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20140922T14:35:46Z
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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

Modelling of a clampedpinned pipeline conveying fluid for vibrational stability analysis
http://hdl.handle.net/2117/24129
Title: Modelling of a clampedpinned pipeline conveying fluid for vibrational stability analysis
Authors: Mediano Valiente, Begoña; García Planas, María Isabel
Abstract: Recent developments in materials and cost reduction
have led the study of the vibrational stability of
pipelines conveying fluid to be an important issue.
Nowadays, this analysis is done both by means of simulation
with specialized softwares and by laboratory
testing of the preferred materials. The former usually
requires of complex modelling of the pipeline and the
internal fluid to determine if the material will ensure vibrational
stability; and in the latter case, each time there
is a mistake on the material selection is necessary to
restart all the process making this option expensive. In
this paper, the classical mathematical description of the
dynamic behavior of a clampedpinned pipeline conveying
fluid is presented. Then, they are approximated
to a Hamiltonian system through Garlekin’s method being
modelled as a simple linear system. The system
stability has been studied by means of the eigenvalues
of the linear system. From this analysis, characteristic
expressions dependent on material constants has been
developed as inequalities, which ensures the stability
of the material if it matches all expressions. This new
model provides a simplified dynamical approximation
of the pipeline conveying fluid depending on material
and fluid constants that is useful to determine if it is
stable or not. It is worth to determine that the model
dynamics does not correspond with the real, but the
global behaviour is well represented. Finally, some
simulations of specific materials have been use to validate
the results obtained from the Hamiltonian model
and a more complex model done with finite element
software.
Mon, 22 Sep 2014 10:36:12 GMT
http://hdl.handle.net/2117/24129
20140922T10:36:12Z
Mediano Valiente, Begoña; García Planas, María Isabel
no
Stability, eigenvalues analysis, pipe conveying fluid, material selection, Garlekin’s method, Hamiltonian
systems.
Recent developments in materials and cost reduction
have led the study of the vibrational stability of
pipelines conveying fluid to be an important issue.
Nowadays, this analysis is done both by means of simulation
with specialized softwares and by laboratory
testing of the preferred materials. The former usually
requires of complex modelling of the pipeline and the
internal fluid to determine if the material will ensure vibrational
stability; and in the latter case, each time there
is a mistake on the material selection is necessary to
restart all the process making this option expensive. In
this paper, the classical mathematical description of the
dynamic behavior of a clampedpinned pipeline conveying
fluid is presented. Then, they are approximated
to a Hamiltonian system through Garlekin’s method being
modelled as a simple linear system. The system
stability has been studied by means of the eigenvalues
of the linear system. From this analysis, characteristic
expressions dependent on material constants has been
developed as inequalities, which ensures the stability
of the material if it matches all expressions. This new
model provides a simplified dynamical approximation
of the pipeline conveying fluid depending on material
and fluid constants that is useful to determine if it is
stable or not. It is worth to determine that the model
dynamics does not correspond with the real, but the
global behaviour is well represented. Finally, some
simulations of specific materials have been use to validate
the results obtained from the Hamiltonian model
and a more complex model done with finite element
software.

Introduction to Poisson Geometry
http://hdl.handle.net/2117/24114
Title: Introduction to Poisson Geometry
Authors: Miranda Galcerán, Eva; Scott, Geoffrey
Fri, 19 Sep 2014 09:04:11 GMT
http://hdl.handle.net/2117/24114
20140919T09:04:11Z
Miranda Galcerán, Eva; Scott, Geoffrey
no

Godement resolutions and sheaf homotopy theory
http://hdl.handle.net/2117/24111
Title: Godement resolutions and sheaf homotopy theory
Authors: Rodríguez González, Beatriz; Roig Martí, Agustín
Abstract: The Godement cosimplicial resolution is available for a wide range of categories
of sheaves. In this paper we investigate under which conditions of the Grothendieck site and the category of coefficients it can be used to obtain fibrant models and hence to do sheaf homotopy theory. For instance, for which Grothendieck sites and coefficients we can define sheaf cohomology and derived functors through it
Fri, 19 Sep 2014 08:39:42 GMT
http://hdl.handle.net/2117/24111
20140919T08:39:42Z
Rodríguez González, Beatriz; Roig Martí, Agustín
no
The Godement cosimplicial resolution is available for a wide range of categories
of sheaves. In this paper we investigate under which conditions of the Grothendieck site and the category of coefficients it can be used to obtain fibrant models and hence to do sheaf homotopy theory. For instance, for which Grothendieck sites and coefficients we can define sheaf cohomology and derived functors through 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.

