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http://hdl.handle.net/2117/127
Sun, 26 Apr 2015 13:11:09 GMT2015-04-26T13:11:09Zwebmaster.bupc@upc.eduUniversitat Politècnica de Catalunya. Servei de Biblioteques i DocumentaciónoNonlinear equations for fractional Laplacians, I: Regularity, maximum principles, and Hamiltonian estimates
http://hdl.handle.net/2117/22391
Title: Nonlinear equations for fractional Laplacians, I: Regularity, maximum principles, and Hamiltonian estimates
Authors: Cabré Vilagut, Xavier; Sire, Yannick
Abstract: This is the first of two articles dealing with the equation (-)sv = f (v) in Rn, with s ¿ (0,1), where (-)s stands for the fractional Laplacian — the in¿nitesimal generator of a Lévy process. This equation can be realized as a local linear degenerate elliptic equation in Rn+1+ together with a nonlinear Neumann boundary condition on ¿Rn+1 + =Rn.
In this ¿rst article, we establish necessary conditions on the nonlinearity f to admit certain type of solutions, with special interest in bounded increasing solutions in all of R. These necessary conditions (which will be proven in a follow-up paper to be also suficient for the existence of a bounded increasing solution) are derived from an equality and an estimate involving a Hamiltonian — in the spirit of a result of Modica for the Laplacian. Our proofs are uniform ass ¿1, establishing in the limit the corresponding known results for the Laplacian.
In addition, we study regularity issues, as well as maximum and Harnack principles associated to the equation.http://hdl.handle.net/2117/22391Cabré Vilagut, Xavier; Sire, YannicknoThis is the first of two articles dealing with the equation (-)sv = f (v) in Rn, with s ¿ (0,1), where (-)s stands for the fractional Laplacian — the in¿nitesimal generator of a Lévy process. This equation can be realized as a local linear degenerate elliptic equation in Rn+1+ together with a nonlinear Neumann boundary condition on ¿Rn+1 + =Rn.
In this ¿rst article, we establish necessary conditions on the nonlinearity f to admit certain type of solutions, with special interest in bounded increasing solutions in all of R. These necessary conditions (which will be proven in a follow-up paper to be also suficient for the existence of a bounded increasing solution) are derived from an equality and an estimate involving a Hamiltonian — in the spirit of a result of Modica for the Laplacian. Our proofs are uniform ass ¿1, establishing in the limit the corresponding known results for the Laplacian.
In addition, we study regularity issues, as well as maximum and Harnack principles associated to the equation.Estructuras A-infinito en la opérada de cactus
http://hdl.handle.net/2117/22097
Title: Estructuras A-infinito en la opérada de cactus
Authors: Gálvez Carrillo, Maria Immaculada; Lombardi, Leandro; Tonks, Andrew
Abstract: Diversas versiones de la opérada de cactus inicialmente definida por Voronov han sido estudiadas. Es conocida su equivalencia débil con la opérada de pequeños discos. Se conoce pues que la opérada de cactus admite una acción de la opérada de Gerstenhaber salvo homotopía. En este proyecto, nuestro objetivo es obtener una realización explícita de dicha acción. Por el momento, hemos construido una acción explícita de la opérada A8 en la opérada de cactus, que presentamos en este pósterhttp://hdl.handle.net/2117/22097Gálvez Carrillo, Maria Immaculada; Lombardi, Leandro; Tonks, AndrewnoDiversas versiones de la opérada de cactus inicialmente definida por Voronov han sido estudiadas. Es conocida su equivalencia débil con la opérada de pequeños discos. Se conoce pues que la opérada de cactus admite una acción de la opérada de Gerstenhaber salvo homotopía. En este proyecto, nuestro objetivo es obtener una realización explícita de dicha acción. Por el momento, hemos construido una acción explícita de la opérada A8 en la opérada de cactus, que presentamos en este pósterJ2 effect and elliptic inclined periodic orbits in the collision three-body problem
http://hdl.handle.net/2117/21117
Title: J2 effect and elliptic inclined periodic orbits in the collision three-body problem
Authors: Barrabes, Esther; Cors Iglesias, Josep Maria; Pinyol, Conxita; Soler Villanueva, Jaume
Abstract: The existence of a new class of inclined periodic orbits of the collision restricted
three{body problem is shown. The symmetric periodic solutions found are perturbations of elliptic
kepler orbits and they exist only for special values of the inclination and are related to the motion
