Artículos (Matemática Aplicada II)

URI permanente para esta colecciónhttps://hdl.handle.net/11441/10899

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Dynamics and bifurcations of a nonholonomic heisenberg system
(World Scientific Publishing, 2012) Molina Becerra, Mónica; Galán Vioque, Jorge Francisco; Freire Macías, Emilio; Universidad de Sevilla. Departamento de Matemática Aplicada II (ETSI); Ministerio de Educación y Ciencia (MEC). España; Universidad de Sevilla. TIC130: Investigación en Sistemas Dinámicos en Ingeniería
We analyze both theoretically and numerically the dynamical behavior of a modification of a nonholonomic Hamiltonian system known as the Heisenberg system. The equations of motion are derived by computing the Lagrange multiplier in terms of the Poisson commutator. The presence of the constraint induces a nontrivial dynamical behavior that has been investigated by plotting the Poincaré section for the reduced system and taking advantage of a conserved quantity and the reversibilities. The dynamics is organized around two Lyapunov families of periodic orbits whose bifurcation behavior has been analyzed with a continuation technique both on the conserved quantity and on the parameters of the problem. The nongeneric branching behavior of the normal modes is theoretically explained by studying the variational equations that reduces to a Hill equation and its well known coexistence property. Invariant tori around the elliptic periodic orbits have been numerically detected but not further analyzed.
On the Restricted Arc-connectivity of s-geodetic Digraphs
(Springer, 2010) Balbuena, C.; García Vázquez, Pedro; Universidad de Sevilla. Departamento de Matemática Aplicada I (ETSII)
Orbital Lipschitzian mappings and semigroup actions on metric spaces
(Juliusz Schauder Centre for Nonlinear Studies, Nicolaus Copernicus University in Toruń, 2024-03) Parasio Sobreira de Souza, Daniel; Espínola García, Rafael; Japón Pineda, María de los Ángeles; Universidad de Sevilla. Departamento de Matemática Aplicada II (ETSI); Universidad de Sevilla. Departamento de Análisis Matemático; Ministerio de Ciencia e Innovación (MICIN). España; Junta de Andalucía; Universidad de Sevilla. FQM127: Análisis Funcional no Lineal
In this paper we study some results on common fixed points of families of mappings on metric spaces by imposing orbit Lipschitzian conditions on them. These orbit Lipschitzian conditions are weaker than asking the mappings to be Lipschitzian in the traditional way. We provide new results under the two classic approaches in the theory of fixed points for uniformly Lipschitzian mappings: the one under the normal structure property of the space (which can be regarded as the Cassini-Maluta's approach) and the one after the Lifschitz characteristic of the metric space (Lifschitz's approach). Although we focus on the case of semigroup of mappings, our results are new even when a mapping is considered by itself.
Characterization of finite shift via Herglotz’s representation
(Elsevier, 2025-02-01) Cruz Zamorano, Francisco José; Universidad de Sevilla. Departamento de Matemática Aplicada II (ETSI); Ministerio de Ciencia e Innovación (MICIN). España; Universidad de Sevilla. FQM133: Grupo de Investigación en Análisis Funcional
A complete characterization of parabolic self-maps of finite shift is given in terms of their Herglotz's representation. This improves a previous result due to Contreras, Díaz-Madrigal, and Pommerenke. We also derive some consequences for the rate of convergence of these functions to their Denjoy-Wolff point, improving a related result of Kourou, Theodosiadis, and Zarvalis for the continuous setting.
Composition operators on the algebra of Dirichlet series
(Springer, 2024-09-03) Contreras Márquez, Manuel Domingo; Gómez Cabello, Carlos; Rodríguez Piazza, Luis; Universidad de Sevilla. Departamento de Análisis Matemático; Universidad de Sevilla. Departamento de Matemática Aplicada II (ETSI); Ministerio de Ciencia e Innovación (MICIN). España; European Commission (EC). Fondo Europeo de Desarrollo Regional (FEDER); Junta de Andalucía; Universidad de Sevilla. FQM133: Grupo de Investigación en Análisis Funcional; Universidad de Sevilla. FQM104: Análisis Matemático
The algebra of Dirichlet series A(C+) consists on those Dirichlet series convergent in the right half-plane C+ and which are also uniformly continuous there. This algebra was recently introduced by Aron, Bayart, Gauthier, Maestre, and Nestoridis. We describe the symbols : C+ → C+ giving rise to bounded composition operators C in A(C+) and denote this class by GA. We also characterise when the operator C is compact in A(C+). As a byproduct, we show that the weak compactness is equivalent to the compactness for C. Next, the closure under the local uniform convergence of several classes of symbols of composition operators in Banach spaces of Dirichlet series is discussed. We also establish a one-to-one correspondence between continuous semigroups of analytic functions {t} in the class GA and strongly continuous semigroups of composition operators {Tt}, Tt f = f ◦ t , f ∈ A(C+). We conclude providing examples showing the differences between the symbols of bounded composition operators in A(C+) and the Hardy spaces of Dirichlet series Hp and H∞.
