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http://hdl.handle.net/2117/3917
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20140918T18:04:28Z
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Nonlinear 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/2117/22391
Cabré Vilagut, Xavier; Sire, Yannick
no
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.

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 póster
http://hdl.handle.net/2117/22097
Gálvez Carrillo, Maria Immaculada; Lombardi, Leandro; Tonks, Andrew
no
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 póster

J2 effect and elliptic inclined periodic orbits in the collision threebody problem
http://hdl.handle.net/2117/21117
Title: J2 effect and elliptic inclined periodic orbits in the collision threebody 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/2117/21117
Barrabes, Esther; Cors Iglesias, Josep Maria; Pinyol, Conxita; Soler Villanueva, Jaume
no
collision restricted threebody problem, periodic orbits, symmetric orbits, critical inclination, continuation method
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.

On the representability of the biuniform matroid
http://hdl.handle.net/2117/24101
Title: On the representability of the biuniform matroid
Authors: Ball, Simeon Michael; Padró Laimon, Carles; Weiner, Zsuzsa; Xing, Chaoping
Abstract: Every biuniform matroid is representable over all sufficiently large fields. But it is not known exactly over which finite fields they are representable, and the existence of efficient methods to find a representation for every given biuniform matroid has not been proved. The interest of these problems is due to their implications to secret sharing. The existence of efficient methods to find representations for all biuniform matroids is proved here for the first time. The previously known efficient constructions apply only to a particular class of biuniform matroids, while the known general constructions were not proved to be efficient. In addition, our constructions provide in many cases representations over smaller finite fields.
© 2013, Society for Industrial and Applied Mathematics
Thu, 18 Sep 2014 16:05:12 GMT
http://hdl.handle.net/2117/24101
20140918T16:05:12Z
Ball, Simeon Michael; Padró Laimon, Carles; Weiner, Zsuzsa; Xing, Chaoping
no
matroid theory, representable matroid, biuniform matroid, secret sharing
Every biuniform matroid is representable over all sufficiently large fields. But it is not known exactly over which finite fields they are representable, and the existence of efficient methods to find a representation for every given biuniform matroid has not been proved. The interest of these problems is due to their implications to secret sharing. The existence of efficient methods to find representations for all biuniform matroids is proved here for the first time. The previously known efficient constructions apply only to a particular class of biuniform matroids, while the known general constructions were not proved to be efficient. In addition, our constructions provide in many cases representations over smaller finite fields.
© 2013, Society for Industrial and Applied Mathematics

The degreediameter problem in maximal bipartite planar graphs
http://hdl.handle.net/2117/24097
Title: The degreediameter problem in maximal bipartite planar graphs
Authors: Dalfó Simó, Cristina; Huemer, Clemens; Salas, Julian
Abstract: The (A ,D) (degree/diameter) problem consists of finding the largest possible number of vertices n among all the graphs with maximum degree and diameter D. We consider the (A ,D) problem for maximal planar bipartite graphs, that are simple planar graphs in which every face is a quadrangle. We obtain that for the ( , 2) problem, the number of vertices is n = + 2; and for the ( , 3) problem, n = 3 1 if is odd and n = 3 2 if is even. Then, we study the general case ( A ,D) and obtain that an upper bound on n is approximately 3(2D+1)( 2)bD/2c,
and another one is C(  2)bD/2c if D and C is a sufficiently large constant.
Our upper bounds improve for our kind of graphs the one given by Fellows, Hell and Seyffarth for general planar graphs. We also give a lower bound on n for maximal planar bipartite graphs, which is approximately (  2)k if D = 2k, and 3(  3)k if D = 2k + 1, for and D sufficiently large in both cases.
Thu, 18 Sep 2014 10:55:22 GMT
http://hdl.handle.net/2117/24097
20140918T10:55:22Z
Dalfó Simó, Cristina; Huemer, Clemens; Salas, Julian
no
Maximal planar bipartite graphs
The (A ,D) (degree/diameter) problem consists of finding the largest possible number of vertices n among all the graphs with maximum degree and diameter D. We consider the (A ,D) problem for maximal planar bipartite graphs, that are simple planar graphs in which every face is a quadrangle. We obtain that for the ( , 2) problem, the number of vertices is n = + 2; and for the ( , 3) problem, n = 3 1 if is odd and n = 3 2 if is even. Then, we study the general case ( A ,D) and obtain that an upper bound on n is approximately 3(2D+1)( 2)bD/2c,
and another one is C(  2)bD/2c if D and C is a sufficiently large constant.
Our upper bounds improve for our kind of graphs the one given by Fellows, Hell and Seyffarth for general planar graphs. We also give a lower bound on n for maximal planar bipartite graphs, which is approximately (  2)k if D = 2k, and 3(  3)k if D = 2k + 1, for and D sufficiently large in both cases.

