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Revista Matemática Complutense Nº 17

Nombre de la Revista: Revista Matemática Complutense
Número de Sumario: 17
Fecha de Publicación: 2004/1

Revista Matemática Complutense

Servicio de Publicaciones de la Universidad Complutense de Madrid

Vol 17  Nº 1   (2004)

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



Stability and Gradient Dynamical Systems  
HALE, Yack K.

Palabras Clave: Dynamical Systems, Stability, Attractors, Gradient systems, Partial differential equations, Functional differential equations
The objective in these notes is to present an approach to dynamical systems in infinite dimensions. It does not seem reasonable to make a comparison of all of the orbits of the dynamics of two systems on non locally compact infinite dimensional spaces. Therefore, we choose to compare them on the set of globally defined bounded solutions. Fundamental problems are posed and several important results are stated when this set is compact. We then give results on the dynamical system which will ensure that this set is compact. Many applications are give to partial differential equations of parabolic and hyperbolic type as well as functional differential equations. 


On two recent geometrical characterizations of hyperellipticity  
COSTA, Antonio F. | PORTO, Ana M.

Palabras Clave: Riemann surface, hyperelliptic involution, Fuchsian group, hyperbolic polygon.
We obtain short and unified new proofs of two recent characterizations of hyperellipticity given in [4] and [6], as well as a way of establishing a relation between them. 


Irregular fibers of complex polynomials in two variables  
BODIN, Arnaud

Palabras Clave: irregulars fibers, tube, vanishing cycles, invariant cycles, resolution of singularities
For a complex polynomial in two variables we study the morphism induced in homology by the embedding of an irregular fiber in a regular neighborhood of it. We give necessary and sufficient conditions for this morphism to be injective, surjective. Particularly this morphism is an isomorphism if and only if the corresponding irregular value is regular at infinity. We apply these results to the study of vanishing and invariant cycles. 


Global Problems on Nash Functions.  
COSTE, Michel | RUIZ, Jesús M.

Palabras Clave: Nash function, étale morphism, cohomology, Cartan’s theorems A and B, finite sheaf, semialgebraic topology, approximation theorem, real spectrum.
This is a survey on the history of and the solutions to the basic global problems on Nash functions, which have been only recently solved, namely: separation, extension, global equations, Artin-Mazur description and idempotency, also noetherianness. We discuss all of them in the various possible contexts, from manifolds over the reals to real spectra of arbitrary commutative rings. 


Hecke operators on de Rham cohomology.  
LEE, Min Ho

Palabras Clave: Hecke operators, de Rham cohomology, automorphic forms
We introduce Hecke operators on de Rham cohomology of compact oriented manifolds. When the manifold is a quotient of a Hermitian symmetric domain, we prove that certain types of such operators are compatible with the usual Hecke operators on automorphic forms. 


A capacity approach to the Poincaré inequality and Sobolev imbeddings in variable exponent Sobolev spaces.  
HARJULEHTO, Petteri | HÄSTÖ, Peter

Palabras Clave: Sobolev spaces, variable exponent, Poincaré inequality, Sobolev imbedding, continuity
We study the Poincaré inequality in Sobolev spaces with variable exponent. Under a rather mild and sharp condition on the exponent p we show that the inequality holds. This condition is satisfied e. g. if the exponent p is continuous in the closure of a convex domain. We also give an essentially sharp condition for the exponent p as to when there exists an imbedding from the Sobolev space to the space of bounded functions. 


On the existence of weak solutions to the Cauchy problem for a class of quasilinear hyperbolic equations with a source term.  

Palabras Clave: Quasilinear hyperbolic equations, conservation laws, viscosity approximation, compensated compactness, Young measures
Following the ideas of D. Serre and J. Shearer in [16], we prove in this paper the existence of a weak solution of the Cauchy problem for the second order quasilinear hyperbolic equation Φtt − σ'(Φx) Φ xx + F(Φ) = 0, (x, t) E R x [0,+1[, where F(Φ) is a suitable source term. 


Tail and free poset algebras.   
BEKKALI, Mohamed | ZHANI, Driss

Palabras Clave: Free poset algebra, tail algebra, semigroup algebra
We characterize free poset algebras F(P) over partially ordered sets and show that they can be represented by upper semi-lattice algebras. Hence, the uniqueness, in decomposition into normal form, using symmetric difference, of non-zero elements of F(P) is established. Moreover, a characterization of upper semilattice algebras that are isomorphic to free poset algebras is given in terms of a selected set of generators of B(T). 


Ropes on a line embedded in a Grassmannian variety.  
BALLICO, Edoardo | NOTARI, Roberto | SPREAFICO, Maria Luisa

Palabras Clave: multiple line, Grassmannian variety, normal sheaf, embeddings.
Let L be a line contained in a Grassmannian variety G. A d-rope C _ G supported on L is a locally Cohen-Macaulay curve of degree d with Cred = L and (IL,G)2 _ IC,G. We characterize the d-ropes C supported on L and embedded in G. In some cases we describe also the vector bundles on such a rope C. Finally, we describe the parameter spaces for ropes embedded in G. 


On the nonlinear Neumann problem involving the critical Sobolev exponent and Hardy potential.  

Palabras Clave: Neumann problem, critical Sobolev exponent, singular Hardy potential, least energy solutions, topological linking
In this paper we investigate the solvability of the Neumann problems (1), (12), (16), (32) and (43) involving the critical Sobolev and Hardy exponents. It is assumed that the coefficient Q is a positive and smooth function on ¯, µ and _ are real parameters. We examine the common effect of the mean curvature of the boundary @, the shape of the graph of the coefficient Q and the singular Hardy potential on the existence and the nonexistence of solutions of these problems. 


Localization Principle for Triebel-Lizorkin Spaces on Spaces of Homogeneous Type  
YANG, Dachun

Palabras Clave: space of homogeneous type, Triebel-Lizorkin space, localization principle, atom, Littlewood-Paley S-function, Calder´on-Zygmund reproducing formula
The author establishes the localization principle for the Triebel-Lizorkin spaces on spaces of homogeneous type.

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