On spaces of integrable functions associated to vector measures and limiting real interpolation
(Elsevier, 2024-12-01) Fernández Carrión, Antonio; Manzano Rodríguez, Antonio; Universidad de Sevilla. Departamento de Matemática Aplicada II (ETSI); Journal of Mathematical Analysis and Applications; Universidad Complutense de Madrid; Universidad de Sevilla. FQM133: Grupo de Investigación en Análisis Funcional
We investigate which spaces are obtained when considering the limiting class of real interpolation spaces (0, q; J) for ordered Banach couples of spaces of (scalar) integrable functions with respect to a vector measure m, defined on a σ-algebra, with values in a Banach space. If m is in particular a finite positive scalar measure, previous known results are derived from ours. Furthermore, we study the interpolation of p-th power factorable operators by the extreme real interpolation method (1, q; K). We also deduce interpolation results for the (1, q; K)-method that apply to other related classes of operators to p-th power factorable operators, such as bidual (p, q)-power-concave operators and q-concave operators.
Dynamic inversion and optimal tracking control on the ball-plate system based on a linearized nonholonomic multibody model
(Elsevier, 2024-11) García-Agúndez Blanco, Alfonso; Saccon, A.; García Vallejo, Daniel; Freire Macías, Emilio; Universidad de Sevilla. Departamento de Matemática Aplicada II (ETSI); Universidad de Sevilla. Departamento de Ingeniería Mecánica y de Fabricación; Ministerio de Ciencia, Innovación y Universidades (MICINN). España; Junta de Andalucía; Universidad de Sevilla. TEP111: Ingenieria Mecanica; Universidad de Sevilla. TIC-130: Investigación en Sistemas Dinámicos en Ingeniería
This paper addresses the optimal control of the ball-plate system, a well-known nonholonomic system in the context of nonprehensile manipulation, using a multibody dynamics approach. The trajectory tracking control of a steady-state circular motion of the ball on the plate, for any radius and potentially off-centric with respect to the plate's pivoting point, is achieved by designing a Linear-Quadratic Regulator. A spatial multibody model of the ball-plate system is considered. A key contribution is the analytical computation of the circular steady motion of the ball by dynamic inversion, including the control actions to achieve this reference solution. This enables the analytical computation of the linearized equations along this reference motion, resulting in a periodic linear time-varying (LTV) system, and the application of linear controllability criteria for LTV systems. A controllable linear system, involving the Cartesian coordinates of the contact point and the yaw angle of the sphere, is obtained using a convenient coordinate partition in the linearization. Compared to existing results on the same problem, closed-loop stability about the desired trajectory is achieved for any radius of the circular trajectory. © 2024 The Authors
Complex interpolation of Orlicz spaces with respect to a vector measure
(Wiley, 2014) Campo Acosta, Ricardo del; Fernández Carrión, Antonio; Manzano, A.; Mayoral Masa, Fernando; Naranjo Naranjo, Francisco José; Universidad de Sevilla. Departamento de Matemática Aplicada I (ETSII); Universidad de Sevilla. Departamento de Matemática Aplicada II (ETSI); Ministerio de Economía y Competitividad; FEDER
We apply the Calderon interpolation methods to Orlicz and weakly Orlicz function spaces with respect to a Banach-space-valued measure defined on a σ-algebra. The results we obtain generalize those in the case of Banach lattices of p-integrable and weakly p-integrable functions with respect to such a vector measure.
