DSpace Collection:
http://hdl.handle.net/2117/3228
2015-07-07T07:06:08ZNonlinear equations for fractional Laplacians, I: Regularity, maximum principles, and Hamiltonian estimates
http://hdl.handle.net/2117/22391
Title: Nonlinear equations for fractional Laplacians, I: Regularity, maximum principles, and Hamiltonian estimates
Authors: Cabré Vilagut, Xavier; Sire, Yannick
Abstract: This is the first of two articles dealing with the equation (-)sv = f (v) in Rn, with s ¿ (0,1), where (-)s stands for the fractional Laplacian — the in¿nitesimal generator of a Lévy process. This equation can be realized as a local linear degenerate elliptic equation in Rn+1+ together with a nonlinear Neumann boundary condition on ¿Rn+1 + =Rn.
In this ¿rst article, we establish necessary conditions on the nonlinearity f to admit certain type of solutions, with special interest in bounded increasing solutions in all of R. These necessary conditions (which will be proven in a follow-up paper to be also suficient for the existence of a bounded increasing solution) are derived from an equality and an estimate involving a Hamiltonian — in the spirit of a result of Modica for the Laplacian. Our proofs are uniform ass ¿1, establishing in the limit the corresponding known results for the Laplacian.
In addition, we study regularity issues, as well as maximum and Harnack principles associated to the equation.Generic bifurcations of low codimension of planar Filippov Systems
http://hdl.handle.net/2117/26671
Title: Generic bifurcations of low codimension of planar Filippov Systems
Authors: Martínez-Seara Alonso, M. Teresa; Guàrdia Munarriz, Marcel; Teixeira, Marco Antonio
Abstract: In this article some qualitative and geometric aspects of non-smooth dynamical systems theory are discussed. The main aim of
this article is to develop a systematic method for studying local(and global) bifurcations in non-smooth dynamical systems. Our results deal with the classification and characterization of generic codimension-2 singularities of planar Filippov Systems as well as the presentation of the bifurcation diagrams and some dynamical consequences2015-03-12T10:45:38ZCredit risk contributions under the Vasicek one-factor model: a fast wavelet expansion approximation
http://hdl.handle.net/2117/26597
Title: Credit risk contributions under the Vasicek one-factor model: a fast wavelet expansion approximation
Authors: Masdemont Soler, Josep; Ortiz-Gracia, Luis
Abstract: To measure the contribution of individual transactions inside the total risk of a credit portfolio is a major issue in financial institutions. VaR Contributions (VaRC) and Expected Shortfall Contributions (ESC) have become two popular ways of quantifying the risks. However, the usual Monte Carlo (MC) approach is known to be a very time consum-
ing method for computing these risk contributions. In this paper we consider the Wavelet Approximation (WA) method for Value at Risk (VaR) computation presented in [Mas10] in order to calculate the Expected Shortfall (ES) and the risk contributions under the Vasicek
one-factor model framework. We decompose the VaR and the ES as a sum of sensitivities representing the marginal impact on the total portfolio risk. Moreover, we present technical improvements in the Wavelet Approximation (WA) that considerably reduce the computa-
tional effort in the approximation while, at the same time, the accuracy increases2015-03-05T12:53:03ZCom les Varietats Invariants formen Espirals i Anells en Galàxies barrades
http://hdl.handle.net/2117/26596
Title: Com les Varietats Invariants formen Espirals i Anells en Galàxies barrades
Authors: Romero Gómez, Mercè; Sánchez-Martín, Patricia; Masdemont Soler, Josep
Abstract: L'espectacularitat de les galàxies barrades consisteix no solament en la
presència de la barra, allargada en el centre de la galàxia, sinó també en els braços espirals o anells que es desenvolupen en les parts exteriors. No hi ha una teoria clara per a la formació d'anells i, fins fa poc, només n'hi havia una que explicava l'origen dels braços espirals en galàxies no barrades. En els darrers anys hem desenvolupat una teoria basada en els sistemes dinàmics que relaciona els braços espirals i els anells amb les varietats invariants hiperbòliques associades a òrbites periòdiques i quasiperiòdiques al voltant de punts d'equilibri colineals del sistema2015-03-05T12:42:01ZStructural stability of planar bimodal linear systems
http://hdl.handle.net/2117/26226
Title: Structural stability of planar bimodal linear systems
Authors: Ferrer Llop, Josep; Peña Carrera, Marta; Susín Sánchez, Antonio
