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http://hdl.handle.net/2117/127
Mon, 24 Nov 2014 12:43:58 GMT2014-11-24T12:43:58Zwebmaster.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 pósterJ2 effect and elliptic inclined periodic orbits in the collision three-body problem
http://hdl.handle.net/2117/21117
Title: J2 effect and elliptic inclined periodic orbits in the collision three-body problem
Authors: Barrabes, Esther; Cors Iglesias, Josep Maria; Pinyol, Conxita; Soler Villanueva, Jaume
Abstract: The existence of a new class of inclined periodic orbits of the collision restricted
three{body problem is shown. The symmetric periodic solutions found are perturbations of elliptic
kepler orbits and they exist only for special values of the inclination and are related to the motion
of a satellite around an oblate planet.http://hdl.handle.net/2117/21117Barrabes, Esther; Cors Iglesias, Josep Maria; Pinyol, Conxita; Soler Villanueva, Jaumenocollision restricted three-body problem, periodic orbits, symmetric orbits, critical inclination, continuation methodThe existence of a new class of inclined periodic orbits of the collision restricted
three{body problem is shown. The symmetric periodic solutions found are perturbations of elliptic
kepler orbits and they exist only for special values of the inclination and are related to the motion
of a satellite around an oblate planet.Signatura de les formes bilineals simètriques
http://hdl.handle.net/2117/24807
Title: Signatura de les formes bilineals simètriques
Authors: Rossell Garriga, Josep Maria; Rubio Díaz, Pedrohttp://hdl.handle.net/2117/24807Rossell Garriga, Josep Maria; Rubio Díaz, PedronoThe graph distance game and some graph operations
http://hdl.handle.net/2117/24796
Title: The graph distance game and some graph operations
Authors: Cáceres, José; Hernando Martín, María del Carmen; Mora Giné, Mercè; Pelayo Melero, Ignacio Manuel; Puertas, M. Luz
Abstract: In the graph distance game, two players alternate in constructing a max-
imal path. The objective function is the distance between the two endpoints of the
path, which one player tries to maximize and the other tries to minimize. In this paper
we examine the distance game for various graph operations: the join, the corona and
the lexicographic product of graphs. We provide general bounds and exact results for
special graphsFri, 21 Nov 2014 12:24:49 GMThttp://hdl.handle.net/2117/247962014-11-21T12:24:49ZCáceres, José; Hernando Martín, María del Carmen; Mora Giné, Mercè; Pelayo Melero, Ignacio Manuel; Puertas, M. LuznoDistance game, graph operationsIn the graph distance game, two players alternate in constructing a max-
imal path. The objective function is the distance between the two endpoints of the
path, which one player tries to maximize and the other tries to minimize. In this paper
we examine the distance game for various graph operations: the join, the corona and
the lexicographic product of graphs. We provide general bounds and exact results for
special graphsAn 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.Fri, 21 Nov 2014 11:27:55 GMThttp://hdl.handle.net/2117/247942014-11-21T11:27:55ZFrank, Rupert L.; González Nogueras, María del Mar; Monticelli, Dario D.; Tan, JinggangnoWe 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.Preservation of controllability-observability in expanded systems
http://hdl.handle.net/2117/24791
Title: Preservation of controllability-observability in expanded systems
Authors: Bakule, Lubomir; Rodellar Benedé, José; Rossell Garriga, Josep Maria; Rubio Díaz, Pedro
Abstract: The result contributed by the article is that controllability-observability of an original continuous-time LTI dynamic system can always be simultaneously preserved in expanded systems within the inclusion principle when using block structured complementary matrices. This new structure offers more degrees of freedom for the selection of specific complementary matrices than well known used cases, such as aggregations and restrictions, which enable such preservation only in certain special cases. A complete unrestricted transmission of these qualitative properties from the original controllable-observable system to its expansion is a basic requirement on the expansion/contraction process, mainly when controllers/observers are designed in expanded systems to be consequently contracted for implementation in initially given systems. An original system composed of two overlapped subsystems is adopted as a general prototype ease. A numerical example is suppliedThu, 20 Nov 2014 16:55:31 GMThttp://hdl.handle.net/2117/247912014-11-20T16:55:31ZBakule, Lubomir; Rodellar Benedé, José; Rossell Garriga, Josep Maria; Rubio