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http://hdl.handle.net/2117/3227
Sat, 20 Dec 2014 22:37:11 GMT20141220T22:37:11Zwebmaster.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 followup 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 followup 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 Ainfinito en la opérada de cactus
http://hdl.handle.net/2117/22097
Title: Estructuras Ainfinito 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 pósterSufficient 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 continuoustimeinvariant 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 outputcontrollability of the
first one.Thu, 11 Dec 2014 12:39:29 GMThttp://hdl.handle.net/2117/2500220141211T12:39:29ZGarcía Planas, María Isabel; Domínguez García, José Luis; Um, Laurence EmilienoLinear systems, serial composite
systems, parallel composite systems, controllability, observability, functionaloutput controllabilityThis paper deals with the sufficient conditions
for controllability and observability characters of finitedimensional
linear continuoustimeinvariant 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 outputcontrollability 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 nonisotrivial fibration
f satisfy the inequality q_f=gc_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/2117/2499920141211T12:05:29ZBarja 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 nonisotrivial fibration
f satisfy the inequality q_f=gc_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/2117/2499820141211T12:01:17ZBarja 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/2117/2499620141211T09:15:25ZÁlvarez 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 nonhyperelliptic genus 3 curves C which are 2fold coverings of elliptic curves E, we give an explicit algebraic description of all birationally nonequivalent 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/2117/2499420141211T08:09:29ZFedorov, Yuri; Enolski, Viktor Z.noFor a class of nonhyperelliptic genus 3 curves C which are 2fold coverings of elliptic curves E, we give an explicit algebraic description of all birationally nonequivalent 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 Lagranged'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 nonzero 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'AlembertLagrange principle. We provide a new point of view on the transpositional relations for the constrained mechanical systems: the virtual variations can produce zero or nonzero transpositional relations. In particular, the independent virtual variations can produce nonzero 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/2117/2499320141211T08:01:15ZLlibre Saló, Jaume; Ramírez Ros, Rafael; Sadovskaia Nurimanova, Natalia GuennadievnanoVariational principle, Generalized Hamiltonian principle, d'AlembertLagrange 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 Lagranged'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 nonzero 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'AlembertLagrange principle. We provide a new point of view on the transpositional relations for the constrained mechanical systems: the virtual variations can produce zero or nonzero transpositional relations. In particular, the independent virtual variations can produce nonzero 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.Zero, minimum and maximum relative radial acceleration for planar formation flight dynamics near triangular libration points in the EarthMoon 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 EarthMoon 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 L4 or L5 in the EarthMoon 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 L4 or L5. This study corresponds to a preliminar planar formation flight dynamics about triangular libration points in the EarthMoon 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.Thu, 11 Dec 2014 07:49:26 GMThttp://hdl.handle.net/2117/2499220141211T07:49:26ZSalazar, F.J.T; Masdemont Soler, Josep; Gómez Muntané, Gerard; Macau, E.E.N.; Winter, O. C.noFormation flight of satellites, Zero Relative Radial Acceleration, EarthMoon system, Circular Restricted Three Body Problem, Stable Lagrangian points, Residual acceleration, PERIODICORBITS, ELLIPTIC ORBITS, QUADRATIC DRAG, MOTION, STABILITY, MISSIONAssume a constellation of satellites is flying near a given nominal trajectory around L4 or L5 in the EarthMoon 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 L4 or L5. This study corresponds to a preliminar planar formation flight dynamics about triangular libration points in the EarthMoon 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.Symplectic and poisson structures with symmetries in interaction
http://hdl.handle.net/2117/24854
Title: Symplectic and poisson structures with symmetries in interaction
Authors: Miranda Galcerán, Eva
Abstract: Hamiltonian actions constitute a central object of study in symplectic
geometry. Special attention has been devoted to the toric case. Toric
symplectic manifolds provide natural examples of integrable systems
and every integrable system on a symplectic manifold is a toric manifold
in a neighbourhood of a compact fiber (Arnold–Liouville). The
classification of toric symplectic manifolds is given by Delzant’s theorem
in terms of the image of the moment map (Delzant polytope)....Wed, 26 Nov 2014 13:04:51 GMThttp://hdl.handle.net/2117/2485420141126T13:04:51ZMiranda Galcerán, EvanoHamiltonian actions constitute a central object of study in symplectic
geometry. Special attention has been devoted to the toric case. Toric
symplectic manifolds provide natural examples of integrable systems
