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http://hdl.handle.net/2117/3227
Thu, 30 Oct 2014 18:37:15 GMT
20141030T18:37:15Z
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Universitat Politècnica de Catalunya. Servei de Biblioteques i Documentació
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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

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 GMT
http://hdl.handle.net/2117/24422
20141020T10:27:38Z
Consul Porras, M. Nieves; Oliva, Sergio M.; Pellicer, Marta
no
Wound 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 field
Tue, 30 Sep 2014 09:46:24 GMT
http://hdl.handle.net/2117/24185
20140930T09:46:24Z
Álvarez Montaner, Josep; Yanagawa, Kohji
no
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 field

A methodology for obtaining asymptotic estimates for the exponentially small splitting of separatrices to whiskered tori with quadratic frequencies
http://hdl.handle.net/2117/24155
Title: A methodology for obtaining asymptotic estimates for the exponentially small splitting of separatrices to whiskered tori with quadratic frequencies
Authors: Delshams Valdés, Amadeu; Gonchenko, Marina; Gutiérrez Serrés, Pere
Thu, 25 Sep 2014 08:12:02 GMT
http://hdl.handle.net/2117/24155
20140925T08:12:02Z
Delshams Valdés, Amadeu; Gonchenko, Marina; Gutiérrez Serrés, Pere
no

Using integral eportfolio to learn linear algebra
http://hdl.handle.net/2117/24141
Title: Using integral eportfolio to learn linear algebra
Authors: García Planas, María Isabel; Taberna Torres, Judit
Abstract: The use of eportfolio is becoming common
in the learning and assessment of students. This is due to
the need of teachers to enhance student autonomy making
them to reflect on the process of learning. Lately, we have
worked with different software, facilitating its generation
and use. In this paper, the recent experience in the use of
eportfolio for undergraduate students of the Universitat
Polit`ecnica de Catalunya are set.
Tue, 23 Sep 2014 10:24:06 GMT
http://hdl.handle.net/2117/24141
20140923T10:24:06Z
García Planas, María Isabel; Taberna Torres, Judit
no
Eportfolio, integral eportfolio, linear
algebra.
The use of eportfolio is becoming common
in the learning and assessment of students. This is due to
the need of teachers to enhance student autonomy making
them to reflect on the process of learning. Lately, we have
worked with different software, facilitating its generation
and use. In this paper, the recent experience in the use of
eportfolio for undergraduate students of the Universitat
Polit`ecnica de Catalunya are set.

Continuation of the exponentially small lower bounds for the splitting of separatrices to a whiskered torus with silver ratio
http://hdl.handle.net/2117/24138
Title: Continuation of the exponentially small lower bounds for the splitting of separatrices to a whiskered torus with silver ratio
Authors: Delshams Valdés, Amadeu; Gonchenko, Marina; Gutiérrez Serrés, Pere
Abstract: We study the exponentially small splitting of invariant manifolds of whiskered (hyperbolic) tori with two fast
frequencies in nearlyintegrable Hamiltonian systems whose hyperbolic part is given by a pendulum. We consider a torus whose frequency ratio is the silver number $\Omega=\sqrt21$. We show that the oincareMelnikov method can be applied to establish the existence of 4 transverse homoclinic orbits to the whiskered torus, and provide
asymptotic estimates for the tranversality of the splitting whose dependence on the perturbation parameter $\varepsilon$ satisffies a periodicity property. We also prove the continuation of the transversality of the homoclinic orbits for all the sufficiently small values of $\varepsilon
Tue, 23 Sep 2014 09:33:01 GMT
http://hdl.handle.net/2117/24138
20140923T09:33:01Z
Delshams Valdés, Amadeu; Gonchenko, Marina; Gutiérrez Serrés, Pere
no
transverse homoclinic orbits, splitting of separatrices, Melnikov integrals, silver ratio
We study the exponentially small splitting of invariant manifolds of whiskered (hyperbolic) tori with two fast
frequencies in nearlyintegrable Hamiltonian systems whose hyperbolic part is given by a pendulum. We consider a torus whose frequency ratio is the silver number $\Omega=\sqrt21$. We show that the oincareMelnikov method can be applied to establish the existence of 4 transverse homoclinic orbits to the whiskered torus, and provide
asymptotic estimates for the tranversality of the splitting whose dependence on the perturbation parameter $\varepsilon$ satisffies a periodicity property. We also prove the continuation of the transversality of the homoclinic orbits for all the sufficiently small values of $\varepsilon

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.