of a satellite around an oblate planet.http://hdl.handle.net/2117/21117Barrabes, Esther; Cors Iglesias, Josep Maria; Pinyol, Conxita; Soler Villanueva, Jaumenocollision restricted three-body problem, periodic orbits, symmetric orbits, critical inclination, continuation methodThe existence of a new class of inclined periodic orbits of the collision restricted
three{body problem is shown. The symmetric periodic solutions found are perturbations of elliptic
kepler orbits and they exist only for special values of the inclination and are related to the motion
of a satellite around an oblate planet.Unified formalism for the generalized kth-order Hamilton-Jacobi problem
http://hdl.handle.net/2117/27582
Title: Unified formalism for the generalized kth-order Hamilton-Jacobi problem
Authors: Colombo, Leonardo; De León, Manuel; Prieto Martínez, Pedro Daniel; Román Roy, Narciso
Abstract: The geometric formulation of the Hamilton-Jacobi theory enables us to generalize it to systems of higher-order ordinary differential equations. In this work we introduce the unified Lagrangian-Hamiltonian formalism for the geometric Hamilton-Jacobi theory on higher-order autonomous dynamical systems described by regular Lagrangian functions.Fri, 24 Apr 2015 11:51:21 GMThttp://hdl.handle.net/2117/275822015-04-24T11:51:21ZColombo, Leonardo; De León, Manuel; Prieto Martínez, Pedro Daniel; Román Roy, NarcisonoHamilton-Jacobi equation, higher-order Lagrangian and Hamiltonian systems, Skinner-Rusk formalismThe geometric formulation of the Hamilton-Jacobi theory enables us to generalize it to systems of higher-order ordinary differential equations. In this work we introduce the unified Lagrangian-Hamiltonian formalism for the geometric Hamilton-Jacobi theory on higher-order autonomous dynamical systems described by regular Lagrangian functions.A new approach for Delphi processes based on group consensus with linguistic terms
http://hdl.handle.net/2117/27577
Title: A new approach for Delphi processes based on group consensus with linguistic terms
Authors: Agell Jané, Núria; van Ganzewinkel,, Christ Jan; Sánchez Soler, Monica; Roselló Saurí, Llorenç; Prats Duaygues, Francesc; Andriessen, Peter
Abstract: A new approach for Delphi processes including a
measure of consensus based on linguistic terms is introduced in this paper. The measure of consensus involves qualitative reasoning techniques and is based on the concept of entropy. In the proposed approach, consensus is reached automatically
without the need for neither a moderator nor a final interaction among panelists. In addition, it permits panelists to answer with different levels of precision depending on their knowledge on each question. An illustrative example considering the opinions of stake holders in neonate health-care to reach a final
consensual definition of chronic pain in neonates is presented.Fri, 24 Apr 2015 11:13:58 GMThttp://hdl.handle.net/2117/275772015-04-24T11:13:58ZAgell Jané, Núria; van Ganzewinkel,, Christ Jan; Sánchez Soler, Monica; Roselló Saurí, Llorenç; Prats Duaygues, Francesc; Andriessen, PeternoQualitative Reasoning, Group Decision systems, Consensus measures, Knowledge Management, Knowledge acquisition, Delphi techniqueA new approach for Delphi processes including a
measure of consensus based on linguistic terms is introduced in this paper. The measure of consensus involves qualitative reasoning techniques and is based on the concept of entropy. In the proposed approach, consensus is reached automatically
without the need for neither a moderator nor a final interaction among panelists. In addition, it permits panelists to answer with different levels of precision depending on their knowledge on each question. An illustrative example considering the opinions of stake holders in neonate health-care to reach a final
consensual definition of chronic pain in neonates is presented.Asymptotic behavior of Palais-Smale sequences associated with fractional Yamabe type equations
http://hdl.handle.net/2117/27563
Title: Asymptotic behavior of Palais-Smale sequences associated with fractional Yamabe type equations
Authors: González Nogueras, María del Mar; Fang, Yi
Abstract: In this paper, we analyze the asymptotic behavior of Palais-Smale sequences associated to fractional Yamabe type equations on an asymptotically hyperbolic Riemannian manifold. We prove that Palais-Smale sequences can be decomposed into the solution of the limit equation plus a finite number of bubbles, which are the rescaling of the fundamental solution for the fractional Yamabe equation on Euclidean space. We also verify the non-interfering fact for multi-bubbles.
