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http://hdl.handle.net/2117/3917
Thu, 02 Oct 2014 00:45:42 GMT20141002T00:45:42Zwebmaster.bupc@upc.eduUniversitat Politècnica de Catalunya. Servei de Biblioteques i DocumentaciónoNonlinear equations for fractional Laplacians, I: Regularity, maximum principles, and Hamiltonian estimates
http://hdl.handle.net/2117/22391
Title: Nonlinear equations for fractional Laplacians, I: Regularity, maximum principles, and Hamiltonian estimates
Authors: Cabré Vilagut, Xavier; Sire, Yannick
Abstract: This is the first of two articles dealing with the equation ()sv = f (v) in Rn, with s ¿ (0,1), where ()s stands for the fractional Laplacian — the in¿nitesimal generator of a Lévy process. This equation can be realized as a local linear degenerate elliptic equation in Rn+1+ together with a nonlinear Neumann boundary condition on ¿Rn+1 + =Rn.
In this ¿rst article, we establish necessary conditions on the nonlinearity f to admit certain type of solutions, with special interest in bounded increasing solutions in all of R. These necessary conditions (which will be proven in a followup paper to be also suficient for the existence of a bounded increasing solution) are derived from an equality and an estimate involving a Hamiltonian — in the spirit of a result of Modica for the Laplacian. Our proofs are uniform ass ¿1, establishing in the limit the corresponding known results for the Laplacian.
In addition, we study regularity issues, as well as maximum and Harnack principles associated to the equation.http://hdl.handle.net/2117/22391Cabré Vilagut, Xavier; Sire, YannicknoThis is the first of two articles dealing with the equation ()sv = f (v) in Rn, with s ¿ (0,1), where ()s stands for the fractional Laplacian — the in¿nitesimal generator of a Lévy process. This equation can be realized as a local linear degenerate elliptic equation in Rn+1+ together with a nonlinear Neumann boundary condition on ¿Rn+1 + =Rn.
In this ¿rst article, we establish necessary conditions on the nonlinearity f to admit certain type of solutions, with special interest in bounded increasing solutions in all of R. These necessary conditions (which will be proven in a followup paper to be also suficient for the existence of a bounded increasing solution) are derived from an equality and an estimate involving a Hamiltonian — in the spirit of a result of Modica for the Laplacian. Our proofs are uniform ass ¿1, establishing in the limit the corresponding known results for the Laplacian.
In addition, we study regularity issues, as well as maximum and Harnack principles associated to the equation.Estructuras Ainfinito en la opérada de cactus
http://hdl.handle.net/2117/22097
Title: Estructuras Ainfinito en la opérada de cactus
Authors: Gálvez Carrillo, Maria Immaculada; Lombardi, Leandro; Tonks, Andrew
Abstract: Diversas versiones de la opérada de cactus inicialmente definida por Voronov han sido estudiadas. Es conocida su equivalencia débil con la opérada de pequeños discos. Se conoce pues que la opérada de cactus admite una acción de la opérada de Gerstenhaber salvo homotopía. En este proyecto, nuestro objetivo es obtener una realización explícita de dicha acción. Por el momento, hemos construido una acción explícita de la opérada A8 en la opérada de cactus, que presentamos en este pósterhttp://hdl.handle.net/2117/22097Gálvez Carrillo, Maria Immaculada; Lombardi, Leandro; Tonks, AndrewnoDiversas versiones de la opérada de cactus inicialmente definida por Voronov han sido estudiadas. Es conocida su equivalencia débil con la opérada de pequeños discos. Se conoce pues que la opérada de cactus admite una acción de la opérada de Gerstenhaber salvo homotopía. En este proyecto, nuestro objetivo es obtener una realización explícita de dicha acción. Por el momento, hemos construido una acción explícita de la opérada A8 en la opérada de cactus, que presentamos en este pósterJ2 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/2117/21117Barrabes, Esther; Cors Iglesias, Josep Maria; Pinyol, Conxita; Soler Villanueva, Jaumenocollision restricted threebody 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.Lyubeznik numbers of local rings and linear strands of graded ideals
http://hdl.handle.net/2117/24185
Title: Lyubeznik numbers of local rings and linear strands of graded ideals
Authors: Álvarez Montaner, Josep; Yanagawa, Kohji
Abstract: n this work we intro duce a new set of invariants asso ciated to the linear
strands of a minimal free resolution of a
Z
graded ideal
I
R
=

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

[
x
1
;:::;x
n
]
. We
also prove that these invariants satisfy some prop erties analogous to those of Lyub eznik