A bound for the maximum weight of a linear code
http://hdl.handle.net/2117/24092
Title: A bound for the maximum weight of a linear code
Authors: Ball, Simeon Michael; Blokhuis, Aart
Abstract: It is shown that the parameters of a linear code over Fq of length n, dimension k, minimum weight d, and maximum weight m satisfy a certain congruence relation. In the case that q = p is a prime, this leads to the bound m &le (nd)pe(p1), where e {0, 1,.., k2} is maximal with the property that (nde) 0 (mod pk1e). Thus, if C contains a codeword of weight n, then nd/(p1)+d+e. The results obtained for linear codes are translated into corresponding results for (n, t)arcs and tfold blocking sets of AG(k1, q). The bounds obtained in these spaces are better than the known bounds for these geometrical objects for many parameters
Wed, 17 Sep 2014 17:03:50 GMT
http://hdl.handle.net/2117/24092
20140917T17:03:50Z
Ball, Simeon Michael; Blokhuis, Aart
no
Mathematical techniques
It is shown that the parameters of a linear code over Fq of length n, dimension k, minimum weight d, and maximum weight m satisfy a certain congruence relation. In the case that q = p is a prime, this leads to the bound m &le (nd)pe(p1), where e {0, 1,.., k2} is maximal with the property that (nde) 0 (mod pk1e). Thus, if C contains a codeword of weight n, then nd/(p1)+d+e. The results obtained for linear codes are translated into corresponding results for (n, t)arcs and tfold blocking sets of AG(k1, q). The bounds obtained in these spaces are better than the known bounds for these geometrical objects for many parameters

An individualbased model for the study of Paracoccus denitrificans, a denitrifying bacterium
http://hdl.handle.net/2117/24089
Title: An individualbased model for the study of Paracoccus denitrificans, a denitrifying bacterium
Authors: Araujo Granda, Pablo Alejandro; Gras Moreu, Anna Maria; Ginovart Gisbert, Marta
Abstract: In order to understand some environmental factors that control N2O production by microbes in agricultural soils, a
virtual bioreactor for Paracoccus denitrificans was designed using a culture medium containing succinate as a
carbon source, ammonium as nitrogen source and various electron acceptors such as oxygen, nitrate, nitrite,
nitrogen monoxide and dinitrogen oxide. INDISIM was the core individualbased model for the bacterial behavior
and five metabolic pathways were selected and translated into balanced chemical equations using the
Thermodynamic Electron Equivalents Model. This thermodynamic approach is the basis of the individual
metabolism that this microbe carries out for its cellular maintenance and production of new biomass. The
preliminary simulation results achieved with the implementation of this model in NetLogo showed that it is
possible to investigate the behavior of this denitrifying bacterium and some of the outputs regarding the temporal
evolutions of the diverse substrates are consistent with previous experimental data carried out with it.
Wed, 17 Sep 2014 16:39:36 GMT
http://hdl.handle.net/2117/24089
20140917T16:39:36Z
Araujo Granda, Pablo Alejandro; Gras Moreu, Anna Maria; Ginovart Gisbert, Marta
no
Denitrification, Paracoccus denitrificans, Individualbased model, Thermodymanic Electron
Equivalents Model, NetLogo
In order to understand some environmental factors that control N2O production by microbes in agricultural soils, a
virtual bioreactor for Paracoccus denitrificans was designed using a culture medium containing succinate as a
carbon source, ammonium as nitrogen source and various electron acceptors such as oxygen, nitrate, nitrite,
nitrogen monoxide and dinitrogen oxide. INDISIM was the core individualbased model for the bacterial behavior
and five metabolic pathways were selected and translated into balanced chemical equations using the
Thermodynamic Electron Equivalents Model. This thermodynamic approach is the basis of the individual
metabolism that this microbe carries out for its cellular maintenance and production of new biomass. The
preliminary simulation results achieved with the implementation of this model in NetLogo showed that it is
possible to investigate the behavior of this denitrifying bacterium and some of the outputs regarding the temporal
evolutions of the diverse substrates are consistent with previous experimental data carried out with it.