Abstract: Structural stability ensures that the qualitative behavior of a system is preserved under small perturbations. We study it for planar bimodal linear dynamical systems, that is, systems consisting of two linear dynamics acting on each side of a given hyperplane and assuming continuity along the separating hyperplane. We describe which one of these systems is structurally stable when (real) spiral does not appear and when it does we give necessary and sufficient conditions concerning finite periodic orbits and saddle connections. In particular, we study the finite periodic orbits and the homoclinic orbits in the saddle/spiral case.2015-02-05T10:53:33ZEMtree for phylogenetic topology reconstruction on nonhomogeneous data
http://hdl.handle.net/2117/26031
Title: EMtree for phylogenetic topology reconstruction on nonhomogeneous data
Authors: Ibáñez Marcelo, Esther; Casanellas Rius, Marta2015-01-22T12:04:00ZLow degree equations for phylogenetic group-based models
http://hdl.handle.net/2117/26029
Title: Low degree equations for phylogenetic group-based models
Authors: Casanellas Rius, Marta; Fernández Sánchez, Jesús; Michalek, Mateusz
Abstract: Motivated by phylogenetics, our aim is to obtain a system of low degree equations that define a phylogenetic variety on an open set containing the biologically meaningful points. In this paper we consider phylogenetic varieties defined via group-based models. For any finite abelian group G , we provide an explicit construction of codimX polynomial equations (phylogenetic invariants) of degree at most |G| that define the variety X on a Zariski open set U . The set U contains all biologically meaningful points when G is the group of the Kimura 3-parameter model. In particular, our main result confirms (Michalek, Toric varieties: phylogenetics and derived categories, PhD thesis, Conjecture 7.9, 2012) and, on the set U , Conjectures 29 and 30 of Sturmfels and Sullivant (J Comput Biol 12:204–228, 2005).2015-01-22T12:01:03ZOn the integrability of polynomial vector fields in the plane by means of Picard-Vessiot theory
http://hdl.handle.net/2117/26024
Title: On the integrability of polynomial vector fields in the plane by means of Picard-Vessiot theory
Authors: Acosta-Humànez, Primitivo; Lázaro Ochoa, José Tomás; Morales Ruiz, Juan José; Pantazi, Chara
Abstract: We study the integrability of polynomial vector fields using Galois theory of linear differential equations when the associated foliations is reduced to a Riccati type foliation. In particular we obtain integrability results for some families of quadratic vector fields, Lienard equations and equations related with special functions such as Hypergeometric and Heun ones. The Poincare problem for some families is also approached.2015-01-22T11:17:38ZLayer solutions for the fractional Laplacian on hyperbolic space: existence, uniqueness and qualitative properties
http://hdl.handle.net/2117/25175
Title: Layer solutions for the fractional Laplacian on hyperbolic space: existence, uniqueness and qualitative properties
Authors: González Nogueras, María del Mar; Saéz, Mariel; Sire, Yannick
Abstract: We investigate the equation; (-Delta(Hn))(gamma) w = f(w) in H-n,; where (-Delta(Hn))(gamma) corresponds to the fractional Laplacian on hyperbolic space for gamma is an element of(0, 1) and f is a smooth nonlinearity that typically comes from a double well potential. We prove the existence of heteroclinic connections in the following sense; a so-called layer solution is a smooth solution of the previous equation converging to +/- 1 at any point of the two hemispheres S-+/- subset of partial derivative H-infinity(n) and which is strictly increasing with respect to the signed distance to a totally geodesic hyperplane Pi. We prove that under additional conditions on the nonlinearity uniqueness holds up to isometry. Then we provide several symmetry results and qualitative properties of the layer solutions. Finally, we consider the multilayer case, at least when gamma is close to one.2015-01-08T12:16:16ZSufficient conditions for controllability and observability of serial and parallel concatenated linear systems
http://hdl.handle.net/2117/25002
Title: Sufficient conditions for controllability and observability of serial and parallel concatenated linear systems
Authors: García Planas, María Isabel; Domínguez García, José Luis; Um, Laurence Emilie
Abstract: This paper deals with the sufficient conditions
for controllability and observability characters of finitedimensional
linear continuous-time-invariant systems of serial
and parallel concatenated systems. The obtained conditions
depend on the controllability and observability of the systems
and in some cases, the functional output-controllability of the
first one.2014-12-11T12:39:29ZAddendum to “Frobenius and Cartier algebras of Stanley–Reisner rings” [J. Algebra 358 (2012) 162–177]
http://hdl.handle.net/2117/24996
Title: Addendum to “Frobenius and Cartier algebras of Stanley–Reisner rings” [J. Algebra 358 (2012) 162–177]
Authors: Álvarez Montaner, Josep; Yanagawa, Kohji
Abstract: We give a purely combinatorial characterization of complete Stanley–Reisner rings having a principally generated (equivalently, finitely generated) Cartier algebra.2014-12-11T09:15:25ZA new approach to the vakonomic mechanics