numb ers of lo cal rings. In particular, they satisfy a consecutiveness prop erty that we
prove rst for Lyub eznik numb ers. For the case of squarefree monomial ideals we get
more insight on the relation b etween Lyub eznik numb ers and the linear strands of their
asso ciated Alexander dual ideals. Finally, we prove that Lyub eznik numb ers of Stanley
Reisner rings are not only an algebraic invariant but also a top ological invariant, meaning
that they dep end on the homeomorphic class of the geometric realization of the asso ciated
simplicial complex and the characteristic of the base fieldAutomatic validation of flowmeter data in transport water networks: Application to the ATLLc water network
http://hdl.handle.net/2117/24173
Title: Automatic validation of flowmeter data in transport water networks: Application to the ATLLc water network
Authors: García Valverde, Diego; Quevedo Casín, Joseba Jokin; Puig Cayuela, Vicenç; Saludes Closa, Jordi; Espín, Santiago; Roquet, Jaume; Valero, Fernando
Abstract: In this paper, a methodology for data validation and reconstruction of flow meter sensor data in water networks is presented. The raw data validation is inspired on the Spanish norm (AENORUNE norm 500540). The methodology consists in assigning a quality level to data. These quality levels are assigned according to the number of tests that data have passed. The methodology takes into account not only spatial models but also temporal models relating the different sensors. The methodology is applied to realdata acquired from the ATLLc Water Network. The results demonstrate the performance of the proposed methodology in detecting errors in measurements and in reconstructing them.Fri, 26 Sep 2014 09:22:11 GMThttp://hdl.handle.net/2117/2417320140926T09:22:11ZGarcía Valverde, Diego; Quevedo Casín, Joseba Jokin; Puig Cayuela, Vicenç; Saludes Closa, Jordi; Espín, Santiago; Roquet, Jaume; Valero, FernandonoIn this paper, a methodology for data validation and reconstruction of flow meter sensor data in water networks is presented. The raw data validation is inspired on the Spanish norm (AENORUNE norm 500540). The methodology consists in assigning a quality level to data. These quality levels are assigned according to the number of tests that data have passed. The methodology takes into account not only spatial models but also temporal models relating the different sensors. The methodology is applied to realdata acquired from the ATLLc Water Network. The results demonstrate the performance of the proposed methodology in detecting errors in measurements and in reconstructing them.Automatic validation of flowmeter data in transport water networks: application to the ATLLc water network
http://hdl.handle.net/2117/24166
Title: Automatic validation of flowmeter data in transport water networks: application to the ATLLc water network
Authors: García Valverde, Diego; Quevedo Casín, Joseba Jokin; Puig Cayuela, Vicenç; Saludes Closa, Jordi; Espín, Santiago; Roquet, Jaume; Valero, Fernando
Abstract: In this paper, a methodology for data validation and reconstruction of flow meter sensor data in water networks is presented. The raw data validation is inspired on the Spanish norm (AENORUNE norm 500540). The methodology consists in assigning a quality level to data. These quality levels are assigned according to the number of tests that data have passed. The methodology takes into account not only spatial models but also temporal models relating the different sensors. The methodology is applied to realdata acquired from the ATLLc Water Network. The results demonstrate the performance of the proposed methodology in detecting errors in measurements and in reconstructing themFri, 26 Sep 2014 06:20:55 GMThttp://hdl.handle.net/2117/2416620140926T06:20:55ZGarcía Valverde, Diego; Quevedo Casín, Joseba Jokin; Puig Cayuela, Vicenç; Saludes Closa, Jordi; Espín, Santiago; Roquet, Jaume; Valero, FernandonoIn this paper, a methodology for data validation and reconstruction of flow meter sensor data in water networks is presented. The raw data validation is inspired on the Spanish norm (AENORUNE norm 500540). The methodology consists in assigning a quality level to data. These quality levels are assigned according to the number of tests that data have passed. The methodology takes into account not only spatial models but also temporal models relating the different sensors. The methodology is applied to realdata acquired from the ATLLc Water Network. The results demonstrate the performance of the proposed methodology in detecting errors in measurements and in reconstructing themA new estimation of the lower error bound in balanced truncation method
http://hdl.handle.net/2117/24162
