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Identification of a quasilinear parabolic equation from final data

Luis a. FernándezCecilia Pola — 2001

International Journal of Applied Mathematics and Computer Science

We study the identification of the nonlinearities A,(→)b and c appearing in the quasilinear parabolic equation y_t − div(A(y)∇y + (→)b(y)) + c(y) = u inΩ × (0,T), assuming that the solution of an associated boundary value problem is known at the terminal time, y(x,T), over a (probably small) subset of Ω, for each source term u. Our work can be divided into two parts. Firstly, the uniqueness of A,(→)b and c is proved under appropriate assumptions. Secondly, we consider a finite-dimensional optimization...

Variational theory of non-perfect relativistic fluids.

A. FernándezP. L. García — 1999

Extracta Mathematicae

A basic question in General Relativity from the point of view of the general field theory is to obtain the Einstein equations coupled with the stress-energy-momentum tensor of a dissipative fluid from a variational principle. We believe that this problem, whose solution for perfect fluids is well known, has not been faced in a systematic way, maybe by the thought of a possible nonsense, for the concept of dissipation is believed to be incompatible with the essentially conservative character of the...

Numerical simulation of blood flows through a porous interface

Miguel A. FernándezJean-Frédéric GerbeauVincent Martin — 2008

ESAIM: Mathematical Modelling and Numerical Analysis

We propose a model for a medical device, called a stent, designed for the treatment of cerebral aneurysms. The stent consists of a grid, immersed in the blood flow and located at the inlet of the aneurysm. It aims at promoting a clot within the aneurysm. The blood flow is modelled by the incompressible Navier-Stokes equations and the stent by a dissipative surface term. We propose a stabilized finite element method for this model and we analyse its convergence in the case of the Stokes...

Foliations by curves with curves as singularities

M. Corrêa JrA. Fernández-PérezG. Nonato CostaR. Vidal Martins — 2014

Annales de l’institut Fourier

Let be a holomorphic one-dimensional foliation on n such that the components of its singular locus Σ are curves C i and points p j . We determine the number of p j , counted with multiplicities, in terms of invariants of and C i , assuming that is special along the C i . Allowing just one nonzero dimensional component on Σ , we also prove results on when the foliation happens to be determined by its singular locus.

Estimación de la función de densidad con observaciones obtenidas en instantes aleatorios.

Sea X(t) un proceso estacionario en tiempo continuo con función de densidad marginal univariante f(x). A partir de un conjunto de n observaciones; X(τ1), X(τ2), ..., X(τn) recogidas en instantes muestrales τi, espaciados irregularmente o aletorios, se estudia la estimación no paramétrica de f(x), utilizando un estimador recursivo tipo núcleo. Asumiendo condiciones débiles de dependencia (α-mixing) se obtiene...

Deficiencias del test de la razón de verosimilitud para contrastar ciertas hipótesis con restricciones de orden.

José A. Menéndez FernándezBonifacio Salvador González — 1987

Trabajos de Estadística

En este trabajo se estudian problemas de test de hipótesis para el vector de las medidas de poblaciones normales independientes con varianzas conocidas, cuando ambas, la hipótesis nula y la alternativa, imponen restricciones de orden sobre los parámetros. Se demuestra que para las hipótesis planteadas el test de razón de verosimilitud (TRV) está dominado por otro TRV para hipótesis que desprecian parte de la información de que se dispone.

A hierarchy in the family of real surjective functions

This expository paper focuses on the study of extreme surjective functions in ℝℝ. We present several different types of extreme surjectivity by providing examples and crucial properties. These examples help us to establish a hierarchy within the different classes of surjectivity we deal with. The classes presented here are: everywhere surjective functions, strongly everywhere surjective functions, κ-everywhere surjective functions, perfectly everywhere surjective functions and Jones functions. The...

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