Central cohomology operations and Ktheory
http://hdl.handle.net/2117/23645
Title: Central cohomology operations and Ktheory
Authors: Gálvez Carrillo, Maria Immaculada; Whitehouse, Sarah
Abstract: For stable degree 0 operations, and also for additive unstable operations of bidegree (0, 0), it is known that the centre of the ring of operations for complex cobordism is isomorphic to the corresponding ring of connective complex Ktheory operations. Similarly, the centre of the ring of BP operations is the corresponding ring for the Adams summand of plocal connective complex Ktheory. Here we show that, in the additive unstable context, this result holds with BP replaced by BP<n> for any n. Thus, for all chromatic heights, the only central operations are those coming from Ktheory.
Tue, 29 Jul 2014 08:35:40 GMT
http://hdl.handle.net/2117/23645
20140729T08:35:40Z
Gálvez Carrillo, Maria Immaculada; Whitehouse, Sarah
no
Ktheory, Operations, Cobordism
For stable degree 0 operations, and also for additive unstable operations of bidegree (0, 0), it is known that the centre of the ring of operations for complex cobordism is isomorphic to the corresponding ring of connective complex Ktheory operations. Similarly, the centre of the ring of BP operations is the corresponding ring for the Adams summand of plocal connective complex Ktheory. Here we show that, in the additive unstable context, this result holds with BP replaced by BP<n> for any n. Thus, for all chromatic heights, the only central operations are those coming from Ktheory.

El eportafolio del estudiante en MaharaMoodle y Google Sites
http://hdl.handle.net/2117/23534
Title: El eportafolio del estudiante en MaharaMoodle y Google Sites
Authors: García Planas, María Isabel; Taberna Torres, Judit
Abstract: Es bien conocido el potencial que tiene el uso del eportfolio del estudiante para hacer visible tanto para el mismo como para los demás, de cómo y hasta que nivel ha logrado sus objetivos.
Para realizar un eportafolio se pueden utilizar distintas aplicaciones, entre ellas se encuentran Google Sites y Mahara.
Google Sites permite de forma sencilla editando una plantilla previamente preparada por el profesor, crear una página web como muestra de sus trabajos desarrollados a lo largo de sus estudios.
Mahara es un sistema de eportafolio que puede conectarse a Moodle y el cual puede ser controlado por el estudiante y puede ser visible por el grupo. Debido a la interoperabilidad de Mahara especialmente con Moodle, este permite que desde la plataforma de Atenea se puedan interconectar el profesorado con el eportafolio del estudiante.
En este trabajo presentamos los resultados obtenidos desde el año 2011 hasta la actualidad en las investigaciones realizadas sobre el eportafolio en el marco de la Universidad Politècnica de Catalunya.
Thu, 17 Jul 2014 07:51:51 GMT
http://hdl.handle.net/2117/23534
20140717T07:51:51Z
García Planas, María Isabel; Taberna Torres, Judit
no
eportafolio, Moodle, Mahara, Google Sites
Es bien conocido el potencial que tiene el uso del eportfolio del estudiante para hacer visible tanto para el mismo como para los demás, de cómo y hasta que nivel ha logrado sus objetivos.
Para realizar un eportafolio se pueden utilizar distintas aplicaciones, entre ellas se encuentran Google Sites y Mahara.
Google Sites permite de forma sencilla editando una plantilla previamente preparada por el profesor, crear una página web como muestra de sus trabajos desarrollados a lo largo de sus estudios.
Mahara es un sistema de eportafolio que puede conectarse a Moodle y el cual puede ser controlado por el estudiante y puede ser visible por el grupo. Debido a la interoperabilidad de Mahara especialmente con Moodle, este permite que desde la plataforma de Atenea se puedan interconectar el profesorado con el eportafolio del estudiante.
En este trabajo presentamos los resultados obtenidos desde el año 2011 hasta la actualidad en las investigaciones realizadas sobre el eportafolio en el marco de la Universidad Politècnica de Catalunya.

Noise and adaptation in multistable perception: noise drives when to switch, adaptation determines percept choice.
http://hdl.handle.net/2117/23524
Title: Noise and adaptation in multistable perception: noise drives when to switch, adaptation determines percept choice.
Authors: Huguet Casades, Gemma; Rinzel, John; Hupé, JeanMichel
Abstract: We study the dynamics of perceptual switching in ambiguous visual scenes that admit more than two interpretations/percepts to gain insight into the dynamics of perceptual multistability and its underlying neural mechanisms. We focus on visual plaids that are tristable and we present both experimental and computational results. We develop a firingrate model based on mutual inhibition and adaptation that involves stochastic dynamics of multipleattractor systems. The model can account for the dynamic properties (transition probabilities, distributions of percept durations, etc.) observed in the experiments. Noise and adaptation have both been shown to play roles in the dynamics of bistable perception. Here, tristable perception allows us to specify the roles of noise and adaptation in our model. Noise is critical in considering the time of a switch. On the other hand, adaptation mechanisms are critical in considering perceptual choice (in tristable perception, each time a percept ends, there is a possible choice between two new percepts).
Wed, 16 Jul 2014 07:35:44 GMT
http://hdl.handle.net/2117/23524
20140716T07:35:44Z
Huguet Casades, Gemma; Rinzel, John; Hupé, JeanMichel
no
We study the dynamics of perceptual switching in ambiguous visual scenes that admit more than two interpretations/percepts to gain insight into the dynamics of perceptual multistability and its underlying neural mechanisms. We focus on visual plaids that are tristable and we present both experimental and computational results. We develop a firingrate model based on mutual inhibition and adaptation that involves stochastic dynamics of multipleattractor systems. The model can account for the dynamic properties (transition probabilities, distributions of percept durations, etc.) observed in the experiments. Noise and adaptation have both been shown to play roles in the dynamics of bistable perception. Here, tristable perception allows us to specify the roles of noise and adaptation in our model. Noise is critical in considering the time of a switch. On the other hand, adaptation mechanisms are critical in considering perceptual choice (in tristable perception, each time a percept ends, there is a possible choice between two new percepts).