Description: preprintFri, 24 Apr 2015 09:05:51 GMThttp://hdl.handle.net/2117/275632015-04-24T09:05:51ZGonzález Nogueras, María del Mar; Fang, YinoIn this paper, we analyze the asymptotic behavior of Palais-Smale sequences associated to fractional Yamabe type equations on an asymptotically hyperbolic Riemannian manifold. We prove that Palais-Smale sequences can be decomposed into the solution of the limit equation plus a finite number of bubbles, which are the rescaling of the fundamental solution for the fractional Yamabe equation on Euclidean space. We also verify the non-interfering fact for multi-bubbles.Linearly dependent vectorial decomposition of clutters
http://hdl.handle.net/2117/27557
Title: Linearly dependent vectorial decomposition of clutters
Authors: Martí Farré, Jaume
Abstract: This paper deals with the question of completing a monotone increas- ing family of subsets G of a finite set ¿ to obtain the linearly dependent subsets of a family of vectors of a vector space. Specifically, we demonstrate that such vec- torial completions of the family of subsets G exist and, in addition, we show that the minimal vectorial completions of the family G provide a decomposition of the clutter ¿ of the inclusion-minimal elements of G . The computation of such vectorial decomposition of clutters is also discussed in some casesFri, 24 Apr 2015 07:44:16 GMThttp://hdl.handle.net/2117/275572015-04-24T07:44:16ZMartí Farré, JaumenoClutter, Antichain, Hypergraph, Matroid, DecompositionThis paper deals with the question of completing a monotone increas- ing family of subsets G of a finite set ¿ to obtain the linearly dependent subsets of a family of vectors of a vector space. Specifically, we demonstrate that such vec- torial completions of the family of subsets G exist and, in addition, we show that the minimal vectorial completions of the family G provide a decomposition of the clutter ¿ of the inclusion-minimal elements of G . The computation of such vectorial decomposition of clutters is also discussed in some casesOn the generalitzed arc routing problem
http://hdl.handle.net/2117/27556
Title: On the generalitzed arc routing problem
Authors: Fernández Aréizaga, ElenaFri, 24 Apr 2015 07:13:28 GMThttp://hdl.handle.net/2117/275562015-04-24T07:13:28ZFernández Aréizaga, ElenanoComputing jumping numbers and multiplier ideals in two-dimensional regular local rings
http://hdl.handle.net/2117/27546
Title: Computing jumping numbers and multiplier ideals in two-dimensional regular local rings
Authors: Alberich Carramiñana, Maria; Álvarez Montaner, Josep; Dachs Cadefau, Ferran
Abstract: We give a new algorithm that computes the jumping numbers with their multiplicities and multiplier ideals of any ideal in a regular two-dimensional local ring.Thu, 23 Apr 2015 10:39:14 GMThttp://hdl.handle.net/2117/275462015-04-23T10:39:14ZAlberich Carramiñana, Maria; Álvarez Montaner, Josep; Dachs Cadefau, FerrannoJumping number, multiplier ideal, regular local ringWe give a new algorithm that computes the jumping numbers with their multiplicities and multiplier ideals of any ideal in a regular two-dimensional local ring.An axiomatic characterization of the potential decisiveness index
http://hdl.handle.net/2117/27526
Title: An axiomatic characterization of the potential decisiveness index
Authors: Freixas Bosch, Josep; Pons Navarro, Montserrat
Abstract: Let us consider that somebody is extremely interested in increasing the probability of a proposal to be approved by a certain committee and that to achieve this goal he/she is prepared to pay off one member of the committee. In a situation like this one, and assuming that vote-buying is allowed and free of stigma, which voter should be offered a bribe? The potential decisiveness index for simple games, which measures the effect that ensuring one positive vote produces for the probability of passing the issue at hand, is a good tool with which to acquire the answer. An axiomatic characterization of this index is given in this paper, and