Bichromatic separability with two boxes: A general approach
(Elsevier, 2009) Cortés Parejo, María del Carmen; Díaz Báñez, José Miguel; Pérez-Lantero, P.; Seara, C.; Urrutia, J.; Ventura Molina, Inmaculada; Universidad de Sevilla. Departamento de Matemática Aplicada I (ETSII); Universidad de Sevilla. Departamento de Matemática Aplicada II (ETSI)
Let S be a set of n points on the plane in general position such that its elements are colored red or blue. We study the following problem: Find a largest subset of S which can be enclosed by the union of two, not necessarily disjoint, axis-aligned rectangles R and B such that R (resp. B) contains only red (resp. blue) points. We prove that this problem can be solved in O(n2 logn) time and O(n) space. Our approach is based on solving some instances of Bentley’s maximum-sum consecutive subsequence problem. We introduce the first known data structure to dynamically maintain the optimal solution of this problem. We show that our techniques can be used to efficiently solve a more general class of problems in data analysis.
Limit Cycle and Boundary Equilibrium Bifurcations in Continuous Planar Piecewise Linear Systems
(World Scientific Publishing Co., 2015-03) Ponce Núñez, Enrique; Ros Padilla, Francisco Javier; Vela Felardo, Elisabet; Universidad de Sevilla. Departamento de Matemática Aplicada II (ETSI); Ministerio de Ciencia y Tecnología (MCYT). España; Consejería de Economía, Innovación, Ciencia y Empleo, Junta de Andalucía; Universidad de Sevilla. TIC130: Investigación en Sistemas Dinámicos en Ingeniería
Boundary equilibrium bifurcations in continuous planar piecewise linear systems with two and three zones are considered, with emphasis on the possible simultaneous appearance of limit cycles. Situations with two limit cycles surrounding the only equilibrium point are detected and rigorously shown for the first time in the family of systems under study. The theoretical results are applied to the analysis of an electronic Wien bridge oscillator with biased polarization, characterizing the different parameter regions of oscillation.
Algebraically computable piecewise linear nodal oscillators
(Elsevier, 2013-01) Ponce Núñez, Enrique; Ros Padilla, Francisco Javier; Vela Felardo, Elisabet; Universidad de Sevilla. Departamento de Matemática Aplicada II (ETSI); Ministerio de Ciencia y Tecnología (MCYT). España; Consejeria de Educación y Ciencia, Junta de Andalucía; Universidad de Sevilla, TIC130: Investigación en Sistemas Dinámicos en Ingeniería
A family of piecewise linear oscillators whose oscillation can be completely characterized by algebraic methods is studied. It represents up to the best of authors’s knowledge, the first planar example where all the oscillation properties can be determined for all the values of the bifurcation parameter. In fact, algebraic expressions for coordinates of representative points, period and characteristic multiplier of the corresponding periodic orbit are provided. Thus, the studied family of oscillators deserves to be considered a good benchmark for testing approximate methods of analysis in nonlinear oscillation theory. The piecewise linear oscillators studied are called nodal oscillators, since their relevant linear parts are of node type, and they are not perturbations of the harmonic oscillator. They represent real models in practice, as it is shown for an electronic circuit modeling a piecewise linear version of the classical Van der Pol oscillator.
Unfolding the fold-Hopf bifurcation in piecewise linear continuous differential systems with symmetry
(Elsevier, 2013-05) Ponce Núñez, Enrique; Ros Padilla, Francisco Javier; Vela Felardo, Elisabet; Universidad de Sevilla. Departamento de Matemática Aplicada II (ETSI); Ministerio de Ciencia y Tecnología (MCYT). España; Consejería de Educación y Ciencia, Junta de Andalucía; Universidad de Sevilla. TIC130: Investigación en Sistemas Dinámicos en Ingeniería
Three-dimensional symmetric piecewise linear differential systems near the conditions corresponding to the fold-Hopf bifurcation for smooth systems are considered. By introducing one small parameter, we study the bifurcation of limit cycles in passing through its critical value, when the three eigenvalues of the linear part at the origin are at the imaginary axis of the complex plane. The simultaneous bifurcation of three limit cycles is proved. Conditions for stability of these limit cycles are provided, and analytical expressions for their period and amplitude are obtained. Finally, we apply the achieved theoretical results to a generalized version of Chua’s circuit, showing that the fold-Hopf bifurcation takes place for a certain range of parameters.
