Artículos (Matemática Aplicada II)

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

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Optimal Bounds for POD Approximations of Infinite Horizon Control Problems Based on Time Derivatives
(Springer, 2025) De Frutos, Javier; García-Archilla, Bosco; Novo, Julia; Universidad de Sevilla. Departamento de Matemática Aplicada II (ETSI); Agencia Estatal de Investigación. España; European Commission (EC). Fondo Europeo de Desarrollo Regional (FEDER); Junta de Castilla y León
In this paper we consider the numerical approximation of infinite horizon problems via the dynamic programming approach. The value function of the problem solves a Hamilton–Jacobi–Bellman equation that is approximated by a fully discrete method. It is known that the numerical problem is difficult to handle by the so called curse of dimensionality. To mitigate this issue we apply a reduction of the order by means of a new proper orthogonal decomposition (POD) method based on time derivatives. We carry out the error analysis of the method using recently proved optimal bounds for the fully discrete approximations. Moreover, the use of snapshots based on time derivatives allows us to bound some terms of the error that could not be bounded in a standard POD approach. Some numerical experiments show the good performance of the method in practice.
High-order well-balanced schemes for shallow models for dry avalanches
(2025) Castro Díaz, M. J.; Escalante, C.; Garres-Díaz, José; Morales de Luna, T.; Universidad de Sevilla. Departamento de Matemática Aplicada II (ETSI); Ministerio de Ciencia, Innovación y Universidades (MICIU). España; Junta de Andalucía; Universidad de Sevilla. FQM120: Modelado Matemático y Simulación de Sistemas Medioambientales
In this work we consider a depth-averaged model for granular flows with a Coulomb-type friction force described by the rheology. In this model, the so-called lake-at-rest steady states are of special interest, where velocity is zero and the slope is under a critical threshold defined by the angle of repose of the granular material. It leads to a family with an infinite number of lake-at-rest steady states. We describe a well-balanced reconstruction procedure that allows to define well-balanced finite volume methods for such problem. The technique is generalized to high-order space/time schemes. In particular, the second and third-order schemes are considered in the numerical tests section. An accuracy test is included showing that second and third-order are achieved. A well-balanced test is also considered. The proposed scheme is well-balanced for steady states with non-constant free surface, and it is exactly well-balanced for those steady states given by a simple characterization.
Pointwise error bounds in POD methods without difference quotients
(Springer, 2025-03-08) García-Archilla, Bosco; Novo Martín, Julia; Universidad de Sevilla. Departamento de Matemática Aplicada II (ETSI); Ministerio de Ciencia e Innovación (MICIN). España; European Union (UE); Universidad de Sevilla. TIC130: Investigación en Sistemas Dinámicos en Ingeniería
In this paper we consider proper orthogonal decomposition (POD) methods that do not include difference quotients (DQs) of snapshots in the data set. The inclusion of DQs have been shown in the literature to be a key element in obtaining error bounds that do not degrade with the number of snapshots. More recently, the inclusion of DQs has allowed to obtain pointwise (as opposed to averaged) error bounds that decay with the same convergence rate (in terms of the POD singular values) as averaged ones. In the present paper, for POD methods not including DQs in their data set, we obtain error bounds that do not degrade with the number of snapshots if the function from where the snapshots are taken has certain degree of smoothness. Moreover, the rate of convergence is as close as that of methods including DQs as the smoothness of the function providing the snapshots allows. We do this by obtaining discrete counterparts of Agmon and interpolation inequalities in Sobolev spaces. Numerical experiments validating these estimates are also presented.
p-Strong Roman Domination in Graphs
(World Scientific and Engineering Academy and Society, 2024) Valenzuela-Tripodoro, J. C.; Mateos-Camacho, M. A.; Cera López, Martín; Moreno Casablanca, Rocío; Álvarez-Ruiz, M. P.; Universidad de Sevilla. Departamento de Matemática Aplicada I (ETSII); Universidad de Sevilla. Departamento de Matemática Aplicada II (ETSI)
Examples in Discrete Iteration of Arbitrary Intervals of Slopes
(Springer, 2025) Contreras Márquez, Manuel Domingo; Cruz Zamorano, Francisco José; Rodríguez Piazza, Luis; Universidad de Sevilla. Departamento de Matemática Aplicada II (ETSI); Universidad de Sevilla. Departamento de Análisis Matemático
Given a compact interval [a, b]⊂[0, π], we construct a parabolic self-map of the upper half-plane whose set of slopes is [a, b]. The nature of this construction is completely discrete and explicit: we explicitly construct a self-map and we explicitly show in which way its orbits wander towards the Denjoy–Wolff point. We also analyze some properties of the Herglotz measure corresponding to such example, which yield the regularity of such self-map in its Denjoy–Wolff point.
