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Revista Matemática Complutense Nº 20

Nombre de la Revista: Revista Matemática Complutense
Número de Sumario: 20
Fecha de Publicación: 2007/2

Revista Matemática Complutense

Servicio de Publicaciones de la Universidad Complutense de Madrid     

Volumen 20 - Número 2  (2007)

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


1.  Indice  

Choosing Roots of Polynomials with Symmetries Smoothly     
LOSIK, Mark | RAINER, Armin
Palabras Clave: Smooth roots of polynomials; Invariants; Representations.
The roots of a smooth curve of hyperbolic polynomials may not in general be parameterized smoothly, even not C1,_ for any _ > 0. A sufficient condition for the existence of a smooth parameterization is that no two of the increasingly ordered continuous roots meet of infinite order. We give refined sufficient conditions for smooth solvability if the polynomials have certain symmetries. In general a C3n curve of hyperbolic polynomials of degree n admits twice differentiable parameterizations of its roots. If the polynomials have certain symmetries we are able to weaken the assumptions in that statement.  

Feller Semigroups Obtained by Variable Order Subordination     
EVANS, Kristian P.
Palabras Clave: Feller semigroups; Subordination in the sense of Bochner; Pseudo-differential operators with negative definite symbols of variable order; Hoh’s symbolic calculus 

Critical Neumann Problem with Competing Hardy Potentials    
Palabras Clave: Critical Sobolev exponent; Hardy potential; Concentration-compactness principle; Neumann problem.
In this paper we investigate the solvability of the nonlinear Neumann problem (1) involving a critical Sobolev nonlinearity and two competing Hardy potentials in a bounded domain. We examine the common effect of the shape of the graph of the weight function, the mean curvature of the boundary and Hardy potentials on the existence of solutions of problem (1). We are mainly interested in the existence of positive solutions. We also obtain the existence of sign-changing solutions. 

An Optimal Control Problem for a Generalized Boussinesq Model: The Time Dependent Case     
BOLDRINI, Jose Luiz | FERNÁNDEZ-CARA, Enrique | ROJAS-MEDAR, Marko Antonio
Palabras Clave: Optimal control; Boussinesq model; Dubovitskii-Milyutin formalism.
We consider an optimal control problem governed by a system of nonlinear partial differential equations modelling viscous incompressible flows submitted to variations of temperature. We use a generalized Boussinesq approximation. We obtain the existence of the optimal control as well as first order optimality conditions of Pontryagin type by using the Dubovitskii-Milyutin formalism.  

On the Brudny˘ı-Krugljak Duality Theory of Spaces Formed by the K-Method of Interpolation     
Palabras Clave: Interpolation spaces; Rearrangement-invariant spaces; Lorentz spaces; Orlicz spaces; Duality.
The Brudny˘ı-Krugljak duality theory for the K-method is elaborated for a class of parameters derived from rearrangement-invariant spaces. As examples, concrete expressions are given for the norms dual to certain interpolation spaces between two rearrangement-invariant spaces. These interpolation spaces are formed by the K-method using parameters related to classical Lorentz spaces or Orlicz spaces.  

Primitive Spatial Graphs and Graph Minors     
OZAWA, Makoto | TSUTSUMI, Yukihiro
Palabras Clave: Spatial graph; Graph minor.
Robertson, Seymour, and Thomas characterized linkless embeddings of graphs by flat embeddings, and determined the obstruction set for linkless embeddings. In this paper, we extend flat embeddings to “primitive embeddings” as linkless embeddings to knotless embeddings. Although the obstruction set for knotless embeddings has not been determined, fundamental theorems and conjectures are obtained.  

Besov Characteristic of a Distribution     
VEDEL, Béatrice
Palabras Clave: Besov spaces; Wavelet analysis; Weighted Besov spaces; Anisotropic Besov spaces; Anisotropic wavelet analysis
The Besov characteristic of a distribution f is the function sf defined for 0 _ t < 1 by sf (t) = sup{ s 2 R; f 2 Bs  

A Home-Made Hartshorne-Serre Correspondence    
ARRONDO, Enrique
Palabras Clave: Codimension two; Hartshorne-Serre correspondence.
We provide an elementary proof of the Hartshorne-Serre correspondence for constructing vector bundles from local complete intersection subschemes of codimension two. This will be done, as in the correspondence of hypersurfaces and line bundles, by patching together local determinantal equations in order to produce sections of a vector bundle.  

Sharp Estimates of the Embedding Constants for Besov Spaces bs p,q, 0 < p < 1    
EDMUNDS, David E. | EVANS, W. Desmond | KARADZHOV, Gyorgi E.
Palabras Clave: Besov spaces; Lorentz spaces; Embedding norms; Rates of blow-up
Sharp estimates are obtained for the rates of blow up of the norms of embeddings of Besov spaces bs p,q in Lorentz spaces as the parameters approach critical values. In [8] the case 1 _ p < 1 was investigated. The case 0 < p < 1 of the present paper requires different methods as the pointwise estimates established are different and the interpolation argument used in [8] is no longer available.  

Lie Algebras of Formal Power Series    
LEE, Min Ho
Palabras Clave: Lie algebras; Pseudodifferential operators; Jacobi-like forms; Modular forms.
Pseudodifferential operators are formal Laurent series in the formal inverse @−1 of the derivative operator @ whose coefficients are holomorphic functions. Given a pseudodifferential operator, the corresponding formal power series can be obtained by using some constant multiples of its coefficients. The space of pseudodifferential operators is a noncommutative algebra over C and therefore has a natural structure of a Lie algebra. We determine the corresponding Lie algebra structure on the space of formal power series and study some of its properties. We also discuss these results in connection with automorphic pseudodifferential operators, Jacobi-like forms, and modular forms for a discrete subgroup of SL(2,R).  

Presentation of Hyperelliptic Periodic Monodromies and Splitting Families     
Palabras Clave: Mapping class group; Degeneration. 

On Rectifying Dual Space Curves
YÜCESAN, Ahmet | AYYILDIZ, Nihat | CÖKEN, A. Ceylan
Palabras Clave: Dual space; Rectifying dual space curve; Frenet formulae; Dual Darboux
We give some characterizations of the rectifying curves in the dual space and show that rectifying dual space curves can be stated with the aid of dual unit spherical curves. Thus, we have a link between rectifying dual space curves and classical surfaces in the Euclidean three-space.  

On the Motivic Measure on the Space of Functions    
GORSKY, Evgeny
Palabras Clave: Motivic integration; Milnor number.
Motivic measure on the space of functions was introduced by Campillo, Delgado, and Gusein-Zade as an analog of the motivic measure on the space of arcs. In this paper we prove that the measure on the space of functions can be related to the motivic measure on the space of arcs by a factor, which can be defined explicitly in geometric terms. This provides a possibility to rewrite motivic integrals over the space of functions as integrals over the union of all symmetric powers of the space of arcs.  

Continuity of Calderón-Zygmund Operators on the Space BMO    
YANG, Qixiang
Palabras Clave: T(1) theorem for BMO; Hörmander condition; Daubechies wavelets; Bony paraproducts; BCR algorithm; Pseudo-annular decomposition.
David and Journé discovered a criterion for the continuity on L2 of Calder´on- Zygmund operators defined by singular integrals. In their approach the distributional kernel of the given operator is locally H¨older continuous outside the diagonal. The aim of this paper is to prove a David-Journ´e theorem where this smoothness assumption is replaced by a weaker one. Our approach strongly relies on an algorithm developed by Beylkin, Coifman, and Rokhlin.

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