Díaz, PedronoControllability, Inclusion principle, Large-scale systems, Observability, Overlapping decompositionThe result contributed by the article is that controllability-observability of an original continuous-time LTI dynamic system can always be simultaneously preserved in expanded systems within the inclusion principle when using block structured complementary matrices. This new structure offers more degrees of freedom for the selection of specific complementary matrices than well known used cases, such as aggregations and restrictions, which enable such preservation only in certain special cases. A complete unrestricted transmission of these qualitative properties from the original controllable-observable system to its expansion is a basic requirement on the expansion/contraction process, mainly when controllers/observers are designed in expanded systems to be consequently contracted for implementation in initially given systems. An original system composed of two overlapped subsystems is adopted as a general prototype ease. A numerical example is suppliedOverlapping reliable control for a cable-stayed bridge benchmark
http://hdl.handle.net/2117/24790
Title: Overlapping reliable control for a cable-stayed bridge benchmark
Authors: Bakule, Lubomir; Paulet-Crainiceanu, Fideliu; Rodellar Benedé, José; Rossell Garriga, Josep Maria
Abstract: The brief presents a reliable 1-out-2 reduced order control design strategy for a cable-stayed bridge benchmark using two overlapping subsystems and the linear quadratic Gaussian (LQG) design. Reliability with regard to controller failures is considered. Local controllers are designed for reduced order subsystems of expanded system. They are implemented and evaluated on the original overall system model. Two different sets of numerical experiments of reliable control design within 1-out-2 controller failure structure have been systematically tested using a SIMULINK scheme and compared to the benchmark sample centralized LQG design. The performance of the reliable control design has been assessed by means of given benchmark evaluation criteria. The dynamics of the closed-loop benchmark model with this multiple controller exhibits an acceptable behavior though slightly worse than in the centralized case. Thereby, the main result is a practical well working 1-out-2 reliable controller designed for a real world large-scale system. The significance of this new strategy lies in its practical systematic approach for reliable control design for large scale systems.Thu, 20 Nov 2014 16:48:44 GMThttp://hdl.handle.net/2117/247902014-11-20T16:48:44ZBakule, Lubomir; Paulet-Crainiceanu, Fideliu; Rodellar Benedé, José; Rossell Garriga, Josep MarianoDecentralized linear quadratic Gaussian (LQG) design, Inclusion principle, Large scale systems, Overlapping decompositions, Reduced order control design, Reliable controlThe brief presents a reliable 1-out-2 reduced order control design strategy for a cable-stayed bridge benchmark using two overlapping subsystems and the linear quadratic Gaussian (LQG) design. Reliability with regard to controller failures is considered. Local controllers are designed for reduced order subsystems of expanded system. They are implemented and evaluated on the original overall system model. Two different sets of numerical experiments of reliable control design within 1-out-2 controller failure structure have been systematically tested using a SIMULINK scheme and compared to the benchmark sample centralized LQG design. The performance of the reliable control design has been assessed by means of given benchmark evaluation criteria. The dynamics of the closed-loop benchmark model with this multiple controller exhibits an acceptable behavior though slightly worse than in the centralized case. Thereby, the main result is a practical well working 1-out-2 reliable controller designed for a real world large-scale system. The significance of this new strategy lies in its practical systematic approach for reliable control design for large scale systems.Generalized selection of complementary matrices in the inclusion principle
http://hdl.handle.net/2117/24789
Title: Generalized selection of complementary matrices in the inclusion principle
Authors: Bakule, Lubomir; Rodellar Benedé, José; Rossell Garriga, Josep Maria