Peaks and jumps reconstruction with Bsplines scaling functions
http://hdl.handle.net/2117/24078
Title: Peaks and jumps reconstruction with Bsplines scaling functions
Authors: Ortiz Gracia, Luis; Masdemont Soler, Josep
Abstract: We consider a methodology based on Bsplines scaling functions to numerically invert Fourier or Laplace transforms of functions in the space L2(R). The original function is approximated by a finite combination of jth order Bsplines 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.
Wed, 17 Sep 2014 11:25:15 GMT
http://hdl.handle.net/2117/24078
20140917T11:25:15Z
Ortiz Gracia, Luis; Masdemont Soler, Josep
no
Haar wavelets, Bsplines, Fourier inversion, Peaks and jumps, COS method, FilteredCOS, EUROPEAN OPTIONS
We consider a methodology based on Bsplines scaling functions to numerically invert Fourier or Laplace transforms of functions in the space L2(R). The original function is approximated by a finite combination of jth order Bsplines 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.

Differentiable families of planar bimodal linear control systems
http://hdl.handle.net/2117/24076
Title: Differentiable families of planar bimodal linear control systems
Authors: Ferrer Llop, Josep; Magret Planas, Maria dels Dolors; Peña Carrera, Marta
Abstract: We consider bimodal linear control systems consisting of two subsystems acting on each side of a given hyperplane, assuming continuity along it. For a differentiable family of planar bimodal linear control systems, we obtain its stratification diagram and, if controllability holds for each value of the parameters, we construct a differentiable family of feedbacks which stabilizes both subsystems for each value of the parameters.
Wed, 17 Sep 2014 10:22:24 GMT
http://hdl.handle.net/2117/24076
20140917T10:22:24Z
Ferrer Llop, Josep; Magret Planas, Maria dels Dolors; Peña Carrera, Marta
no
We consider bimodal linear control systems consisting of two subsystems acting on each side of a given hyperplane, assuming continuity along it. For a differentiable family of planar bimodal linear control systems, we obtain its stratification diagram and, if controllability holds for each value of the parameters, we construct a differentiable family of feedbacks which stabilizes both subsystems for each value of the parameters.

Description of characteristic nonhyperinvariant subspaces in GF(2)
http://hdl.handle.net/2117/24075
Title: Description of characteristic nonhyperinvariant subspaces in GF(2)
Authors: Mingueza, David; Montoro López, María Eulalia; Pacha Andújar, Juan Ramón
Abstract: Given a square matrix A , an A invariant subspace is called hyperinvariant (respectively, characteristic) if and only if it is also invariant for all matrices T (respectively, nonsingular matrices T ) that commute with A . Shoda's Theorem gives a necessary and sufficient condition for the existence of characteristic nonhyperinvariant subspaces for a nilpotent matrix in GF(2)GF(2). Here we present an explicit construction for all subspaces of this type.
Wed, 17 Sep 2014 10:09:27 GMT
http://hdl.handle.net/2117/24075
20140917T10:09:27Z
Mingueza, David; Montoro López, María Eulalia; Pacha Andújar, Juan Ramón
no
Hyperinvariant subspaces, Characteristic subspaces, Shoda's Theorem
Given a square matrix A , an A invariant subspace is called hyperinvariant (respectively, characteristic) if and only if it is also invariant for all matrices T (respectively, nonsingular matrices T ) that commute with A . Shoda's Theorem gives a necessary and sufficient condition for the existence of characteristic nonhyperinvariant subspaces for a nilpotent matrix in GF(2)GF(2). Here we present an explicit construction for all subspaces of this type.

