DSpace Collection:
http://hdl.handle.net/2117/3228
2015-01-26T14:33:31ZNonlinear 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.EMtree 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 presented2014-11-11T12:18:07ZA PDE approach of inflammatory phase dynamics in diabetic wounds.
http://hdl.handle.net/2117/24422
Title: A PDE approach of inflammatory phase dynamics in diabetic wounds.
Authors: Consul Porras, M. Nieves; Oliva, Sergio M.; Pellicer, Marta
Abstract: The objective of the present paper is the modeling and analysis of the
dynamics of macrophages and certain growth factors in the in
ammatory phase, the rst one of the wound healing process. It is the phase where there exists a majordi erence between diabetic and non-diabetic wound healing, an e ect that we will
consider in this paper.2014-10-20T10:27:38ZModelling of a clamped-pinned pipeline conveying fluid for vibrational stability analysis
http://hdl.handle.net/2117/24129
Title: Modelling of a clamped-pinned pipeline conveying fluid for vibrational stability analysis
Authors: Mediano Valiente, Begoña; García Planas, María Isabel
Abstract: Recent developments in materials and cost reduction
have led the study of the vibrational stability of
pipelines conveying fluid to be an important issue.
Nowadays, this analysis is done both by means of simulation
with specialized softwares and by laboratory
testing of the preferred materials. The former usually
requires of complex modelling of the pipeline and the
internal fluid to determine if the material will ensure vibrational
stability; and in the latter case, each time there
is a mistake on the material selection is necessary to
restart all the process making this option expensive. In
this paper, the classical mathematical description of the
dynamic behavior of a clamped-pinned pipeline conveying
fluid is presented. Then, they are approximated
to a Hamiltonian system through Garlekin’s method being
modelled as a simple linear system. The system
stability has been studied by means of the eigenvalues
of the linear system. From this analysis, characteristic
expressions dependent on material constants has been
developed as inequalities, which ensures the stability
of the material if it matches all expressions. This new
model provides a simplified dynamical approximation
of the pipeline conveying fluid depending on material
and fluid constants that is useful to determine if it is
stable or not. It is worth to determine that the model
dynamics does not correspond with the real, but the
global behaviour is well represented. Finally, some
simulations of specific materials have been use to validate
the results obtained from the Hamiltonian model
and a more complex model done with finite element
software.2014-09-22T10:36:12ZGodement resolutions and sheaf homotopy theory
http://hdl.handle.net/2117/24111
Title: Godement resolutions and sheaf homotopy theory
Authors: Rodríguez González, Beatriz; Roig Martí, Agustín
Abstract: The Godement cosimplicial resolution is available for a wide range of categories
of sheaves. In this paper we investigate under which conditions of the Grothendieck site and the category of coefficients it can be used to obtain fibrant models and hence to do sheaf homotopy theory. For instance, for which Grothendieck sites and coefficients we can define sheaf cohomology and derived functors through it2014-09-19T08:39:42ZPeaks and jumps reconstruction with B-splines scaling functions
http://hdl.handle.net/2117/24078
Title: Peaks and jumps reconstruction with B-splines scaling functions
Authors: Ortiz Gracia, Luis; Masdemont Soler, Josep
Abstract: We consider a methodology based on B-splines scaling functions to numerically invert Fourier or Laplace transforms of functions in the space L-2(R). The original function is approximated by a finite combination of jth order B-splines basis functions and we provide analytical expressions for the recovered coefficients. The methodology is particularly well suited when the original function or its derivatives present peaks or jumps due to discontinuities in the domain. We will show in the numerical experiments the robustness and accuracy of the method. (C) 2014 Elsevier B.V. All rights reserved.2014-09-17T11:25:15Z