and every integrable system on a symplectic manifold is a toric manifold
in a neighbourhood of a compact fiber (Arnold–Liouville). The
classification of toric symplectic manifolds is given by Delzant’s theorem
in terms of the image of the moment map (Delzant polytope)....An 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 subLaplacian
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.Fri, 21 Nov 2014 11:27:55 GMThttp://hdl.handle.net/2117/2479420141121T11:27:55ZFrank, Rupert L.; González Nogueras, María del Mar; Monticelli, Dario D.; Tan, JinggangnoWe show that the conformally invariant fractional powers of the subLaplacian
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.Functional outputcontrollability of timeinvariant singular linear systems
http://hdl.handle.net/2117/24676
Title: Functional outputcontrollability of timeinvariant singular linear systems
Authors: García Planas, María Isabel; Tarragona Romero, Sonia
Abstract: In the space of finitedimensional
singular linear continuoustimeinvariant 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}{\kern1mm}\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 outputcontrollability 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 presentedTue, 11 Nov 2014 12:18:07 GMThttp://hdl.handle.net/2117/2467620141111T12:18:07ZGarcía Planas, María Isabel; Tarragona Romero, SonianoSingular Systems, Functional outputcontrollabilityIn the space of finitedimensional
singular linear continuoustimeinvariant 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}{\kern1mm}\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 outputcontrollability 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 presentedRigidity of Poisson Lie group actions
http://hdl.handle.net/2117/24632
Title: Rigidity of Poisson Lie group actions
Authors: Miranda Galcerán, Eva
Abstract: n this paper we prove that close infinitesimal momentum maps associated to Poisson Lie actions are equivalent under some mild assumptions. We also obtain rigidity theorems for actual momentum maps (when the acting Lie group G is endowed with an arbitrary Poisson structure) combining a rigidity result for canonical Hamiltonian actions (\cite{MMZ}) and a linearization theorem(\cite{GW}). These results have applications to quantization of symmetries since these infinitesimal momentum maps appear as the classical limit of quantum momentum maps (\cite{BEN}).Mon, 10 Nov 2014 12:51:24 GMThttp://hdl.handle.net/2117/2463220141110T12:51:24ZMiranda Galcerán, Evanon this paper we prove that close infinitesimal momentum maps associated to Poisson Lie actions are equivalent under some mild assumptions. We also obtain rigidity theorems for actual momentum maps (when the acting Lie group G is endowed with an arbitrary Poisson structure) combining a rigidity result for canonical Hamiltonian actions (\cite{MMZ}) and a linearization theorem(\cite{GW}). These results have applications to quantization of symmetries since these infinitesimal momentum maps appear as the classical limit of quantum momentum maps (\cite{BEN}).A 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 nondiabetic wound healing, an e ect that we will
consider in this paper.Mon, 20 Oct 2014 10:27:38 GMThttp://hdl.handle.net/2117/2442220141020T10:27:38ZConsul Porras, M. Nieves; Oliva, Sergio M.; Pellicer, MartanoWound healing modelling, diabetes infuence, analytical wellposedness, bifurcation diagrams, numerical analysis of equilibria.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 nondiabetic wound healing, an e ect that we will
consider in this paper.Lyubeznik numbers of local rings and linear strands of graded ideals
http://hdl.handle.net/2117/24185
Title: Lyubeznik numbers of local rings and linear strands of graded ideals
Authors: Álvarez Montaner, Josep; Yanagawa, Kohji
Abstract: n this work we intro duce a new set of invariants asso ciated to the linear
strands of a minimal free resolution of a
Z
graded ideal
I
R
=

[
x
1
;:::;x
n
]
. We
also prove that these invariants satisfy some prop erties analogous to those of Lyub eznik
numb ers of lo cal rings. In particular, they satisfy a consecutiveness prop erty that we
prove rst for Lyub eznik numb ers. For the case of squarefree monomial ideals we get
more insight on the relation b etween Lyub eznik numb ers and the linear strands of their
asso ciated Alexander dual ideals. Finally, we prove that Lyub eznik numb ers of Stanley
Reisner rings are not only an algebraic invariant but also a top ological invariant, meaning
that they dep end on the homeomorphic class of the geometric realization of the asso ciated
simplicial complex and the characteristic of the base fieldTue, 30 Sep 2014 09:46:24 GMThttp://hdl.handle.net/2117/2418520140930T09:46:24ZÁlvarez Montaner, Josep; Yanagawa, Kohjinon this work we intro duce a new set of invariants asso ciated to the linear
strands of a minimal free resolution of a
Z
graded ideal
I
R
=

[
x
1
;:::;x
n
]
. We
also prove that these invariants satisfy some prop erties analogous to those of Lyub eznik
numb ers of lo cal rings. In particular, they satisfy a consecutiveness prop erty that we
prove rst for Lyub eznik numb ers. For the case of squarefree monomial ideals we get
more insight on the relation b etween Lyub eznik numb ers and the linear strands of their
asso ciated Alexander dual ideals. Finally, we prove that Lyub eznik numb ers of Stanley
Reisner rings are not only an algebraic invariant but also a top ological invariant, meaning
that they dep end on the homeomorphic class of the geometric realization of the asso ciated
simplicial complex and the characteristic of the base field