Title: A new estimation of the lower error bound in balanced truncation method
Authors: Ha Binh, Minh; Batlle Arnau, Carles; Fossas Colet, Enric
Abstract: For a singleinput/singleoutput (SISO) linear timeinvariant dynamical system, the standard Hinfinitynorm lower error bound of balanced truncation method is parallel to G(s)  G(r)(s)parallel to(H infinity) >= sigma(r+1), where sigma(i), i = 1,..., n, are the Hankel singular values of system in decreasing order. In this paper we provide a new estimation of the lower error, namely; parallel to G(s)  G(r)(s)parallel to(H infinity) >= max{sigma(d), 2 vertical bar Sigma(i is not an element of g) s(i)sigma(i)vertical bar},; where s(i) is the sign associated with the Hankel singular value sigma(i) in Ober's canonical form. The subset g and the index d in the above inequality will be introduced in the paper. We show by means of an example that the new bound may be relevant in deciding which states need to be kept in the balanced truncation method, and that using the standard result does not always yield the best approximationThu, 25 Sep 2014 14:10:06 GMThttp://hdl.handle.net/2117/2416220140925T14:10:06ZHa Binh, Minh; Batlle Arnau, Carles; Fossas Colet, EnricnoLinear timeinvariant systems, Hinfinitynorm, Lower error bound, Balanced truncation, Model order reduction, Ober's canonical form, modelreduction, linearsystemsFor a singleinput/singleoutput (SISO) linear timeinvariant dynamical system, the standard Hinfinitynorm lower error bound of balanced truncation method is parallel to G(s)  G(r)(s)parallel to(H infinity) >= sigma(r+1), where sigma(i), i = 1,..., n, are the Hankel singular values of system in decreasing order. In this paper we provide a new estimation of the lower error, namely; parallel to G(s)  G(r)(s)parallel to(H infinity) >= max{sigma(d), 2 vertical bar Sigma(i is not an element of g) s(i)sigma(i)vertical bar},; where s(i) is the sign associated with the Hankel singular value sigma(i) in Ober's canonical form. The subset g and the index d in the above inequality will be introduced in the paper. We show by means of an example that the new bound may be relevant in deciding which states need to be kept in the balanced truncation method, and that using the standard result does not always yield the best approximationA 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, PereThu, 25 Sep 2014 08:12:02 GMThttp://hdl.handle.net/2117/2415520140925T08:12:02ZDelshams Valdés, Amadeu; Gonchenko, Marina; Gutiérrez Serrés, PerenoUsing 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 GMThttp://hdl.handle.net/2117/2414120140923T10:24:06ZGarcía Planas, María Isabel; Taberna Torres, JuditnoEportfolio, 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 $\varepsilonTue, 23 Sep 2014 09:33:01 GMThttp://hdl.handle.net/2117/2413820140923T09:33:01ZDelshams Valdés, Amadeu; Gonchenko, Marina; Gutiérrez Serrés, Perenotransverse homoclinic orbits, splitting of separatrices, Melnikov integrals, silver ratioWe 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 $\varepsilonThe automorphism group of the nonsplit Cartan modular curve of level 11
http://hdl.handle.net/2117/24136
Title: The automorphism group of the nonsplit Cartan modular curve of level 11
Authors: Dose, Valerio; Fernández González, Julio; González Rovira, Josep; Schoof, Rene
Abstract: We derive equations for the modular curve Xns(11) associated to a nonsplit Cartan subgroup of GL(2)(F11). This allows us to compute the automorphism group of the curve and show that it is isomorphic to Klein's four group. (C) 2014 Elsevier Inc. All rights reserved.Mon, 22 Sep 2014 16:34:59 GMThttp://hdl.handle.net/2117/2413620140922T16:34:59ZDose, Valerio; Fernández González, Julio; González Rovira, Josep; Schoof, RenenoModular curve, Nonsplit Cartan subgroupWe derive equations for the modular curve Xns(11) associated to a nonsplit Cartan subgroup of GL(2)(F11). This allows us to compute the automorphism group of the curve and show that it is isomorphic to Klein's four group. (C) 2014 Elsevier Inc. All rights reserved.A secure communication system based on a modified chaotic chua oscillator
http://hdl.handle.net/2117/24135
Title: A secure communication system based on a modified chaotic chua oscillator
Authors: Zapateiro, Mauricio; Acho Zuppa, Leonardo; Vidal Seguí, Yolanda