R+aR2 loop quantum cosmology
http://hdl.handle.net/2117/23514
Title: R+aR2 loop quantum cosmology
Authors: Amorós Torrent, Jaume; De Haro, Jaume; Odintsov, Sergei D.
Abstract: Working in Einstein frame, we introduce, in order to avoid singularities, holonomy corrections to the f(R)=R+aR2 model. We perform a detailed analytical and numerical study when holonomy corrections are taken into account in both Jordan and Einstein frames, obtaining, in Jordan frame, a dynamics which differs qualitatively, at early times, from the one of the original model. More precisely, when holonomy corrections are taken into account, the Universe is not singular, starting at early times in the contracting phase and bouncing to enter the expanding one where, as in the original model, it inflates. This dynamics is completely different from the one obtained in the original R+aR2 model, where the Universe is singular at early times and never bounces. Moreover, we show that these holonomy corrections may lead to better predictions for the inflationary phase as compared with current observations.
Tue, 15 Jul 2014 11:00:50 GMT
http://hdl.handle.net/2117/23514
20140715T11:00:50Z
Amorós Torrent, Jaume; De Haro, Jaume; Odintsov, Sergei D.
no
Working in Einstein frame, we introduce, in order to avoid singularities, holonomy corrections to the f(R)=R+aR2 model. We perform a detailed analytical and numerical study when holonomy corrections are taken into account in both Jordan and Einstein frames, obtaining, in Jordan frame, a dynamics which differs qualitatively, at early times, from the one of the original model. More precisely, when holonomy corrections are taken into account, the Universe is not singular, starting at early times in the contracting phase and bouncing to enter the expanding one where, as in the original model, it inflates. This dynamics is completely different from the one obtained in the original R+aR2 model, where the Universe is singular at early times and never bounces. Moreover, we show that these holonomy corrections may lead to better predictions for the inflationary phase as compared with current observations.

AutoBacklund transformations and special integrals for differentialdelay Painlevé hierarchies
http://hdl.handle.net/2117/23511
Title: AutoBacklund transformations and special integrals for differentialdelay Painlevé hierarchies
Authors: Fedorov, Yuri; Ruiz Gordoa, Maria Pilar; Pickering, Andrew
Abstract: The six Painleve equations have attracted much interest over the last thirty years or so. More recently many authors have begun to explore properties of higherorder versions of both these equations and their discrete analogues. However, little attention has been paid to differentialdelay Painleve equations, i.e., analogues of the Painleve equations involving both shifts in and derivatives with respect to the independent variable, and even less to higherorder analogues of these last. In the current paper we discuss the phenomenon whereby members of one differentialdelay Painleve hierarchy define solutions of higherorder members of a second differentialdelay Painleve hierarchy. We also give an autoBacklund transformation for a differentialdelay Painleve hierarchy. The key to our approach is the underlying Hamiltonian structure of related completely integrable lattice hierarchies. (C) 2014 Elsevier B.V. All rights reserved.
Tue, 15 Jul 2014 10:29:35 GMT
http://hdl.handle.net/2117/23511
20140715T10:29:35Z
Fedorov, Yuri; Ruiz Gordoa, Maria Pilar; Pickering, Andrew
no
Differentialdelay Painleve hierarchies, MONODROMY PRESERVING DEFORMATION, RATIONAL COEFFICIENTS, EQUATIONS
The six Painleve equations have attracted much interest over the last thirty years or so. More recently many authors have begun to explore properties of higherorder versions of both these equations and their discrete analogues. However, little attention has been paid to differentialdelay Painleve equations, i.e., analogues of the Painleve equations involving both shifts in and derivatives with respect to the independent variable, and even less to higherorder analogues of these last. In the current paper we discuss the phenomenon whereby members of one differentialdelay Painleve hierarchy define solutions of higherorder members of a second differentialdelay Painleve hierarchy. We also give an autoBacklund transformation for a differentialdelay Painleve hierarchy. The key to our approach is the underlying Hamiltonian structure of related completely integrable lattice hierarchies. (C) 2014 Elsevier B.V. All rights reserved.