its relation to other classical power indices is shown.http://hdl.handle.net/2117/27526Freixas Bosch, Josep; Pons Navarro, MontserratnoGame theory, Potential decisiveness index, Measure for bribes, Axiomatization, Standard power indices, Relationship among several measures, Ordinal equivalence, Voting games, Power, Sucess, Voters, Values, LuckyLet us consider that somebody is extremely interested in increasing the probability of a proposal to be approved by a certain committee and that to achieve this goal he/she is prepared to pay off one member of the committee. In a situation like this one, and assuming that vote-buying is allowed and free of stigma, which voter should be offered a bribe? The potential decisiveness index for simple games, which measures the effect that ensuring one positive vote produces for the probability of passing the issue at hand, is a good tool with which to acquire the answer. An axiomatic characterization of this index is given in this paper, and its relation to other classical power indices is shown.Generalized Clifford-Severi inequality and the volume of irregular varieties
http://hdl.handle.net/2117/27518
Title: Generalized Clifford-Severi inequality and the volume of irregular varieties
Authors: Barja Yáñez, Miguel Ángel
Abstract: We give a sharp lower bound for the self-intersection of a nef line bundle L on an irregular variety X in terms of its continuous global sections and the Albanese dimension of X, which we call the generalized Clifford-Severi inequality. We also extend the result to nef vector bundles and give a slope inequality for fibered irregular varieties. As a by-product we obtain a lower bound for the volume of irregular varieties; when X is of maximal Albanese dimension the bound is vol(X) >= 2n!chi(omega(X)) and it is sharp.Wed, 22 Apr 2015 13:43:14 GMThttp://hdl.handle.net/2117/275182015-04-22T13:43:14ZBarja Yáñez, Miguel ÁngelnoMAXIMAL ALBANESE DIMENSION, ABELIAN-VARIETIES, CANONICAL VOLUME, BICANONICAL MAP, SURFACES, CURVES, FIBRATIONS, FAMILIES, 3-FOLDS, MODULIWe give a sharp lower bound for the self-intersection of a nef line bundle L on an irregular variety X in terms of its continuous global sections and the Albanese dimension of X, which we call the generalized Clifford-Severi inequality. We also extend the result to nef vector bundles and give a slope inequality for fibered irregular varieties. As a by-product we obtain a lower bound for the volume of irregular varieties; when X is of maximal Albanese dimension the bound is vol(X) >= 2n!chi(omega(X)) and it is sharp.A real-time world-wide ionospheric model for single and multi-frequency precise navigation
http://hdl.handle.net/2117/27516
Title: A real-time world-wide ionospheric model for single and multi-frequency precise navigation
Authors: Rovira Garcia, Adrià; Juan Zornoza, José Miguel; Sanz Subirana, Jaume
Abstract: The ionosphere plays an important role in satellite-based navigation, either in standard navigation, with single frequency mass-market receivers, or in precise navigation, with dual frequency receivers.
In this work, the requirements of a real-time ionospheric model suitable for GNSS applications are explored, in terms of accuracy and confidence bounds. Key factors for an ionospheric determination better than 1 Total Electron Content Unit (TECU) (16 centimeters in L1) are shown to be whether the model has been derived using an ambiguity-fixing strategy and the number of layers used to reproduce the ionospheric delay. Different models are assessed both in mid-latitudes and equatorial regions, near the Solar Cycle maximum.
It will be shown how dual-frequency users take benefit from a precise modelling of the ionosphere. If accurate enough, the convergence of the navigation filter is reduced to achieve high accuracy positioning quickly, (i.e., the Fast Precise Point Positioning technique). Satellite orbits and clocks computed for Fast-PPP will be shown to be accurate to few centimeters and few tenths of nanoseconds, respectively.
