fixed points; Ramified coverings of Riemann surfaces; Hyperellipticity.
 
Resumen: The classical Castelnuovo-Severi theorem implies that for g > (p-1)², a p-gonal automorphism group of a cyclic p-gonal Riemann surface X of genus g is unique. Here we deal with the case g ≤ (p-1)² we give a new and short proof of a result of Gonzalez-Diez that a cyclic p-gonal Riemann surface of such genus has one conjugacy class of p-gonal automorphism groups in the group of automorphisms of X.  

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Study of a Complete Abstract Differential Equation of Elliptic Type with Variable Operator Coefficients, I.  
FAVINI, Angelo | LABBAS, Rabah | LEMRABET, Keddour | SADALLAH, Boubaker-khaled
89 
Palabras Clave: Abstract differential equations of second order; Variable operator coefficients; Mixed boundary conditions; Maximal regularity; Compatibility conditions.
 
Resumen: The aim of this first work is the resolution of an abstract complete second order differential equation of elliptic type with variable operator coefficients set in a small length interval. We obtain existence, uniqueness and maximal regularity results under some appropriate differentiability assumptions combining those of Yagi [13] and Da Prato-Grisvard [6]. An example for the Laplacian in a regular domain of R³ will illustrate the theory. A forthcoming work (Part II) will complete the present one by the study of the Steklov-Poincaré operator related to this equation when the length δ of the interval tends to zero.  

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Entropy and Approximation Numbers of Embeddings of Function Spaces with Muckenhoupt Weights, I.  
HAROSKE, Dorothee D. | SKRZYPCZAK, Leszek
135 
Palabras Clave: Wavelet bases; Muckenhoupt weighted function spaces; Compact embeddings; Entropy numbers; Approximation numbers.
 
Resumen: We study compact embeddings for weighted spaces of Besov and Triebel-Lizorkin type where the weight belongs to some Muckenhoupt Ap class. For weights of purely polynomial growth, both near some singular point and at infinity, we obtain sharp asymptotic estimates for the entropy numbers and approximation numbers of this embedding. The main tool is a discretization in terms of wavelet bases.  

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Construction of Extended Steiner Systems for Information Retrieval.  
PARK, Eun- Young | BLAKE, Ian
179 
Palabras Clave: Information retrieval; Batch codes; Combinatorial designs; Steiner systems.
 
Resumen: A multiset batch code is a variation of information retrieval where a t-multiset of items can be retrieved by reading at most one bit from each server. We study a problem at the other end of the spectrum, namely that of retrieving a t-multiset of items by accessing exactly one server. Our solution to the problem is a combinatorial notion called an extended Steiner system, which was first studied by Johnson and Mendelsohn [11]. An extended Steiner system ES(t; k; v) is a collection of k-multisets (thus, allowing repetition of elements in a block) of a v-set such that every t-multiset belongs to exactly one block. An extended triple system, with t = 2 and k = 3, has been investigated and constructed previously [3, 11]. We study extended systems over v elements with k = t + 1, denoted as ES(t, t + 1, v). We show constructions of ES(t, t + 1, v) for all t ≥ 3 and v ≥ t + 1.  

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The Schur-Szegö Composition of Real Polynomials of Degree 2.  
ALKHATIB, Soliman | KOSTOV, Vladimir Petrov
191 
Palabras Clave: Composition of Schur-Szegö; Hyperbolic polynomial. 

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Invertibility of Operators in Spaces of Real Interpolation.  
ASEKRITOVA, Irina | KRUGLYAK, Natan
207 
Palabras Clave: Real interpolation; Invertible operators.
 
Resumen: Let A be a linear bounded operator from a couple X = (X0,X1) to a couple Y = (Y0; Y1) such that the restrictions of A on the spaces X0 and X1 have bounded inverses. This condition does not imply that the restriction of A on the real interpolation space (X0,X1)θ,q has a bounded inverse for all values of the parameters θ and q. In this paper under some conditions on the kernel of A we describe all spaces (X0,X1)θ,q such that the operator A : (x0,X1)θ,q → (Y0,Y1) has a bounded inverse.  

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Decoherence in Pre-symmetric Spaces.  
EDWARDS, C. Martin | HÜGLI, Remo V.
219 
Palabras Clave: JBW∗-triple; Pre-symmetric space; Decoherence; Involutive grading; Exchange automorphism.
 
Resumen: Pre-symmetric complex Banach spaces have been proposed as models for state spaces of physical systems. A structural projection on a pre-symmetric space A∗ represents an operation on the corresponding system, and has as its range a further pre-symmetric space which represents the state space of the resulting system and symmetries of the system are represented by elements of the group Aut(A∗) of linear isometries of A∗. Two structural projections R and S on the pre-symmetric space A∗ represent decoherent operations when their ranges are rigidly collinear. It is shown that, for decoherent elements x and y of A∗, there exists an involutive element φ∗ in Aut(A∗) which conjugates the structural projections corresponding to x and y, and conditions are found for φ∗ to exchange x and y. The results are used to investigate when certain subspaces of A∗ are the ranges of contractive projections and, therefore, represent systems arising from filtering operations.  

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Generalized Polarized Manifolds.  
AWANE, Azzouz
251 
Palabras Clave: Hamiltonian systems; Poisson manifolds; Symplectic structures; Generalized Hamiltonian dynamics of Nambu.
 
Resumen: We introduce and develop the notion of generalized Poisson manifolds and analyze their main properties. Several generalized Hamiltonian maps for polarized Poisson manifolds and vectorial Hamiltonian maps for systems in dimension smaller or equal than 4 are given.  

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On Binomial Set-Theoretic Complete Intersections in Characteristic p.    
BARILE, Margherita
265 
Palabras Clave: Toric variety; Set-theoretic complete intersection; Affine semigroup; p-gluing.
 
Resumen: Using arithmetic conditions on a_ne semigroups we prove that for a simplicial toric variety of codimension 2 the property of being a set-theoretic complete intersection on binomials in characteristic p holds either for all primes p, or for no prime p, or for exactly one prime p.