Abstract: This paper presents a strategy for choosing complementary matrices in the framework of the inclusion principle with state LQ optimal control of LTI systems, it is based on translating the basic restrictions given by the inclusion principle into explicit block structures for these matrices, the degree of freedom given by these structures is illustrated by means of an example of overlapping decentralized control designThu, 20 Nov 2014 16:12:13 GMThttp://hdl.handle.net/2117/247892014-11-20T16:12:13ZBakule, Lubomir; Rodellar Benedé, José; Rossell Garriga, Josep MarianoDecentralization, Inclusion principle, Large-scale systems, Optimal control, Overlapping decompositionThis paper presents a strategy for choosing complementary matrices in the framework of the inclusion principle with state LQ optimal control of LTI systems, it is based on translating the basic restrictions given by the inclusion principle into explicit block structures for these matrices, the degree of freedom given by these structures is illustrated by means of an example of overlapping decentralized control designNonuniform Fuchsian codes for noisy channels
http://hdl.handle.net/2117/24788
Title: Nonuniform Fuchsian codes for noisy channels
Authors: Blanco Chacón, Iván; Remón Adell, Dionís; Hollanti, Camilla; Alsina Aubach, Montserrat
Abstract: We develop a new transmission scheme for additive white Gaussian noisy (AWGN) channels based on Fuchsian groups from rational quaternion algebras. The structure of the proposed Fuchsian codes is nonlinear and nonuniform, hence conventional decoding methods based on linearity and symmetry do not apply. Previously, only brute force decoding methods with complexity that is linear in the code size exist for general nonuniform codes. However, the properly discontinuous character of the action of the Fuchsian groups on the complex upper half-plane translates into decoding complexity that is logarithmic in the code size via a recently introduced point reduction algorithm.Thu, 20 Nov 2014 15:52:25 GMThttp://hdl.handle.net/2117/247882014-11-20T15:52:25ZBlanco Chacón, Iván; Remón Adell, Dionís; Hollanti, Camilla; Alsina Aubach, MontserratnoNoisy channelWe develop a new transmission scheme for additive white Gaussian noisy (AWGN) channels based on Fuchsian groups from rational quaternion algebras. The structure of the proposed Fuchsian codes is nonlinear and nonuniform, hence conventional decoding methods based on linearity and symmetry do not apply. Previously, only brute force decoding methods with complexity that is linear in the code size exist for general nonuniform codes. However, the properly discontinuous character of the action of the Fuchsian groups on the complex upper half-plane translates into decoding complexity that is logarithmic in the code size via a recently introduced point reduction algorithm.Fixed subgroups in free groups: a survey
http://hdl.handle.net/2117/24787
Title: Fixed subgroups in free groups: a survey
Authors: Ventura Capell, Enric
Abstract: This note is a survey of the main results known about fixed subgroups
of endomorphisms of finitely generated free groups. A historic point
of view is taken, emphasizing the evolution of this line of research, from its
beginning to the present time. The article concludes with a section containing the main open problems and conjectures, with some comments and discussions on them.Thu, 20 Nov 2014 13:38:23 GMThttp://hdl.handle.net/2117/247872014-11-20T13:38:23ZVentura Capell, EnricnoThis note is a survey of the main results known about fixed subgroups
of endomorphisms of finitely generated free groups. A historic point
of view is taken, emphasizing the evolution of this line of research, from its
beginning to the present time. The article concludes with a section containing the main open problems and conjectures, with some comments and discussions on them.On automorphism-fixed subgroups of a free group
http://hdl.handle.net/2117/24777
Title: On automorphism-fixed subgroups of a free group
Authors: Martino, Armando; Ventura Capell, Enric
Abstract: Let F be a flnitely generated free group, and let n denote its rank. A subgroup H of F is said to be automorphism-flxed, or auto-flxed for short, if there exists a set S of automorphisms of F such that H is precisely the set of elements flxed by every element of S; similarly, H is 1-auto-flxed if there exists a single automorphism of F whose set of flxed elements is precisely H. We show that each auto-flxed subgroup of F is a free factor of a 1-auto-flxed subgroup of F. We show also that if (and only if) n ‚ 3, then there exist free factors of 1-auto-flxed subgroups of F which are not auto-flxed subgroups of F. A 1-auto-flxed subgroup H of F has rank at most n, by the Bestvina-Handel Theorem, and if H has rank exactly n, then H is said to be a maximum-rank 1-auto-flxed subgroup of F, and similarly for auto-flxed subgroups. Hence a maximum-rank auto-flxed subgroup of F is a (maximum-rank) 1-auto-flxed subgroup of F. We further prove that if H is a maximum-rank 1-auto-flxed subgroup of F, then the group of automorphisms of F which flx every