A semilinear interface elliptic equation with sublinear and logistic reactions terms
(Springer, 2025-02-13) Molina Becerra, Mónica; Morales Rodrigo, Cristian; Suárez Fernández, Antonio; Universidad de Sevilla. Departamento de Matemática Aplicada II (ETSI); Universidad de Sevilla. Departamento de Ecuaciones Diferenciales y Análisis Numérico; Universidad de Sevilla. TIC130: Investigación en Sistemas Dinámicos en Ingeniería; Universidad de Sevilla. FQM131: Ecuaciones diferenciales, Simulación Num. y Desarrollo Software
In this paper, the structure of the set of positive solutions of a semilinear interface elliptic problem is studied in detail. In this kind of problem, the domain is the union of two different regions, separated by a membrane or interface where it happens an interchange of flux. In each region, we assume a nonlinear reaction term: a sublinear function in one of them, and a logistic function in the other. The combination of both terms, as well as the interface, give an interesting structure to the set of positive solutions. In particular, we will show that the existence of the interface provides the model a cooperative effect that makes populations from both regions coexist in situations where without the interface they would disappear.
On priority in multi-issue bankruptcy problems with crossed claims
(MDPI, 2025-01-13) Acosta Vega, Rick; Algaba Durán, Encarnación; Sánchez Soriano, Joaquín; Universidad de Sevilla. Departamento de Matemática Aplicada II (ETSI); Agencia Estatal de Investigación. España; Generalitat Valenciana
In this paper, we analyze the problem of how to adapt the concept of priority to situations where several perfectly divisible resources have to be allocated among a certain set of agents that have exactly one claim that is used for all resources. In particular, we introduce constrained sequential priority rules and two constrained random arrival rules which extend the classical sequential priority rules and the random arrival rule to these situations. We also provide an axiomatic analysis of these rules. Finally, we present a numerical example to compare the constrained random arrival rule to other solutions in this context.
A new family of solutions for graph-restricted cooperative games: rethinking the weight of intermediary power
(John Wiley and Sons Inc., 2024) Alarcón, Antonio C.; Gallardo Morilla, José Manuel; Jiménez Losada, Andrés; Universidad de Sevilla. Departamento de Matemática Aplicada II (ETSI); Ministerio de Ciencia, Innovación y Universidades (MICIU). España; Universidad de Sevilla. FQM237: Juegos con Estructuras Combinatorias y de Orden
In graph-restricted cooperative games, a group of agents, represented by the nodes of a graph, work together to make a profit. However, two agents can cooperate within a coalition only if they are connected by the graph in the coalition. Several allocation rules have been proposed for these games, but there is something in common in all of them: if a player is an indispensable intermediary to communicate with the players in a coalition, this player will receive, at least, the same share of the profit generated by the coalition as the players who belong to it. In other words, intermediation power is valued, at least, as much as active cooperation. In some situations, this is neither fair nor realistic. In this paper, we introduce a family of values for graph-restricted games that value intermediary power less than active cooperation.
On the Hardy number of Koenigs domains
(Springer Nature, 2024-12) Contreras Márquez, Manuel Domingo; Cruz Zamorano, Francisco José; Kourou, María; Rodríguez Piazza, Luis; Universidad de Sevilla. Departamento de Matemática Aplicada II (ETSI); Ministerio de Ciencia, Innovación y Universidades (MICIU). España; Junta de Andalucía,; Universidad de Sevilla. FQM133: Grupo de Investigación en Análisis Funcional
This work studies the Hardy number of hyperbolic planar domains satisfying Abel’s inclusion property, which are usually known as Koenigs domains. More explicitly, we prove that the Hardy number of a Koenings domains whose complement is non-polar is greater than or equal to 1/2, and this lower bound is sharp. In contrast to this result, we provide examples of general domains whose Hardy numbers are arbitrarily small. Additionally, we outline the connection of the aforementioned class of domains with the discrete dynamics of the unit disc and obtain results on the range of Hardy number of Koenigs maps, in the hyperbolic and parabolic case.
Manoeuvre detection in Low Earth Orbit with radar data
(Elsevier, 2023-10) Montilla García, José Manuel; Sánchez Merino, Julio César; Vázquez Valenzuela, Rafael; Galán Vioque, Jorge Francisco; Rey Benayas, Javier; Siminski, Jan A.; Universidad de Sevilla. Departamento de Ingeniería Aeroespacial y Mecánica de Fluidos; Universidad de Sevilla. Departamento de Matemática Aplicada II (ETSI); Universidad de Sevilla
This work outlines and assesses several methods for the detection of manoeuvres in Low Earth Orbit (LEO) from surveillance radar data. To be able to detect manoeuvres, the main starting assumption is that the object under analysis has an orbit known with a sufficient degree of precision. Based on the precise (a posteriori) orbit and radar data, several manoeuvre detection methods are presented; one is based on unscented Kalman filtering, whereas two others algorithms are based on reachability analysis of the state, which correlates its prediction set with the next track from the radar. The filtering algorithm can be extended for several radar tracks, whereas the reachability-based methods are more precise in detecting manoeuvres. Then, to inherit the best properties of both classes of algorithms, a manoeuvre detection filter that combines both concepts is finally presented. Manoeuvre detection results are analysed first for simulated scenarios—for validation and calibration purposes—and later for real data. Radar information comes from the Spanish Space Surveillance Radar (S3TSR), with real manoeuvre information and high-quality ephemerides. The results show promise, taking into account that a single surveillance radar is the only source of data, obtaining manoeuvre detection rates of more than 50% and false positive rates of less than 10%.