Single-frequency users correct its measurements with the predictions provided by any ionospheric model. Thence, the accuracy of the Fast-PPP ionospheric corrections is directly translated to the measurements modelling and, consequently, to the user solution.
Horizontal and vertical 95% accuracies are shown to be better than 36 and 63 centimeters for single-frequency users and 11 and 15 centimeters for dual-frequency users. The assessment is done for several locations, including the equatorial region, for a month of data close to the last Solar Maximum. The trade-off between the formal and actual positioning errors has been carefully studied by means of the Stanford plots to set realistic confidence bounds to the corrections.Wed, 22 Apr 2015 12:46:58 GMThttp://hdl.handle.net/2117/275162015-04-22T12:46:58ZRovira Garcia, Adrià; Juan Zornoza, José Miguel; Sanz Subirana, JaumenoThe ionosphere plays an important role in satellite-based navigation, either in standard navigation, with single frequency mass-market receivers, or in precise navigation, with dual frequency receivers.
In this work, the requirements of a real-time ionospheric model suitable for GNSS applications are explored, in terms of accuracy and confidence bounds. Key factors for an ionospheric determination better than 1 Total Electron Content Unit (TECU) (16 centimeters in L1) are shown to be whether the model has been derived using an ambiguity-fixing strategy and the number of layers used to reproduce the ionospheric delay. Different models are assessed both in mid-latitudes and equatorial regions, near the Solar Cycle maximum.
It will be shown how dual-frequency users take benefit from a precise modelling of the ionosphere. If accurate enough, the convergence of the navigation filter is reduced to achieve high accuracy positioning quickly, (i.e., the Fast Precise Point Positioning technique). Satellite orbits and clocks computed for Fast-PPP will be shown to be accurate to few centimeters and few tenths of nanoseconds, respectively.
Single-frequency users correct its measurements with the predictions provided by any ionospheric model. Thence, the accuracy of the Fast-PPP ionospheric corrections is directly translated to the measurements modelling and, consequently, to the user solution.
Horizontal and vertical 95% accuracies are shown to be better than 36 and 63 centimeters for single-frequency users and 11 and 15 centimeters for dual-frequency users. The assessment is done for several locations, including the equatorial region, for a month of data close to the last Solar Maximum. The trade-off between the formal and actual positioning errors has been carefully studied by means of the Stanford plots to set realistic confidence bounds to the corrections.Geometric Hamilton-Jacobi theory for higher-order autonomous systems
http://hdl.handle.net/2117/27514
Title: Geometric Hamilton-Jacobi theory for higher-order autonomous systems
Authors: Colombo, Leonardo; De León, Manuel; Prieto Martínez, Pedro Daniel; Román Roy, Narciso
Abstract: The geometric framework for the Hamilton-Jacobi theory is used to study this theory in the background of higher-order mechanical systems, in both the Lagrangian and Hamiltonian formalisms. Thus, we state the corresponding Hamilton-Jacobi equations in these formalisms and apply our results to analyze some particular physical examples.Wed, 22 Apr 2015 12:16:35 GMThttp://hdl.handle.net/2117/275142015-04-22T12:16:35ZColombo, Leonardo; De León, Manuel; Prieto Martínez, Pedro Daniel; Román Roy, NarcisonoHamilton-Jacobi equation, higher-order Lagrangian and Hamiltonian systems, Symplectic geometry, Field-theories, Mechanics, Constraints, Equation, DynamicsThe geometric framework for the Hamilton-Jacobi theory is used to study this theory in the background of higher-order mechanical systems, in both the Lagrangian and Hamiltonian formalisms. Thus, we state the corresponding Hamilton-Jacobi equations in these formalisms and apply our results to analyze some particular physical examples.Isometries on L-2(X) and monotone functions
http://hdl.handle.net/2117/27512
Title: Isometries on L-2(X) and monotone functions
Authors: Boza Rocho, Santiago; Soria, Javier