element of H is free abelian of rank at most n ¡ 1. All of our results apply also to endomorphisms.Wed, 19 Nov 2014 16:52:21 GMThttp://hdl.handle.net/2117/247772014-11-19T16:52:21ZMartino, Armando; Ventura Capell, EnricnoLet F be a flnitely generated free group, and let n denote its rank. A subgroup H of F is said to be automorphism-flxed, or auto-flxed for short, if there exists a set S of automorphisms of F such that H is precisely the set of elements flxed by every element of S; similarly, H is 1-auto-flxed if there exists a single automorphism of F whose set of flxed elements is precisely H. We show that each auto-flxed subgroup of F is a free factor of a 1-auto-flxed subgroup of F. We show also that if (and only if) n ‚ 3, then there exist free factors of 1-auto-flxed subgroups of F which are not auto-flxed subgroups of F. A 1-auto-flxed subgroup H of F has rank at most n, by the Bestvina-Handel Theorem, and if H has rank exactly n, then H is said to be a maximum-rank 1-auto-flxed subgroup of F, and similarly for auto-flxed subgroups. Hence a maximum-rank auto-flxed subgroup of F is a (maximum-rank) 1-auto-flxed subgroup of F. We further prove that if H is a maximum-rank 1-auto-flxed subgroup of F, then the group of automorphisms of F which flx every element of H is free abelian of rank at most n ¡ 1. All of our results apply also to endomorphisms.Twisted conjugacy in braid groups
http://hdl.handle.net/2117/24771
Title: Twisted conjugacy in braid groups
Authors: Gonzalez Meneses, Juan; Ventura Capell, Enric
Abstract: In this note we solve the twisted conjugacy problem for braid groups, i.e., we propose an algorithm which, given two braids u,v is an element of B-n and an automorphism phi is an element of Aut(B-n), decides whether v = (phi(x))(-1)-ux for some x is an element of B-n. As a corollary, we deduce that each group of the form B-n x H, a semidirect product of the braid group B-n by a torsion-free hyperbolic group H, has solvable conjugacy problem.Wed, 19 Nov 2014 15:52:22 GMThttp://hdl.handle.net/2117/247712014-11-19T15:52:22ZGonzalez Meneses, Juan; Ventura Capell, EnricnoBraid group, Twisted conjugacyIn this note we solve the twisted conjugacy problem for braid groups, i.e., we propose an algorithm which, given two braids u,v is an element of B-n and an automorphism phi is an element of Aut(B-n), decides whether v = (phi(x))(-1)-ux for some x is an element of B-n. As a corollary, we deduce that each group of the form B-n x H, a semidirect product of the braid group B-n by a torsion-free hyperbolic group H, has solvable conjugacy problem.Robust treatment of degenerate elements in interactive corotational FEM simulations
http://hdl.handle.net/2117/24735
Title: Robust treatment of degenerate elements in interactive corotational FEM simulations
Authors: Civit Flores, Oscar; Susín Sánchez, Antonio
Abstract: We address the problem of robust and efficient treatment of element collapse and inversion in corotational FEM simulations of deformable objects in two and three dimensions, and show that existing degeneration treatment methods have previously unreported flaws that seriously threaten robustness and physical plausibility in interactive applications. We propose a new method that avoids such flaws, yields faster and smoother degeneration recovery and extends the range of well-behaved degenerate configurations without adding significant complexity or computational cost to standard explicit and quasi-implicit solvers.Mon, 17 Nov 2014 11:06:59 GMThttp://hdl.handle.net/2117/247352014-11-17T11:06:59ZCivit Flores, Oscar; Susín Sánchez, Antonionodeformable objects, finite element method, interactive simulation, DECOMPOSITIONWe address the problem of robust and efficient treatment of element collapse and inversion in corotational FEM simulations of deformable objects in two and three dimensions, and show that existing degeneration treatment methods have previously unreported flaws that seriously threaten robustness and physical plausibility in interactive applications. We propose a new method that avoids such flaws, yields faster and smoother degeneration recovery and extends the range of well-behaved degenerate configurations without adding significant complexity or computational cost to standard explicit and quasi-implicit solvers.Effect of changing the copular when choosing the primary endpoint in a Randomized Clinical Trial
http://hdl.handle.net/2117/24709
Title: Effect of changing the copular when choosing the primary endpoint in a Randomized Clinical Trial
Authors: Plana Ripoll, Oleguer; Gómez Melis, GuadalupeWed, 12 Nov 2014 18:44:12 GMThttp://hdl.handle.net/2117/247092014-11-12T18:44:12ZPlana Ripoll, Oleguer; Gómez Melis, Guadalupeno