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Revista Matemática Complutense Nº 16

Nombre de la Revista: Revista Matemática Complutense
Número de Sumario: 16
Fecha de Publicación: 2003/2

Revista Matemática Complutense

Servicio de Publicaciones de la Universidad Complutense de Madrid

Vol 16  Nº 2   (2003)

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



An Ostrowski like inequality for convex functions and applications    

Palabras Clave: Ostrowski type inequalities, Convex functions, Hermite-Hadamard type inequalities
In this paper we point out an Ostrowski type inequality for convex functions which complement in a sense the recent results for functions of bounded variation and absolutely continuous functions. Applications in connection with the Hermite-Hadamard inequality are also considered. 


Hypercyclic operators with an in¯nite dimensional closed subspace of periodic points  

Palabras Clave: Hypercyclic operators, chaotic operators
Let X be an infinite dimensional separable Banach space. There exists a hypercyclic operator on X which is equal to the identity operator on an infinite dimensional closed subspace of X. 


The starlikeness and convexity of multivalent functions involving certain inequalities   
IRMAK, HÄuseyin | RAINA, R. K.

Palabras Clave: Open unit disc, analytic, multivalently starlike, multivalently convex, and Jack's Lemma
In the present paper, a theorem for the starlikeness and convexity of multivalent functions involving certain inequalities is given. Some interesting consequences of the main result are also mentioned. 


On the strict convexity of the Besicovitch-Orlicz space of almost periodic functions with Orlicz nor 
MORSLI, Mohamed | BEDOUHENE, Fazia

Palabras Clave: Strict convexity, Besicovitch-Orlicz space, almost periodic functions
The problem of strict convexity of the Besicovitch-Orlicz space of almost periodic functions is considered here in connection with the Orlicz norm. We give necessary and sufficient conditions in terms of the function Á generating the space. 


Boundary stabilization of the linear elastodynamic system by a Lyapunov-type method  
BEY, RAbah | HEMINNA, Amar | LOHÉAC, Jean-Pierre

Palabras Clave: Elastodynamic system, boundary stabilization, feedback
We propose a direct approach to obtain the boundary stabilization of the isotropic linear elastodynamic system by a “natural" feedback; this method uses local coordinates in the expression of boundary integrals as a main tool. It leads to an explicit decay rate of the energy function and requires weak geometrical conditions: for example, the spacial domain can be the difference of two star-shaped sets. 


Fundamental solutions and singular shocks in scalar conservation laws  

Palabras Clave: Conservation laws, fundamental solutions, singular solutions
We study the existence and non-existence of fundamental solutions for the scalar conservation laws ut + f(u)x = 0; related to convexity assumptions on f. We also study the limits of those solutions as the initial mass goes to infinity. We especially prove the existence of so-called Friendly Giants and Infinite Shock Solutions according to the convexity of f, which generalize the explicit power case f(u) = um. We introduce an extended notion of solution and entropy criterion to allow infinite shocks in the theory, and the initial data also has to be understood in a generalized sense, since locally infinite measures appear. 


A Dirichlet problem with asymptotically linear and changing sign nonlinearity    
LUCIA, Marcello | MAGRONE, Paola | ZHOU, Huan-Song

Palabras Clave: Elliptic equation, Asymptotically linear nonlinearity, Mountain Pass Theorem
This paper deals with the problem of finding positive solutions to the equation ¡¢u = g(x; u) on a bounded domain ­; with Dirichlet boundary conditions. The function g can change sign and has asymptotically linear behaviour. The solutions are found using the Mountain Pass Theorem. 


On some nonlinear elliptic systems with coercive perturbations in RN  
EL MANOUNI, Said | TOUZANI, Abdelfattah

Palabras Clave: Nonlinear elliptic system, coercive perturbation, Palais-Smale condition, Mountain Pass Theorem
A nonlinear elliptic system involving the p-Laplacian is considered in the whole RN: Existence of nontrivial solutions is obtained by applying critical point theory; also a regularity result is established. 


The dynamics of a levitated cylindrical permanent magnet above a superconductor  

Palabras Clave: Superconductor, Meissner effect, levitated permanent magnet, rotating permanent magnet
When a permanent magnet is released above a superconductor, it is levitated. This is due to the Meissner-effect, i.e. the repulsion of external magnetic fields within the superconductor. In experiments, an interesting behavior of the levitated magnet can be observed: it might start to oscillate with increasing amamplitude and some magnets even reach a continuous rotation. In this paper we develop a mathematical model for this effect and identify by analytical methods as well with ¯nite element simulations two reasons for the described behavior of the levitated magnet. It is shown, that the oscillations of the magnet are due to inhomogeneities of the magnetization within the magnet, whereas the continuous rotations are due to temperature gradients of the surrounding air. 


Theoretical aspects of a multiscale analysis of the eigenoscillations of the earth  
MICHEL, Volker

Palabras Clave: Cauchy-Navier equation, wavelets, multiresolution, Helmholtz equation,Hansen vectors, geomathematics
The elastic behaviour of the Earth, including its eigenoscillations, is usually described by the Cauchy-Navier equation. Using a standard approach in seismology we apply the Helmholtz decomposition theorem to transform the Fourier transformed Cauchy-Navier equation into two non-coupled Helmholtz equations and then derive sequences of fundamental solutions for this pair of equations using the Mie representation. Those solutions are denoted by the Hansen vectors Ln;j , Mn;j , and Nn;j in geophysics. Next we apply the inverse Fourier transform to obtain a function system depending on time and space. Using this basis for the space of eigenoscillations we construct scaling functions and wavelets to obtain a multiresolution for the solution space of the Cauchy-Navier equation. 


On reduced pairs of bounded closed convex sets   

Palabras Clave: Convex analysis, pairs of convex sets
In this paper certain criteria for reduced pairs of bounded closed convex set are presented. Some examples of reduced and not reduced pairs are enclosed. 


Constructions of thin-tall Boolean spaces  
MARTÍNEZ, Juan Carlos

Palabras Clave: Scattered space, thin-tall, partitions, Δ-functions, walks, forcing, constructibility
This is an expository paper about constructions of locally compact, Hausdorff, scattered spaces whose Cantor-Bendixson height has cardinality greater than their Cantor-Bendixson width. 


Open 3-manifolds, wild subsets of S3 and branched coverings   

Palabras Clave: Wild knots, open manifolds, branched coverings
In this paper, a representation of closed 3-manifolds as branched coverings of the 3-sphere, proved in [13], and showing a relationship between open 3-manifolds and wild knots and arcs will be illustrated by examples. It will be shown that there exist a 3-fold simple covering p : S3 ! S3 branched over the remarkable simple closed curve of Fox [4] (a wild knot). Moves are defined such that when applied to a branching set, the corresponding covering manifold remains unchanged, while the branching set changes and becomes wild. As a consequence every closed, oriented 3-manifold is represented as a 3-fold covering of S3 branched over a wild knot, in plenty of different ways, confirming the versatility of irregular branched coverings. Other collection of examples is obtained by pasting the members of an infinite sequence of two-component strongly-invertible link exteriors. These open 3-manifolds are shown to be 2-fold branched coverings of wild knots in the 3-sphere Two concrete examples, are studied: the solenoidal manifold, and the Whitehead manifold. Both are 2-fold covering of the euclidean space R3 branched over an uncountable collection of string projections in R3.

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