Norming Sets on a Compact Complex Manifold
(Springer Nature, 2019-07) Aguilar-Hernández, Tanausú; Universidad de Sevilla. Departamento de Matemática Aplicada II (ETSI)
We describe the norming sets for the space of global holomorphic sections to a kpower of a positive holomorphic line bundle on a compact complex manifold X. We characterize in metric terms the sequence of measurable subsets {Gk }k of X such that there is a constant C > 0 where s2 ≤ C Gk |s(z)| 2 dV(z) for every s ∈ H0(X, O(L⊗k )) and for all k ∈ N.
The role of dynamic friction in the appearance of periodic oscillations in mechanical systems
(Springer, 2024-09-03) González-Carbajal, Javier; García Vallejo, Daniel; Domínguez Abascal, Jaime; Freire Macías, Emilio; Universidad de Sevilla. Departamento de Matemática Aplicada II (ETSI); Universidad de Sevilla. Departamento de Ingeniería Mecánica y de Fabricación; Universidad de Sevilla. TEP111: Ingeniería Mecánica; Universidad de Sevilla. TIC130: Investigación en Sistemas Dinámicos en Ingeniería
This article investigates the appearance of periodic mechanical oscillations associated with the transition between static and dynamic friction regimes. The study employs a mechanical system with one degree of freedom and a friction model recently proposed by Brown and McPhee, whose continuity and differentiability properties make it particularly appropriate for an analytical treatment of the equations. A bifurcation study of the system, including stability analysis, transformation to normal form and numerical continuation techniques, reveals that stable periodic orbits can be created either by a supercritical Hopf bifurcation or by a saddle-node bifurcation of limit cycles. The influence of all system parameters on the appearance of periodic oscillations is investigated in detail. In particular, the effect of the friction model parameters (static-to-dynamic friction ratio and transition speed between the static and dynamic regimes) on the bifurcation behavior of the system is addressed.
Homoclinic behavior around a degenerate heteroclinic cycle in a Lorenz-like system
(Elsevier, 2024-09) Algaba Durán, Antonio; Fernández Sánchez, Fernando; Merino Morlesín, Manuel; Rodríguez Luis, Alejandro José; Universidad de Sevilla. Departamento de Matemática Aplicada II (ETSI); Ministerio de Economía y Competitividad (MINECO). España; Ministerio de Ciencia, Innovación y Universidades (MICINN). España; Junta de Andalucía; Universidad de Sevilla. TIC130: Investigación en Sistemas Dinámicos en Ingeniería
In this work, we analyze a degenerate heteroclinic cycle that appears in a Lorenz-like system when one of the involved equilibria changes from real saddle to saddle-focus. First, from a theoretical model based on the construction of a Poincaré return map, we demonstrate that an infinite number of homoclinic connections arise from the point of the parameter plane where the degenerate heteroclinic cycle appears. The subsequent numerical study not only illustrates the presence of the first homoclinic orbits in the infinite succession but also allows to find other important local and global organizing centers of codimension two (Bogdanov–Takens bifurcations, degenerate homoclinic and heteroclinic connections, T-points) and three (triple-zero bifurcation, doubly-degenerate heteroclinic cycles, degenerate T-points).
Weighing hierarchical power and active contribution in cooperative games with authorization structure
(Springer, 2024-07-05) Alarcón Carrero, Antonio Carlos; Gallardo Morilla, José Manuel; Jiménez Losada, Andrés; Universidad de Sevilla. Departamento de Matemática Aplicada II (ETSI); Ministerio de Ciencia, Innovación y Universidades (MICINN). España; Universidad de Sevilla. FQM237: Juegos con Estructuras Combinatorias y de Orden
Cooperative games model situations in which a group of players work together to make a profit. Frequently, in cooperative situations there are dependency or hierarchical relationships between the players, which must be taken into account when allocating the common profit obtained by the grand coalition. Multiple structures have been used in the literature to model those relationships, and several values have been proposed, but there is something in common in all of them: if a player can veto the participation of another in any coalition, then both players will receive the same share of the profit derived from the active cooperation of the vetoed player. In other words, actively cooperating and giving permission to cooperate are equally valued. In many situations this is neither fair nor realistic. In this paper we introduce a family of allocation rules for cooperative games with authorization structure, which reward positional power less than active cooperation.
