Institute Ciencias Matematicas CSIC UAM UC3M UCM

Serrano, Spain

Institute Ciencias Matematicas CSIC UAM UC3M UCM

Serrano, Spain
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Carriazo A.,University of Seville | Perez-Garcia M.J.,Institute Ciencias Matematicas CSIC UAM UC3M UCM
Differential Geometry and its Application | Year: 2017

In this paper we define slant submanifolds in neutral almost contact pseudo-metric manifolds, with motivations and examples. We also provide some natural examples of the ambient spaces. © 2017 Elsevier B.V.


Akman M.,Institute Ciencias Matematicas CSIC UAM UC3M UCM | Lewis J.,University of Kentucky | Vogel A.,Syracuse University
Nonlinear Analysis, Theory, Methods and Applications | Year: 2015

In this paper we study a measure, μ associated with a positive p harmonic function û defined in an open set O⊂ℝRn and vanishing on a portion Γ of ∂O. If p>n we show μ is concentrated on a set of σ finite Hn-1 measure while if p=n the same conclusion holds provided Γ is uniformly fat in the sense of n capacity. Our work nearly answers in the affirmative a conjecture in Lewis (2015) and also appears to be the natural extension of Jones and Wolff (1988), Wolff (1993), to higher dimensions. © 2015 Elsevier Ltd. All rights reserved.


Berselli L.C.,University of Pisa | Cordoba D.,Institute Ciencias Matematicas CSIC UAM UC3M UCM | Granero-Belinchon R.,University of California at Davis
Interfaces and Free Boundaries | Year: 2014

In this work we study the evolution of the free boundary between two different fluids in a porous medium where the permeability is a two dimensional step function. The medium can fill the whole plane R2 or a bounded strip S D Rx (-π/2, π/2). The system is in the stable regime if the denser fluid is below the lighter one. First, we show local existence in Sobolev spaces by means of energy method when the system is in the stable regime. Then we prove the existence of curves such that they start in the stable regime and in finite time they reach the unstable one. This change of regime (turning) was first proven in [5] for the homogenous Muskat problem with infinite depth. © European Mathematical Society 2014.


Ascasibar Y.,Autonomous University of Madrid | Granero-Belinchon R.,Institute Ciencias Matematicas CSIC UAM UC3M UCM | Granero-Belinchon R.,University of California at Davis | Moreno J.M.,Institute Ciencias Matematicas CSIC UAM UC3M UCM
Physica D: Nonlinear Phenomena | Year: 2013

This work studies a simplified model of the gravitational instability of an initially homogeneous infinite medium, represented by Td, based on the approximation that the mean fluid velocity is always proportional to the local acceleration. It is shown that, mathematically, this assumption leads to the restricted Patlak-Keller-Segel model considered by Jäger and Luckhaus or, equivalently, the Smoluchowski equation describing the motion of self-gravitating Brownian particles, coupled to the modified Newtonian potential that is appropriate for an infinite mass distribution. We discuss some of the fundamental properties of a non-local generalization of this model where the effective pressure force is given by a fractional Laplacian with 0<α<2 and illustrate them by means of numerical simulations. Local well-posedness in Sobolev spaces is proven, and we show the smoothing effect of our equation, as well as a Beale-Kato-Majda-type criterion in terms of â€-ρâ-L. © 2013 Elsevier B.V. All rights reserved.


Iglesias D.,University of La Laguna | Marrero J.C.,University of La Laguna | Vaquero M.,Institute Ciencias Matematicas CSIC UAM UC3M UCM
Letters in Mathematical Physics | Year: 2013

In this paper we introduce poly-Poisson structures as a higher-order extension of Poisson structures. It is shown that any poly-Poisson structure is endowed with a polysymplectic foliation. It is also proved that if a Lie group acts polysymplectically on a polysymplectic manifold then, under certain regularity conditions, the reduced space is a poly-Poisson manifold. In addition, some interesting examples of poly-Poisson manifolds are discussed. © 2013 Springer Science+Business Media Dordrecht.


Gomez-Ullate D.,Complutense University of Madrid | Gomez-Ullate D.,Institute Ciencias Matematicas CSIC UAM UC3M UCM | Grandati Y.,University of Lorraine | Milson R.,Dalhousie University
Journal of Physics A: Mathematical and Theoretical | Year: 2014

We prove that every rational extension of the quantum harmonic oscillator that is exactly solvable by polynomials is monodromy free, and therefore can be obtained by applying a finite number of state-deleting Darboux transformations on the harmonic oscillator. Equivalently, every exceptional orthogonal polynomial system of Hermite type can be obtained by applying a Darboux-Crum transformation to the classical Hermite polynomials. Exceptional Hermite polynomial systems only exist for even codimension 2 m, and they are indexed by the partitions λ of m. We provide explicit expressions for their corresponding orthogonality weights and differential operators and a separate proof of their completeness. Exceptional Hermite polynomials satisfy a 2ℓ + 3 recurrence relation where ℓ is the length of the partition λ. Explicit expressions for such recurrence relations are given. © 2014 IOP Publishing Ltd.


De Leon M.,Institute Ciencias Matematicas CSIC UAM UC3M UCM | Vilarino S.,Centro Universitario Of La Defensa
International Journal of Geometric Methods in Modern Physics | Year: 2014

In this paper, we extend the geometric formalism of the Hamilton-Jacobi theory for time-dependent Mechanics to the case of classical field theories in the k-cosymplectic framework. © 2014 World Scientific Publishing Company.


Lopez-Fernandez M.,Institute Ciencias Matematicas CSIC UAM UC3M UCM
BIT Numerical Mathematics | Year: 2010

We present a quadrature-based method to evaluate exponential-like operators required by different kinds of exponential integrators. The method approximates these operators by means of a quadrature formula that converges like O(e-cK), with K the number of quadrature nodes, and it is useful when solving parabolic equations. The approach allows also the evaluation of the associated scalar mappings. The method is based on numerical inversion of sectorial Laplace transforms. Several numerical illustrations are provided to test the algorithm, including examples with a mass matrix and the application of the method inside the MATLAB package EXP4, an adaptive solver based on an exponential Runge-Kutta method. © 2010 Springer Science + Business Media B.V.


Luca R.,Institute Ciencias Matematicas CSIC UAM UC3M UCM | Rogers K.M.,Institute Ciencias Matematicas CSIC UAM UC3M UCM
Communications in Mathematical Physics | Year: 2016

We consider Carleson’s problem regarding convergence for the Schrödinger equation in dimensions (Formula presented.). We show that if the solution converges almost everywhere with respect to (Formula presented.)-Hausdorff measure to its initial datum as time tends to zero, for all data (Formula presented.), then (Formula presented.). This strengthens and generalises results of Bourgain and Dahlberg–Kenig. © 2016 Springer-Verlag Berlin Heidelberg


Garcia-Fernandez M.,Institute Ciencias Matematicas CSIC UAM UC3M UCM
Communications in Mathematical Physics | Year: 2014

This work revisits the notions of connection and curvature in generalized geometry, with emphasis on torsion-free generalized connections on a transitive Courant algebroid. As an application, we provide a mathematical derivation of the equations of motion of heterotic supergravity in terms of the Ricci tensor of a generalized metric, inspired by the work of Coimbra, Strickland-Constable and Waldram. © 2014 Springer-Verlag Berlin Heidelberg.

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