DSpace Collection:
http://hdl.handle.net/2117/3228
20140930T12:20:06Z

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.

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.
20140922T10:36:12Z

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
20140919T08:39:42Z

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.
20140917T11:25:15Z

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.
20140917T10:22:24Z

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.
20140917T10:09:27Z

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.
20140917T07:39:47Z

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.
20140729T08:35:40Z

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).
20140716T07:35:44Z

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.
20140715T11:00:50Z

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.
20140715T10:29:35Z

Exponentially small asymptotic estimates for the splitting of separatrices to whiskered tort with quadratic and cubic frequencies
http://hdl.handle.net/2117/23508
Title: Exponentially small asymptotic estimates for the splitting of separatrices to whiskered tort with quadratic and cubic frequencies
Authors: Delshams Valdés, Amadeu; Gonchenko, Marina; Gutiérrez Serrés, Pere
Abstract: We study the splitting of invariant manifolds of whiskered tori with two or three frequencies in nearlyintegrable Hamiltonian systems, such that the hyperbolic part is given by a pendulum. We consider a 2dimensional torus with a frequency vector omega = (1, Omega), where Omega is a quadratic irrational number, or a 3dimensional torus with a frequency vector w = (1, Omega, Omega(2)), where Omega is a cubic irrational number. Applying the PoincareMelnikov method, we find exponentially small asymptotic estimates for the maximal splitting distance between the stable and unstable manifolds associated to the invariant torus, and we show that such estimates depend strongly on the arithmetic properties of the frequencies. In the quadratic case, we use the continued fractions theory to establish a certain arithmetic property, fulfilled in 24 cases, which allows us to provide asymptotic estimates in a simple way. In the cubic case, we focus our attention to the case in which Q is the socalled cubic golden number (the real root of x(3) x  1= 0), obtaining also asymptotic estimates. We point out the similitudes and differences between the results obtained for both the quadratic and cubic cases.
20140715T08:21:36Z

Stationkeeping of real EarthMoon libration point orbits using discretetime sliding mode control
http://hdl.handle.net/2117/23453
Title: Stationkeeping of real EarthMoon libration point orbits using discretetime sliding mode control
Authors: Lian, Yijun; Gómez Muntané, Gerard; Masdemont Soler, Josep; Tang, Guojian
Abstract: In this work, stationkeeping of real Earth–Moon libration point orbits is studied using discretetime sliding mode control (DSMC). For comparison, a discrete linear quadratic regulator (DLQR) controller is also considered. The libration orbits are termed “real” in the sense that they are obtained in a complete Solar System model, taking into account all the gravitational forces of the planets, the Moon, and the Sun. This is a key point for any stationkeeping study, that the use of far from real orbits as nominal ones increases unnecessarily the stationkeeping cost. The resulting controlled system, linearised with respect to some nominal orbit, takes a discretetime form suitable for applying impulsive maneuvers. The DSMC controller is designed by the reaching law with the parameters chosen in an adaptive way. A method for designing the sliding surface is proposed. In order to assess and compare the performance of the two controllers, simulations are done for six libration point orbits around the L2L2 point (three halo orbits and three Lissajous ones) during a time span of 10 years. Several practical constraints are also considered in the simulations. Extensive Monte Carlo results show that the proposed DSMC approach is able to maintain the spacecraft within a close vicinity of the nominal orbits with a maneuver cost less than 2 m/s per year, and it outperforms the DLQR approach in terms of the position controllability. Some comparison with previous results obtained by other authors with different procedures is also given.
20140709T11:19:18Z

Códigos de convolución desde el punto de vista de teoría de control. Análisis de la observabilidad
http://hdl.handle.net/2117/23450
Title: Códigos de convolución desde el punto de vista de teoría de control. Análisis de la observabilidad
Authors: García Planas, María Isabel; Tarragona Romero, Sonia; Um, Laurence Emilie
Abstract: En este trabajo se realiza un estudio detallado
de la estructura algebraica de los códigos de convolución
empleando técnicas de la teoría de sistemas lineales. La
conexión entre estos conceptos ayuda a comprender mejor
las propiedades de los códigos convolucionales. Más
explícitamente, esta conexión es debida a que los
conceptos de controlabilidad y observabilidad, de los
sistemas lineales, pueden ser expresados, en el marco de
los códigos convolucionales, como el carácter no
catastrófico de los códigos. En particular, en este trabajo
se examina la propiedad de “outputobservabilidad” y
damos condiciones que aseguran el cumplimiento de esta
propiedad.
20140709T10:49:12Z

The PicardFuchs equations for complete hyperelliptic integrals of even order curves, and the actions of the generalized Neumann system
http://hdl.handle.net/2117/23448
Title: The PicardFuchs equations for complete hyperelliptic integrals of even order curves, and the actions of the generalized Neumann system
Authors: Fedorov, Yuri; Pantazi, Chara
Abstract: We consider a family of genus 2 hyperelliptic curves of even order and obtain explicitly the systems of 5 linear ordinary differential equations for periods of the corresponding Abelian integrals of first, second, and third kind, as functions of some parameters of the curves. The systems can be regarded as extensions of the wellstudied PicardFuchs equations for periods of complete integrals of first and second kind on odd hyperelliptic curves. The periods we consider are linear combinations of the action variables of several integrable systems, in particular the generalized Neumann system with polynomial separable potentials. Thus the solutions of the extended PicardFuchs equations can be used to study various properties of the actions. (C) 2014 AIP Publishing LLC.
20140709T10:41:57Z