Càlcul numèric. Manual de pràctiques
http://hdl.handle.net/2117/24072
Title: Càlcul numèric. Manual de pràctiques
Authors: Lázaro Ochoa, José Tomás; Ollé Torner, Mercè; Pacha Andújar, Juan Ramón
Wed, 17 Sep 2014 07:45:15 GMT
http://hdl.handle.net/2117/24072
20140917T07:45:15Z
Lázaro Ochoa, José Tomás; Ollé Torner, Mercè; Pacha Andújar, Juan Ramón
no

Miniversal deformations of observable marked matrices
http://hdl.handle.net/2117/24071
Title: Miniversal deformations of observable marked matrices
Authors: Compta Creus, Albert; Ferrer Llop, Josep; Peña Carrera, Marta
Abstract: Given the set of vertical pairs of matrices ${\cal M}\subset M_{m,n}(\mathbb C)\times M_n(\mathbb C)$ keeping the subspace $\mathbb C^d\times\{0\}\subset\mathbb C^n$ invariant,we compute
miniversal deformations of a given pair when it is observable, and the subspace $\mathbb C^d\times\{0\}$ is marked. Moreover, we obtain
the dimension of the orbit, characterize the structurally stable vertical pairs, and study the effect of each deformation
parameter. Copyright © 2013 JohnWiley & Sons, Ltd.
Wed, 17 Sep 2014 07:39:47 GMT
http://hdl.handle.net/2117/24071
20140917T07:39:47Z
Compta Creus, Albert; Ferrer Llop, Josep; Peña Carrera, Marta
no
conditioned invariant subspaces, miniversal deformation, stratified manifold, vertical pairs of matrices
Given the set of vertical pairs of matrices ${\cal M}\subset M_{m,n}(\mathbb C)\times M_n(\mathbb C)$ keeping the subspace $\mathbb C^d\times\{0\}\subset\mathbb C^n$ invariant,we compute
miniversal deformations of a given pair when it is observable, and the subspace $\mathbb C^d\times\{0\}$ is marked. Moreover, we obtain
the dimension of the orbit, characterize the structurally stable vertical pairs, and study the effect of each deformation
parameter. Copyright © 2013 JohnWiley & Sons, Ltd.

Computing a visibility polygon using few variables
http://hdl.handle.net/2117/24062
Title: Computing a visibility polygon using few variables
Authors: Barba, Luis; Korman Cozzetti, Matías; Langerman, Stefan; Silveira, Rodrigo Ignacio
Abstract: We present several algorithms for computing the visibility polygon of a simple polygon P of n vertices (out of which r are reflex) from a viewpoint inside P, when P resides in readonly memory and only few working variables can be used. The first algorithm uses a constant number of variables, and outputs the vertices of the visibility polygon in O (n (r) over bar) time, where (r) over bar denotes the number of reflex vertices of P that are part of the output. Whenever we are allowed to use O(s) variables, the running time decreases to O (nr/2(s) + n log(2) r) (or O (nr/2(s) + n log r) randomized expected time), where s is an element of O (log r). This is the first algorithm in which an exponential spacetime tradeoff for a geometric problem is obtained. (C) 2014 Elsevier B.V. All rights reserved.
Mon, 15 Sep 2014 19:28:08 GMT
http://hdl.handle.net/2117/24062
20140915T19:28:08Z
Barba, Luis; Korman Cozzetti, Matías; Langerman, Stefan; Silveira, Rodrigo Ignacio
no
Computational geometry, Memoryconstrained algorithms, Timespacetradeoff visibility, Simple polygon, LIMITED STORAGE, UPPERBOUNDS
We present several algorithms for computing the visibility polygon of a simple polygon P of n vertices (out of which r are reflex) from a viewpoint inside P, when P resides in readonly memory and only few working variables can be used. The first algorithm uses a constant number of variables, and outputs the vertices of the visibility polygon in O (n (r) over bar) time, where (r) over bar denotes the number of reflex vertices of P that are part of the output. Whenever we are allowed to use O(s) variables, the running time decreases to O (nr/2(s) + n log(2) r) (or O (nr/2(s) + n log r) randomized expected time), where s is an element of O (log r). This is the first algorithm in which an exponential spacetime tradeoff for a geometric problem is obtained. (C) 2014 Elsevier B.V. All rights reserved.

