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http://hdl.handle.net/2117/3227
Sun, 01 Mar 2015 15:16:14 GMT2015-03-01T15:16:14Zwebmaster.bupc@upc.eduUniversitat Politècnica de Catalunya. Servei de Biblioteques i DocumentaciónoNonlinear 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.http://hdl.handle.net/2117/22391Cabré Vilagut, Xavier; Sire, YannicknoThis 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.Estructuras A-infinito en la opérada de cactus
http://hdl.handle.net/2117/22097
Title: Estructuras A-infinito en la opérada de cactus
Authors: Gálvez Carrillo, Maria Immaculada; Lombardi, Leandro; Tonks, Andrew
Abstract: Diversas versiones de la opérada de cactus inicialmente definida por Voronov han sido estudiadas. Es conocida su equivalencia débil con la opérada de pequeños discos. Se conoce pues que la opérada de cactus admite una acción de la opérada de Gerstenhaber salvo homotopía. En este proyecto, nuestro objetivo es obtener una realización explícita de dicha acción. Por el momento, hemos construido una acción explícita de la opérada A8 en la opérada de cactus, que presentamos en este pósterhttp://hdl.handle.net/2117/22097Gálvez Carrillo, Maria Immaculada; Lombardi, Leandro; Tonks, AndrewnoDiversas versiones de la opérada de cactus inicialmente definida por Voronov han sido estudiadas. Es conocida su equivalencia débil con la opérada de pequeños discos. Se conoce pues que la opérada de cactus admite una acción de la opérada de Gerstenhaber salvo homotopía. En este proyecto, nuestro objetivo es obtener una realización explícita de dicha acción. Por el momento, hemos construido una acción explícita de la opérada A8 en la opérada de cactus, que presentamos en este pósterAction-angle variables and a KAM theorem for b-Poisson manifolds
http://hdl.handle.net/2117/26390
Title: Action-angle variables and a KAM theorem for b-Poisson manifolds
Authors: Kiesenhofer, Anna; Miranda Galcerán, Eva; Scott, Geoffrey
Abstract: In this article we prove an action-angle theorem for b-integrable systems on b-Poisson manifolds improving the action-angle theorem contained in [LMV11] for general Poisson manifolds in this setting. As an application, we prove a KAM-type theorem for b-Poisson manifolds.Tue, 17 Feb 2015 12:12:30 GMThttp://hdl.handle.net/2117/263902015-02-17T12:12:30ZKiesenhofer, Anna; Miranda Galcerán, Eva; Scott, GeoffreynoIn this article we prove an action-angle theorem for b-integrable systems on b-Poisson manifolds improving the action-angle theorem contained in [LMV11] for general Poisson manifolds in this setting. As an application, we prove a KAM-type theorem for b-Poisson manifolds.Structural 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.Thu, 05 Feb 2015 10:53:33 GMThttp://hdl.handle.net/2117/262262015-02-05T10:53:33ZFerrer Llop, Josep; Peña Carrera, Marta; Susín Sánchez, AntonionoVECTOR-FIELDSStructural 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.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, MartaThu, 22 Jan 2015 12:04:00 GMThttp://hdl.handle.net/2117/260312015-01-22T12:04:00ZIbáñez Marcelo, Esther; Casanellas Rius, MartanoTree topology reconstruction, Expectation-maximization, Quartet-based method, Evolutionary Markov modelLow 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).Thu, 22 Jan 2015 12:01:03 GMThttp://hdl.handle.net/2117/260292015-01-22T12:01:03ZCasanellas Rius, Marta; Fernández Sánchez, Jesús; Michalek, MateusznoMotivated 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).On 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.Thu, 22 Jan 2015 11:17:38 GMThttp://hdl.handle.net/2117/260242015-01-22T11:17:38ZAcosta-Humànez, Primitivo; Lázaro Ochoa, José Tomás; Morales Ruiz, Juan José; Pantazi, CharanoDifferential Galois theory, Darboux theory of integrability, Poincare problem, rational first integral, integrating factor, Riccati equation, Lienard equation, Liouvillian solution, INVARIANT ALGEBRAIC-CURVES, LINEAR-DIFFERENTIAL EQUATIONS, DARBOUX INTEGRATING FACTORS, INVERSE PROBLEMS, 1ST INTEGRALS, POINCARE PROBLEM, GALOIS THEORY, SYSTEMS, FOLIATIONS, MULTIPLICITYWe 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.Multi-agent linear dynamical systems, analyzing the consensus problem
http://hdl.handle.net/2117/25531
Title: Multi-agent linear dynamical systems, analyzing the consensus problem
Authors: García Planas, María Isabel
Abstract: In this paper the consensus problem is considered
for multi-agent systems having an independent agent
and fixed topology.Thu, 15 Jan 2015 09:18:49 GMThttp://hdl.handle.net/2117/255312015-01-15T09:18:49ZGarcía Planas, María IsabelnoMulti-agent systems, consensus, controlIn this paper the consensus problem is considered
for multi-agent systems having an independent agent
and fixed topology.Layer 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.Thu, 08 Jan 2015 12:16:16 GMThttp://hdl.handle.net/2117/251752015-01-08T12:16:16ZGonzález Nogueras, María del Mar; Saéz, Mariel; Sire, YannicknoFractional Laplacian, Hyperbolic space, Layer solution, Symmetry, SEMILINEAR ELLIPTIC-EQUATIONS, PHASE-TRANSITIONS, SYMMETRY, CONJECTURE, REGULARITY, MANIFOLDS, GIORGIWe 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.Sufficient 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.Thu, 11 Dec 2014 12:39:29 GMThttp://hdl.handle.net/2117/250022014-12-11T12:39:29ZGarcía Planas, María Isabel; Domínguez García, José Luis; Um, Laurence EmilienoLinear systems, serial composite
systems, parallel composite systems, controllability, observability, functional-output controllabilityThis 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.Xiao's conjuecture for general fibred surfaces
http://hdl.handle.net/2117/24999
Title: Xiao's conjuecture for general fibred surfaces
Authors: Barja Yáñez, Miguel Ángel; González Alonso, Víctor; Naranjo del Val, Joan Carles
Abstract: We prove that the genus g, the relative irregularity q_f and the Clifford index c_f of a non-isotrivial fibration
f satisfy the inequality q_f=g-c_f. This gives in particular a proof of Xiao’s conjecture for
fibrations whose general fibres have maximal Clifford index.