http://hdl.handle.net/2117/24993
Title: A new approach to the vakonomic mechanics
Authors: Llibre Saló, Jaume; Ramírez Ros, Rafael; Sadovskaia Nurimanova, Natalia Guennadievna
Abstract: The aim of this paper was to show that the Lagrange-d'Alembert and its equivalent the Gauss and Appel principle are not the only way to deduce the equations of motion of the nonholonomic systems. Instead of them we consider the generalization of the Hamiltonian principle for nonholonomic systems with non-zero transpositional relations. We apply this variational principle, which takes into the account transpositional relations different from the classical ones, and we deduce the equations of motion for the nonholonomic systems with constraints that in general are nonlinear in the velocity. These equations of motion coincide, except perhaps in a zero Lebesgue measure set, with the classical differential equations deduced with the d'Alembert-Lagrange principle. We provide a new point of view on the transpositional relations for the constrained mechanical systems: the virtual variations can produce zero or non-zero transpositional relations. In particular, the independent virtual variations can produce non-zero transpositional relations. For the unconstrained mechanical systems, the virtual variations always produce zero transpositional relations. We conjecture that the existence of the nonlinear constraints in the velocity must be sought outside of the Newtonian mechanics. We illustrate our results with examples.2014-12-11T08:01:15ZZero, minimum and maximum relative radial acceleration for planar formation flight dynamics near triangular libration points in the Earth-Moon system
http://hdl.handle.net/2117/24992
Title: Zero, minimum and maximum relative radial acceleration for planar formation flight dynamics near triangular libration points in the Earth-Moon system
Authors: Salazar, F.J.T; Masdemont Soler, Josep; Gómez Muntané, Gerard; Macau, E.E.N.; Winter, O. C.
Abstract: Assume a constellation of satellites is flying near a given nominal trajectory around L-4 or L-5 in the Earth-Moon system in such a way that there is some freedom in the selection of the geometry of the constellation. We are interested in avoiding large variations of the mutual distances between spacecraft. In this case, the existence of regions of zero and minimum relative radial acceleration with respect to the nominal trajectory will prevent from the expansion or contraction of the constellation. In the other case, the existence of regions of maximum relative radial acceleration with respect to the nominal trajectory will produce a larger expansion and contraction of the constellation. The goal of this paper is to study these regions in the scenario of the Circular Restricted Three Body Problem by means of a linearization of the equations of motion relative to the periodic orbits around L-4 or L-5. This study corresponds to a preliminar planar formation flight dynamics about triangular libration points in the Earth-Moon system. Additionally, the cost estimate to maintain the constellation in the regions of zero and minimum relative radial acceleration or keeping a rigid configuration is computed with the use of the residual acceleration concept. At the end, the results are compared with the dynamical behavior of the deviation of the constellation from a periodic orbit. (C) 2014 COSPAR. Published by Elsevier Ltd. All rights reserved.2014-12-11T07:49:26ZAn extension problem for the CR fractional Laplacian
http://hdl.handle.net/2117/24794
Title: An extension problem for the CR fractional Laplacian
Authors: Frank, Rupert L.; González Nogueras, María del Mar; Monticelli, Dario D.; Tan, Jinggang
Abstract: We show that the conformally invariant fractional powers of the sub-Laplacian
on the Heisenberg group are given in terms of the scattering operator for an extension
problem to the Siegel upper halfspace. Remarkably, this extension problem is di erent
from the one studied, among others, by Ca arelli and Silvestre.2014-11-21T11:27:55ZFunctional output-controllability of time-invariant singular linear systems
http://hdl.handle.net/2117/24676
Title: Functional output-controllability of time-invariant singular linear systems
Authors: García Planas, María Isabel; Tarragona Romero, Sonia
Abstract: In the space of finite-dimensional
singular linear continuous-time-invariant systems described in the form \begin{equation}\label{eq1}\left . \begin{array}{rl} E \dot x(t)&= Ax(t)+Bu(t)\\ y(t)&=Cx(t)\end{array}{\kern-1mm}\right \}\end{equation}
where $E,A\in M=M_{n}(\mathbb{C})$, $B\in M_{n\times m}(\mathbb{C})$, $C\in M_{p\times n}(\mathbb{C})$, functional output-controllability character is considered. A simple test based in
the computation of the rank of a certain constant matrix that can be associated to the system is presented2014-11-11T12:18:07Z