Allocation rules for communication situations with incompatibilities
(Springer, 2024-07-19) Basallote Galván, Manuela; Gallardo Morilla, José Manuel; Hernández Mancera, Carmen; Jiménez Losada, Andrés; Universidad de Sevilla. Departamento de Matemática Aplicada II (ETSI); Ministerio de Ciencia e Innovación (MICIN). España; Universidad de Sevilla. FQM237: Juegos con Estructuras Combinatorias y de Orden
In this article we analyze certain situations with restricted cooperation. To do this we introduce a model that combines two types of games well studied in the literature: graph-restricted games and games with incompatible players. In particular, our model extends Myerson’s model for communication situations and Bergantiños’ model for incompatible relationships. Our approach is based on the concept of profit measure, which allows us to deal simultaneously with both types of bilateral relationships. We show that in the situations considered there are multiple possible definitions of the profit achievable for each coalition. This leads us to introduce different allocation rules for these cooperative situations.
Time and band limiting for exceptional polynomials
(Elsevier, 2024-01) Castro Smirnova, Mirta María; Grünbaum, Francisco Alberto; Zurrián, Ignacio Nahuel; Universidad de Sevilla. Departamento de Matemática Aplicada II (ETSI); European Commission (EC). Fondo Europeo de Desarrollo Regional (FEDER); Agencia Estatal de Investigación. España; Junta de Andalucía; Consejo Nacional de Investigaciones Científicas y Técnicas (CONICET). Argentina; Ministerio de Ciencia e Innovación; Universidad de Sevilla; Universidad de Sevilla. FQM262: Teoría de la Aproximación
The "time-and-band limiting" commutative property was found and exploited by D. Slepian, H. Landau and H. Pollak at Bell Labs in the 1960's, and independently by M. Mehta and later by C. Tracy and H. Widom in Random matrix theory. The property in question is the existence of local operators with simple spectrum that commute with naturally appearing global ones. Here we give a general result that insures the existence of a commuting differential operator for a given family of exceptional orthogonal polynomials satisfying the "bispectral property". As a main tool we go beyond bispectrality and make use of the notion of Fourier Algebras associated to the given sequence of exceptional polynomials. We illustrate this result with two examples, of Hermite and Laguerre type, exhibiting also a nice Perline's form for the commuting differential operator.
Bispectrality for matrix Laguerre-Sobolev polynomials
(Elsevier, 2024-09) Marcellán Español, Francisco; Zurrián, Ignacio Nahuel; Universidad de Sevilla. Departamento de Matemática Aplicada II (ETSI); European Commission (EC). Fondo Europeo de Desarrollo Regional (FEDER); Ministerio de Ciencia e Innovación (MICIN). España; Agencia Estatal de Investigación. España; Consejo Nacional de Investigaciones Científicas y Técnicas (CONICET). Argentina
In this contribution we deal with sequences of polynomials orthogonal with respect to a Sobolev type inner product. A banded symmetric operator is associated with such a sequence of polynomials according to the higher order difference equation they satisfy. Taking into account the Darboux transformation of the corresponding matrix we deduce the connection with a sequence of orthogonal polynomials associated with a Christoffel perturbation of the measure involved in the standard part of the Sobolev inner product. A connection with matrix orthogonal polynomials is stated. The Laguerre-Sobolev type case is studied as an illustrative example. Finally, the bispectrality of such matrix orthogonal polynomials is pointed out.
The Darboux process and time-and-band limiting for matrix orthogonal polynomials
(Elsevier, 2015-12-15) Castro Smirnova, Mirta María; Grünbaum, Francisco Alberto; Universidad de Sevilla. Departamento de Matemática Aplicada II (ETSI); Ministerio de Economía y Competitividad (MINECO). España; Junta de Andalucía; European Commission (EC). Fondo Europeo de Desarrollo Regional (FEDER); Ministerio de Educación, Cultura y Deporte (MECD). España; Universidad de Sevilla. FQM262: Teoría de la Aproximación
We extend to a situation involving matrix valued orthogonal polynomials a scalar result that originates in work of Claude Shannon in laying the mathematical foundations of information theory and a remarkable series of papers by D. Slepian, H. Landau and H. Pollak at Bell Labs in the 1960's. We show that in this case an algebraic miracle that plays a very important role in the classical case survives an application of the so-called Darboux process in the matrix valued context.

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