Description: PrerpintThu, 11 Dec 2014 12:05:29 GMThttp://hdl.handle.net/2117/249992014-12-11T12:05:29ZBarja Yáñez, Miguel Ángel; González Alonso, Víctor; Naranjo del Val, Joan CarlesnoFibration
Slope
Xiao's conjecture
Clifford IndexWe prove that the genus g, the relative irregularity q_f and the Clifford index c_f of a non-isotrivial fibration
f satisfy the inequality q_f=g-c_f. This gives in particular a proof of Xiao’s conjecture for
fibrations whose general fibres have maximal Clifford index.Stability and singularities of relative hypersurfaces
http://hdl.handle.net/2117/24998
Title: Stability and singularities of relative hypersurfaces
Authors: Barja Yáñez, Miguel Ángel; Stoppino, Lidia
Abstract: We study relative hypersurfaces, and prove an instability condition for the fibres. This
is the starting point for an investigation of the geometry of effective divisors on relative
projective bundles.Thu, 11 Dec 2014 12:01:17 GMThttp://hdl.handle.net/2117/249982014-12-11T12:01:17ZBarja Yáñez, Miguel Ángel; Stoppino, LidianoSlope
Hypersurfaces
StabilityWe study relative hypersurfaces, and prove an instability condition for the fibres. This
is the starting point for an investigation of the geometry of effective divisors on relative
projective bundles.Addendum 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.Thu, 11 Dec 2014 09:15:25 GMThttp://hdl.handle.net/2117/249962014-12-11T09:15:25ZÁlvarez Montaner, Josep; Yanagawa, KohjinoStanley–Reisner rings, Cartier algebrasWe give a purely combinatorial characterization of complete Stanley–Reisner rings having a principally generated (equivalently, finitely generated) Cartier algebra.Algebraic description of Jacobians isogeneous to certain Prym varieties with polarization (1,2)
http://hdl.handle.net/2117/24994
Title: Algebraic description of Jacobians isogeneous to certain Prym varieties with polarization (1,2)
Authors: Fedorov, Yuri; Enolski, Viktor Z.
Abstract: For a class of non-hyperelliptic genus 3 curves C which are 2-fold coverings of elliptic curves E, we give an explicit algebraic description of all birationally non-equivalent genus 2 curves whose Jacobians are degree 2 isogeneous to the Prym varieties associated to such coverings. Our description is based on previous studies of Prym varieties with polarization (1,2) in connection with separation of variables in a series of classical and new algebraic integrable systems linearized on such varieties.
We also consider some special cases of the covering C -> E, in particular, when the corresponding Prym varieties contain pairs of elliptic curves and the Jacobian of C is isogeneous (but not isomorphic) to the product of 3 different elliptic curves.
Our description is accompanied with explicit numerical examplesThu, 11 Dec 2014 08:09:29 GMThttp://hdl.handle.net/2117/249942014-12-11T08:09:29ZFedorov, Yuri; Enolski, Viktor Z.noFor a class of non-hyperelliptic genus 3 curves C which are 2-fold coverings of elliptic curves E, we give an explicit algebraic description of all birationally non-equivalent genus 2 curves whose Jacobians are degree 2 isogeneous to the Prym varieties associated to such coverings. Our description is based on previous studies of Prym varieties with polarization (1,2) in connection with separation of variables in a series of classical and new algebraic integrable systems linearized on such varieties.
We also consider some special cases of the covering C -> E, in particular, when the corresponding Prym varieties contain pairs of elliptic curves and the Jacobian of C is isogeneous (but not isomorphic) to the product of 3 different elliptic curves.
Our description is accompanied with explicit numerical examplesA 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.Thu, 11 Dec 2014 08:01:15 GMThttp://hdl.handle.net/2117/249932014-12-11T08:01:15ZLlibre Saló, Jaume; Ramírez Ros, Rafael; Sadovskaia Nurimanova, Natalia GuennadievnanoVariational principle, Generalized Hamiltonian principle, d'Alembert-Lagrange principle, Constrained Lagrangian system, Transpositional relations, Vakonomic mechanic, Equation of motion, Vorones system, Chapligyn system, Newtonian model, NONHOLONOMIC SYSTEMS, CONSTRAINED SYSTEMS, DYNAMICS, REALIZATION, PRINCIPLE, GEOMETRYThe 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.