Abstract: In this paper we propose a new scheme for secure communications us ing a modified Chua oscillator. A modification of the oscillator is proposed in order to facilitate the decryption. The communication system requires two channels for transmitting the message. One of the channels transmits a chaotic signal generated by the oscillator and is used for synchronization. The second channel transmits the message encrypted by a nonlinear function. This function is built in terms of one of the chaotic signals, different from that sent on the first channel. In the receiver side, a synchronizer reconstructs the chaotic oscillator signals, one of which is used for the decryption of the message. The synchronization system is designed via Lyapunov theory and chaoticity proves via Poincar ´e maps and Lyapunov exponents will be pro vided in order to demonstrate the feasibility of our system. Numerical simulations will be used to evaluate the performance of the system.Mon, 22 Sep 2014 12:16:06 GMThttp://hdl.handle.net/2117/2413520140922T12:16:06ZZapateiro, Mauricio; Acho Zuppa, Leonardo; Vidal Seguí, YolandanoChaos, Secure communication, Chua oscillatorIn this paper we propose a new scheme for secure communications us ing a modified Chua oscillator. A modification of the oscillator is proposed in order to facilitate the decryption. The communication system requires two channels for transmitting the message. One of the channels transmits a chaotic signal generated by the oscillator and is used for synchronization. The second channel transmits the message encrypted by a nonlinear function. This function is built in terms of one of the chaotic signals, different from that sent on the first channel. In the receiver side, a synchronizer reconstructs the chaotic oscillator signals, one of which is used for the decryption of the message. The synchronization system is designed via Lyapunov theory and chaoticity proves via Poincar ´e maps and Lyapunov exponents will be pro vided in order to demonstrate the feasibility of our system. Numerical simulations will be used to evaluate the performance of the system.Comparative study of RPSALG algorithm for convex semiinfinite programming
http://hdl.handle.net/2117/24133
Title: Comparative study of RPSALG algorithm for convex semiinfinite programming
Authors: Auslander, Alfred; Ferrer Biosca, Alberto; Goberna, Miguel Ángel; López Cerdá, Marco Antonio
Abstract: The Remez penalty and smoothing algorithm (RPSALG) is a unified framework for penalty and smoothing methods for solving minmax convex semiinfinite programing problems, whose convergence was analyzed in a previous paper of three of the authors. In this paper we consider a partial implementation of RPSALG for solving ordinary convex semiinfinite programming problems. Each iteration of RPSALG involves two types of
auxiliary optimization problems: the Örst one consists of obtaining an approximate solution of some discretized convex problem, while the second one requires to solve a nonconvex optimization problem involving the parametric constraints as objective function with the parameter as variable. In this paper we tackle the latter problem with a variant of the cutting angle method called ECAM, a global optimization procedure for solving Lipschitz programming problems. We implement di§erent variants of RPSALG which are compared with the unique publicly available SIP solver, NSIPS, on a battery of test problems.Mon, 22 Sep 2014 11:36:14 GMThttp://hdl.handle.net/2117/2413320140922T11:36:14ZAuslander, Alfred; Ferrer Biosca, Alberto; Goberna, Miguel Ángel; López Cerdá, Marco AntonionoConvex semiinfinite programming, Remeztype methods, penalty methods, smoothing methods, cutting angle method.The Remez penalty and smoothing algorithm (RPSALG) is a unified framework for penalty and smoothing methods for solving minmax convex semiinfinite programing problems, whose convergence was analyzed in a previous paper of three of the authors. In this paper we consider a partial implementation of RPSALG for solving ordinary convex semiinfinite programming problems. Each iteration of RPSALG involves two types of
auxiliary optimization problems: the Örst one consists of obtaining an approximate solution of some discretized convex problem, while the second one requires to solve a nonconvex optimization problem involving the parametric constraints as objective function with the parameter as variable. In this paper we tackle the latter problem with a variant of the cutting angle method called ECAM, a global optimization procedure for solving Lipschitz programming problems. We implement di§erent variants of RPSALG which are compared with the unique publicly available SIP solver, NSIPS, on a battery of test problems.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 GMThttp://hdl.handle.net/2117/2412920140922T10:36:12ZMediano Valiente, Begoña; García Planas, María IsabelnoStability, 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, GeoffreyFri, 19 Sep 2014 09:04:11 GMThttp://hdl.handle.net/2117/2411420140919T09:04:11ZMiranda Galcerán, Eva; Scott, Geoffreyno