The representativeness reliability importance measure
http://hdl.handle.net/2117/24048
Title: The representativeness reliability importance measure
Authors: Freixas Bosch, Josep; Pons Vallès, Montserrat
Abstract: A new reliability importance measure for
components in a system, that we call Representativeness
measure, is introduced. It evaluates to which extent the
performance of a component is representative of the
performance of the whole system. Its relationship with
Birnbaum’s measure is analyzed, and the ranking of
components given by both measures are compared. These
rankings happen to be equal when all components have the
same reliability but different in general. In contrast with
Birnbaum’s, the Representativeness reliability importance
measure of a component does depend on its reliability.
Fri, 12 Sep 2014 10:45:20 GMT
http://hdl.handle.net/2117/24048
20140912T10:45:20Z
Freixas Bosch, Josep; Pons Vallès, Montserrat
no
Reliability importance measures, Structural importance measures, Criticality relation, Coherent systems, node criticality relation, Birnbaum RIM, Birnbaum SIM
A new reliability importance measure for
components in a system, that we call Representativeness
measure, is introduced. It evaluates to which extent the
performance of a component is representative of the
performance of the whole system. Its relationship with
Birnbaum’s measure is analyzed, and the ranking of
components given by both measures are compared. These
rankings happen to be equal when all components have the
same reliability but different in general. In contrast with
Birnbaum’s, the Representativeness reliability importance
measure of a component does depend on its reliability.

Static outputfeedback controller design for structural vibration control: a twostep LMI approach
http://hdl.handle.net/2117/24047
Title: Static outputfeedback controller design for structural vibration control: a twostep LMI approach
Authors: Palacios Quiñonero, Francisco; Rubió Massegú, Josep; Rossell Garriga, Josep Maria; Karimi, Hamid Reza
Abstract: This paper presents a novel controller design strategy, which allows computing static outputfeedback controllers by
solving two successive linear matrix inequality (LMI) optimization problems. This strategy is conceptually simple, easy
to implement, computationally efficient, and it can be potentially applied to a wide variety of control problems, in which
effective statefeedback controllers can be synthesized by using standard LMI optimization tools. To illustrate the application
of the new approach in the field of structural vibration control of large structures, a static velocityfeedback H1 controller
for the seismic protection of a fivestory building is designed with excellent results.
Fri, 12 Sep 2014 10:32:16 GMT
http://hdl.handle.net/2117/24047
20140912T10:32:16Z
Palacios Quiñonero, Francisco; Rubió Massegú, Josep; Rossell Garriga, Josep Maria; Karimi, Hamid Reza
no
This paper presents a novel controller design strategy, which allows computing static outputfeedback controllers by
solving two successive linear matrix inequality (LMI) optimization problems. This strategy is conceptually simple, easy
to implement, computationally efficient, and it can be potentially applied to a wide variety of control problems, in which
effective statefeedback controllers can be synthesized by using standard LMI optimization tools. To illustrate the application
of the new approach in the field of structural vibration control of large structures, a static velocityfeedback H1 controller
for the seismic protection of a fivestory building is designed with excellent results.