BIRD, BCAM's Institutional Repository Data: Recent submissions
Now showing items 1-20 of 1021
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A Hardy-type inequality and some spectral characterizations for the Dirac-Coulomb operator
(Revista Matemática Complutense, 2019-07-02)We prove a sharp Hardy-type inequality for the Dirac operator. We exploit this inequality to obtain spectral properties of the Dirac operator perturbed with Hermitian matrix-valued potentials V of Coulomb type: we characterise ... -
Evolution of Polygonal Lines by the Binormal Flow
(Springer Nature Switzerland AG 2020, 2020-02-05)The aim of this paper is threefold. First we display solutions of the cubic nonlinear Schr ̈odinger equation on R in link with initial data a sum of Dirac masses. Secondly we show a Talbot effect for the same equation. ... -
Some lower bounds for solutions of Schrodinger evolutions
(SIAM J. MATH. ANAL., 2019-08-21)We present some lower bounds for regular solutions of Schr odinger equations with bounded and time dependent complex potentials. Assuming that the solution has some positive mass at time zero within a ball of certain radius, ... -
Uniqueness Properties of Solutions to the Benjamin-Ono equation and related models
(2019-01-31)We prove that if u1, u2 are solutions of the Benjamin- Ono equation defined in (x, t) ∈ R × [0, T ] which agree in an open set Ω ⊂ R × [0,T], then u1 ≡ u2. We extend this uniqueness result to a general class of equations ... -
Absence of eigenvalues of two-dimensional magnetic Schr ̈odinger operators
(2017-10-17)By developing the method of multipliers, we establish sufficient conditions on the electric potential and magnetic field which guarantee that the corresponding two-dimensional Schr ̈odinger operator possesses no point ... -
Asymptotics in Fourier space of self-similar solutions to the modified Korteweg-de Vries equation
(2018-07-06)We give the asymptotics of the Fourier transform of self-similar solutions to the modified Korteweg-de Vries equation, through a fixed point argument in weighted W1,8 around a carefully chosen, two term ansatz. Such knowledge ... -
On the improvement of the Hardy inequality due to singular magnetic fields
(2018-07-12)We establish magnetic improvements upon the classical Hardy inequality for two specific choices of singular magnetic fields. First, we consider the Aharonov-Bohm field in all dimensions and establish a sharp Hardy-type ... -
Self-similar dynamics for the modified Korteweg-de Vries equation
(2019-04-09)We prove a local well posedness result for the modified Korteweg-de Vries equa- tion in a critical space designed so that is contains self-similar solutions. As a consequence, we can study the flow of this equation around ... -
On the energy of critical solutions of the binormal flow
(2019-07-20)The binormal flow is a model for the dynamics of a vortex filament in a 3-D inviscid incompressible fluid. The flow is also related with the classical continuous Heisen- berg model in ferromagnetism, and the 1-D cubic Schr ... -
Bilinear identities involving the k-plane transform and Fourier extension operators
(2019-11-30)We prove certain L2pRnq bilinear estimates for Fourier extension operators associ- ated to spheres and hyperboloids under the action of the k-plane transform. As the estimates are L2-based, they follow from bilinear ... -
On the Evolution of the Vortex Filament Equation for regular M-polygons with nonzero torsion
(2019-09-03)In this paper, we consider the evolution of the Vortex Filament equa- tion (VFE): Xt = Xs ∧ Xss, taking M-sided regular polygons with nonzero torsion as initial data. Us- ing algebraic techniques, backed by numerical ... -
Carleman type inequalities for fractional relativistic operators
(2019-09-22)In this paper, we derive Carleman estimates for the fractional relativistic operator. Firstly, we consider changing-sign solutions to the heat equation for such operators. We prove monotonicity inequalities and convexity ... -
Numerical approximations for fractional elliptic equations via the method of semigroups
(ESAIM: Mathematical Modelling and Numerical Analysis, 2020)We provide a novel approach to the numerical solution of the family of nonlocal elliptic equations $(-\Delta)^su=f$ in $\Omega$, subject to some homogeneous boundary conditions $\mathcal{B}(u)=0$ on $\partial \Omega$, where ... -
Neron models of intermediate Jacobians associated to moduli spaces
(Revista Matemática Complutense, 2019-12-01)Let $\pi_1:\mathcal{X} \to \Delta$ be a flat family of smooth, projective curves of genus $g \ge 2$, degenerating to an irreducible nodal curve $X_0$ with exactly one node. Fix an invertible sheaf $\mathcal{L}$ on $\mathcal{X}$ ... -
FREE-FORM TOOLS DESIGN AND FABRICATION FOR FLANK SUPER ABRASIVE MACHINING (FSAM) NON DEVELOPABLE SURFACES
(MM Science Journal, 2019)Manufacturing improvements are becoming a real need in industry. In order to satisfy these industrial requirements, they should be targeted in two different directions: new manufacturing processes and surface optimization ... -
Maximal estimates for a generalized spherical mean Radon transform acting on radial functions
(Annali de Matematica Pura et Applicata, 2020)We study a generalized spherical means operator, viz.\ generalized spherical mean Radon transform, acting on radial functions. As the main results, we find conditions for the associated maximal operator and its local ... -
A theoretical approach for the electrochemical characterization of ciliary epithelium
(Life, 2020-01-23)The ciliary epithelium (CE) is the primary site of aqueous humor (AH) production, which results from the combined action of ultrafiltration and ionic secretion. Modulation of ionic secretion is a fundamental target for ... -
Multiplicity of singularities is not a bi-Lipschitz invariant
(Mathematische Annalen, 2020-01-17)It was conjectured that multiplicity of a singularity is bi-Lipschitz invariant. We disprove this conjecture constructing examples of bi-Lipschitz equivalent complex algebraic singularities with different values of multiplicity. -
Key aspects for effective mathematical modelling of fractional-diffusion in cardiac electrophysiology: A quantitative study
(Communications in Nonlinear Science and Numerical Simulation, 2020-05)Microscopic structural features of cardiac tissue play a fundamental role in determining complex spatio-temporal excitation dynamics at the macroscopic level. Recent efforts have been devoted to the development of mathematical ... -
Some classes of homeomorphisms that preserve multiplicity and tangent cones
(Contemporary Mathematics, 2019-05-28)In this paper we present some applications of A'Campo-Lê's Theorem and we study some relations between Zariski's Questions A and B. It is presented some classes of homeomorphisms that preserve multiplicity and tangent cones ...