Abstract: We study necessary and sufficient conditions on a bounded operator T defined on the Hilbert space L-2(X) to be an isometry and show that, under suitable hypotheses, it suffices to restrict T to a smaller class of functions (e.g., if X = R+, to the cone of positive and decreasing functions). We also consider the problem of characterizing the sets Y subset of X for which the orthogonal projection of the operator T on L-2(Y) is also an isometry. Finally, we illustrate our results with several examples involving classical operators on different settings. (C) 2013 WILEY-VCH Verlag GmbH & Co. KGaA, WeinheimWed, 22 Apr 2015 11:07:17 GMThttp://hdl.handle.net/2117/275122015-04-22T11:07:17ZBoza Rocho, Santiago; Soria, JaviernoIsometries, Hardy operator, monotone functions, Hardy operator, Minus, Decreasing functions, Measure-spaces, Inequalities, Identity, ConeWe study necessary and sufficient conditions on a bounded operator T defined on the Hilbert space L-2(X) to be an isometry and show that, under suitable hypotheses, it suffices to restrict T to a smaller class of functions (e.g., if X = R+, to the cone of positive and decreasing functions). We also consider the problem of characterizing the sets Y subset of X for which the orthogonal projection of the operator T on L-2(Y) is also an isometry. Finally, we illustrate our results with several examples involving classical operators on different settings. (C) 2013 WILEY-VCH Verlag GmbH & Co. KGaA, WeinheimReal-time monitoring of thermal processes by reduced order modeling
http://hdl.handle.net/2117/27502
Title: Real-time monitoring of thermal processes by reduced order modeling
Authors: Aguado, José Vicente; Huerta, Antonio; Chinesta, Francisco; Cueto Prendes, Elias
Abstract: This work presents a simple technique for real-time monitoring of thermal processes. Real-time simulationbased control of thermal processes is a big challenge because high-fidelity numerical simulations are costly and cannot be used, in general, for real-time decision making. Very often, processes are monitored or controlled with a few measurements at some specific points. Thus, the strategy presented here is centered on fast evaluation of the response only where it is needed. To accomplish this, classical harmonic analysis is combined with recent model reduction techniques. This leads to an advanced harmonic methodology, which solves in real-time the transient heat equation at the monitored point. In order to apply the reciprocity principle, harmonic analysis is used in the space-frequency domain. Then, Proper Generalized Decomposition, a reduced order approach, pre-computes a transfer function able to produce the output response for a given excitation. This transfer function is computed offline and only once. The response at the monitoring point can be recovered performing a computationally inexpensive post-processing step. This last step can be performed online for real-time monitoring of the thermal process. Examples show the applicability of this approach for a wide range of problems ranging from fast temperature evaluation to inverse problems.Wed, 22 Apr 2015 07:31:08 GMThttp://hdl.handle.net/2117/275022015-04-22T07:31:08ZAguado, José Vicente; Huerta, Antonio; Chinesta, Francisco; Cueto Prendes, EliasnoReal-time, Heat Transfer, Monitoring, Model Reduction, Proper Generalized Decomposition, Harmonic AnalysisThis work presents a simple technique for real-time monitoring of thermal processes. Real-time simulationbased control of thermal processes is a big challenge because high-fidelity numerical simulations are costly and cannot be used, in general, for real-time decision making. Very often, processes are monitored or controlled with a few measurements at some specific points. Thus, the strategy presented here is centered on fast evaluation of the response only where it is needed. To accomplish this, classical harmonic analysis is combined with recent model reduction techniques. This leads to an advanced harmonic methodology, which solves in real-time the transient heat equation at the monitored point. In order to apply the reciprocity principle, harmonic analysis is used in the space-frequency domain. Then, Proper Generalized Decomposition, a reduced order approach, pre-computes a transfer function able to produce the output response for a given excitation. This transfer function is computed offline and only once. The response at the monitoring point can be recovered performing a computationally inexpensive post-processing step. This last step can be performed online for real-time monitoring of the thermal process. Examples show the applicability of this approach for a wide range of problems ranging from fast temperature evaluation to inverse problems.