# Artículos (Matemática Aplicada II)

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

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Artículo 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 FuncionalA 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.Artículo 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 MatemáticoThe 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∞.Artículo 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 FuncionalWe 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.Artículo 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 IngenieríaThis 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 AuthorsArtículo 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; FEDERWe 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.Artículo 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.Artículo 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 IngenieríaBoundary 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.Artículo 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 IngenieríaA 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.Artículo 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 IngenieríaThree-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.Artículo 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.Artículo 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 IngenieríaThis 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.Artículo 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 IngenieríaIn 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).Artículo 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 OrdenCooperative 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.Artículo 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 OrdenIn 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.Artículo 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 AproximaciónThe "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.Artículo 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). ArgentinaIn 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.Artículo 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 AproximaciónWe 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.Artículo Generalized eigenvalue problem for an interface elliptic equation(Elsevier, 2024-05-05) Maia, Braulio Brendo Vasconcelos; Molina Becerra, Mónica; Morales Rodrigo, Cristian; Suárez Fernández, Antonio; Universidad de Sevilla. Departamento de Ecuaciones Diferenciales y Análisis Numérico; Universidad de Sevilla. Departamento de Matemática Aplicada II (ETSI); Junta de Andalucía; Universidad de Sevilla. TIC130: Investigación en Sistemas Dinámicos en Ingeniería; Universidad de Sevilla. FQM131: Ec.diferenciales, Simulación Num. y Desarrollo SoftwareIn this paper we deal with an eigenvalue problem in an interface elliptic equation. We characterize the set of principal eigenvalues as a level set of a concave and regular function. As application, we study a problem arising in population dynamics. In these problems each species lives in a subdomain, and they interact in a common border, which acts as a geographical barrier; but unlike previous results, we consider the case of different growth rates in each subdomain.Artículo An electric kickscooter multibody model: equations of motion and linear stability analysis(Springer, 2024-03-14) García-Agúndez Blanco, Alfonso; 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; Universidad de Sevilla. TEP111: Ingeniería Mecánica; Universidad de Sevilla. TIC130: Investigación en Sistemas Dinámicos en IngenieríaIn this work, a detailed multibody model of an electric kickscooter is presented. The model includes toroidal wheels as well as rear and front suspensions. The equations of motion are derived and linearized along the steady forward motion of the vehicle. Using an efficient linearization approach, suitable for complex multibody systems with holonomic and nonholonomic constraints, allows for obtaining the reduced linearized equations of motion as a function of the geometric, dynamic, wheels’, and suspensions’ parameters. The proposed electric kickscooter multibody model is validated with the stability results of a previously presented electric kickscooter benchmark. Since the resulting eigenvalues are parameterized regarding the design parameters, a detailed linear stability analysis of the system is performed. In particular, the influence on the stability of the toroidal geometry of the wheels, the elliptic cross-section of the toroidal wheels, the rider model, the steering axis inclination angle, the inertia tensor of the front frame, and the rear and front suspensions is analyzed. The model presented, together with the linearized equations of motion obtained in this work, enables a systematic analysis of the stability of these vehicles, which helps design new electric kickscooters with improved vehicle safety conditions and oriented to a wider range of potential users.Artículo Comparative effect of different patient education modalities on quality of life in breast cancer survivors: A systematic review and network meta-analysis(Elsevier Science Ltd, 2023) Martínez-Miranda, Patricia; Jiménez Rejano, José Jesús; Rosales Tristancho, Abel; Casuso-Holgado, María Jesús; Universidad de Sevilla. Departamento de Matemática Aplicada II (ETSI); Universidad de Sevilla. Departamento de FisioterapiaPurpose: To assess the comparative effect of patient education modalities (online, telephonic, mixed, in-person meetings) on the improvement of quality-of-life in breast cancer survivors. Methods: A search was conducted in different databases, being only included randomised controlled trials. The methodological quality and the risk of bias were assessed following the criteria of PEDro and Cochrane Rob-2 tools, respectively. The certainty of the evidence was judged using the GRADE tool. These evaluations were performed by two independent reviewers. When possible, data was pooled in a network meta-analysis (95% confidence interval [CI]). Results: Fourteen studies were included in the qualitative synthesis (1632 participants) and 11 in the quantitative (1482 participants). Network comparisons revealed that mixed educational modality was the highest ranked intervention at short (MD = 0.62; 95% CI [-0.35, 1.6]) and long -term (MD = 1.1; 95% CI [-1.5, 3.8); the control condition was the last in both cases, with a good convergence of the model observed. However, comparisons did not show significant differences. Conclusions: Health policies could benefit from mixed modalities of patient education as it is expected to generate socio-economical savings and promote patient self-management. Probably, online mixed modalities, i.e. virtual face to face meetings, could be a more up-to-date option that fit best to nowadays patients‘ lifestyle. However, the limitations of this review force us to interpret our results with caution.