Rodrigues’ formulas for orthogonal matrix polynomials satisfying second-order difference equations
(Taylor and Francis, 2014-06-19) Durán Guardeño, Antonio José; Sánchez Canales, Vanesa; 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); Universidad de Sevilla. FQM: 262: Teoría de la Aproximación
We develop a method to ﬁnd discrete Rodrigues’ formulas for orthogonal matrix polynomials which arealso eigenfunctions of a second-order difference operator. Using it, we produce Rodrigues’ formulas fortwo illustrative examples of arbitrary size.
Orthogonal matrix polynomials whose differences are also orthogonal
(Elsevier, 2014-02) Durán Guardeño, Antonio José; Sánchez Canales, Vanesa; Universidad de Sevilla. Departamento de Matemática Aplicada II (ETSI); Ministerio de Economia y Competitividad; Junta de Andalucía; European Commission (EC). Fondo Europeo de Desarrollo Regional (FEDER); Universidad de Sevilla. FQM262: Teoría de la Aproximación; Universidad de Sevilla. FQM-413: Research Group on Geometric Algorithms & Applications (GALGO)
We characterize orthogonal matrix polynomials (Pn)n whose differences (∇Pn+1)n are also orthogonal by means of a discrete Pearson equation for the weight matrix W with respect to which the polynomials (Pn)n are orthogonal. We also construct some illustrative examples. In particular, we show that contrary to what happens in the scalar case, in the matrix orthogonality the discrete Pearson equation for the weight matrix W is, in general, independent of whether the orthogonal polynomials with respect to W are eigenfunctions of a second order difference operator with polynomial coefficients. ⃝
Time-and-band limiting for matrix orthogonal polynomials of Jacobi type
(World Scientific Publishing, 2017-10) 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 plays an important role in Random Matrix Theory and a few other areas of mathe-matics and signal processing. We consider a case of matrix-valued Jacobi polynomials which arises from the study of representations of SU⁡(𝑁), a group that plays an important role in Random Matrix Theory. We show that in this case an algebraic miracle, namely the existence of a differential operator that commutes with a naturally arising integral one, extends to this matrix-valued situation.
Commuting finite Blaschke products with no fixed points in the unit disk
(Elsevier, 2009-11) Basallote Galván, Manuela; Contreras Márquez, Manuel Domingo; Hernández Mancera, Carmen; Universidad de Sevilla. Departamento de Matemática Aplicada II (ETSI)
In this paper we study when two finite Blaschke products commute. We complete previous results by Chalendar and Mortini (when they have a fixed point in the unit disk) and by Arteaga (when they do not have a fixed point in the unit disk).
A new Shapley value for games with fuzzy coalitions
(Elsevier, 2020) Basallote Galván, Manuela; Hernández Mancera, Carmen; Jiménez Losada, Andrés; Universidad de Sevilla. Departamento de Matemática Aplicada II (ETSI); Jiménez Losada, Andrés; Ministerio de Economia, Industria y Competitividad (MINECO). España; Junta de Andalucía; Universidad de Sevilla. FQM237: Juegos con Estructuras Combinatorias y de Orden
En este artículo se introduce un nuevo valor de Shapley para juegos con coaliciones difusas, identificadas con los puntos del cubo unidad N-dimensional. En los valores existentes en la literatura se usa poca información del juego para elaborar la solución, o bien los vértices del cubo o bien la diagonal. El valor propuesto mejora en el sentido de que utiliza más información de la disponible al usar todas las caras del cubo. Se da también una axiomatización del valor. Además se propone un modelo para elaborar soluciones que van usando cada vez más información.
A logistic type equation in Rᴺ with a nonlocal reaction term via bifurcation method
(Elsevier, 2021-01-01) Delgado Delgado, Manuel; Molina Becerra, Mónica; Suárez Fernández, Antonio; Universidad de Sevilla. Departamento de Matemática Aplicada II (ETSI); Universidad de Sevilla. Departamento de Ecuaciones Diferenciales y Análisis Numérico; European Commission (EC). Fondo Europeo de Desarrollo Regional (FEDER); Universidad de Sevilla. TIC130: Investigación en Sistemas Dinámicos en Ingeniería; Universidad de Sevilla. FQM131: Ecuaciones Diferenciales, Simulación Numérica y Desarrollo Software
We study the existence of positive solutions of a logistic equation in the entire space with a nonlocal reaction term. Mainly, we apply a bifurcation method and singular boundary equations to obtain a priori bounds of the solutions. Our results show a drastic change of behaviour of the set of positive solutions depending on the sign of the nonlocal term.
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.

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