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In this paper we consider linear parabolic problems when some reaction and potential terms are concentrated in a neighborhood of a portion I" of the boundary. This neighborhood shrinks to I" as a parameter epsilon goes to zero. Then we derive the limit equation which has some new terms on I". We also analyze the regularity and convergence of the solutions., Grupo de Investigacion CADEDIF, Spain, Depto. de Análisis Matemático y Matemática Aplicada, Fac. de Ciencias Matemáticas, TRUE, pub

In this paper we give a characterization of uniform convergence on weakly compact sets, for sequences of homogeneous polynomials in terms of the Mosco convergence of their level sets. The result is partially extended for holomorphic functions. Finally we study the relationship with other convergences., DGICYT, Depto. de Análisis Matemático y Matemática Aplicada, Fac. de Ciencias Matemáticas, TRUE, pub

In this paper we prove several results on the existence of analytic functions on an infinite dimensional real Banach space which are bounded on some given collection of open sets and unbounded on others. In addition, we also obtain results on the density of some subsets of the space of all analytic functions for natural locally convex topologies on this space, UCM, Depto. de Análisis Matemático y Matemática Aplicada, Fac. de Ciencias Matemáticas, TRUE, pub

It is proved that any closed orientable 3-manifold is a 3-fold irregular branched covering of the 3-sphere branched over a wildly embedded knot. These branched coverings are obtained by starting with such a branched covering over a tame knot and then inserting into it a particular irregular branched covering of the 3-sphere over the 3-sphere, with a wild branch set. It is also shown how to use related techniques to produce branched coverings of certain open 3-manifolds over tame, properly embedded arcs in R3. For example, the Whitehead contractible open 3-manifold is expressible as a 2-fold branched covering over such an arc, conjecturally in uncountably many different ways. These results should be considered as illustrations of the general construction given in the author's recent paper [Rev. Mat. Complut. 15 (2002), no. 2, 533–542, Depto. de Álgebra, Geometría y Topología, Fac. de Ciencias Matemáticas, TRUE, pub

It is a celebrated result of H. Hilden and the author of the present paper that every closed, connected, oriented 3-manifold is a 3-fold irregular (dihedral) branched covering of the 3-sphere, branched over a knot. Here the author explores a generalization of this result to the case of non-compact manifolds. It is shown that a non-compact, connected, oriented 3-manifold is a 3-fold irregular branched covering of an open subspace of S3, branched over a locally finite family of proper arcs. The branched covering is constructed in such a way that it extends to a branched covering (suitably understood) of the Freudenthal end compactification over the entire 3-sphere. In particular all (uncountably many) contractible open 3-manifolds may be expressed as 3-fold branched coverings of R3, branched over a locally finite collection of proper arcs., Depto. de Álgebra, Geometría y Topología, Fac. de Ciencias Matemáticas, TRUE, pub

Projected entangled pair states (PEPS) are used in practice as an efficient parametrization of the set of ground states of quantum many body systems. The aim of this paper is to present, for a broad mathematical audience, some mathematical questions about PEPS., Unión Europea, Ministerio de Economía y Competitividad (MINECO), Comunidad de Madrid, Depto. de Análisis Matemático y Matemática Aplicada, Instituto de Ciencias Matemáticas (ICMAT), Fac. de Ciencias Matemáticas, FALSE, pub

Dedicado a Francisco González Acuña en su sexagésimo cumpleaños, According to the confirmed Smith Conjecture [The Smith conjecture (New York, 1979), Academic Press, Orlando, FL, 1984;], a tame knot in the 3-sphere has a cyclic branched covering that is also the 3-sphere only if it is trivial. Here the author produces a nontrivial, wild knot whose n-fold cyclic branched cover is S3, for all n. In fact there are uncountably many inequivalent knots with this property, and the knots can be chosen to bound an embedded disk that is tame in its interior. One might conjecture that any wild knot whose nontrivial n-fold cyclic branched cover is S3 must bound such a disk that is tame in its interior., Depto. de Álgebra, Geometría y Topología, Fac. de Ciencias Matemáticas, TRUE, pub

In this article we give a condition, which holds in a very general setting, to smooth a rope, of any dimension, embedded in projective space. As a consequence of this we prove that canonically embedded carpets satisfying mild geometric conditions can be smoothed. Our condition for smoothing a rope can be stated very transparently in terms of the cohomology class of a suitable first order infinitesimal deformation of a morphism I center dot associated to . In order to prove these results we find a sufficient condition, of independent interest, for a morphism I center dot from a smooth variety X to projective space, finite onto a smooth image, to be deformed to an embedding. Another application of this result on deformation of morphisms is the construction of smooth varieties in projective space with given invariants. We illustrate this by constructing canonically embedded surfaces with and deriving some interesting properties of their moduli spaces. The results of this article bear further evidence to the complexity of the moduli of surfaces of general type and its sharp contrast with the moduli of other objects such as curves or K3 surfaces., UCM, General Research Fund (GRF) of the University of Kansas, Depto. de Álgebra, Geometría y Topología, Fac. de Ciencias Matemáticas, Instituto de Matemática Interdisciplinar (IMI), TRUE, pub