Artículos (Matemática Aplicada II)

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

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Characterization of the hyperbolic step of parabolic functions
(2024-10-24) Contreras Márquez, Manuel Domingo; Cruz Zamorano, Francisco José; Rodríguez Piazza, Luis; Matemática Aplicada II (ETSI); Análisis Matemático; Ministerio de Ciencia e Innovación (MICIN). España; Junta de Andalucía; FQM133: Grupo de Investigación en Análisis Funcional; FQM104: Análisis Matemático
A classical problem in complex dynamics on hyperbolic domains is to characterize the hyperbolic step of parabolic functions. This topic has been studied by several authors, leading to different results and providing characterizations that depend on the behaviour of the iterates of such functions. In this work we provide new characterizations in terms of intrinsic properties of the functions.
Flow Methods for Cooperative Games with Generalized Coalition Configuration
(Springer, 2025) Algaba Durán, Encarnación; Rémila, Eric; Solal, Philippe; Matemática Aplicada II (ETSI); Ministerio de Ciencia e Innovación (MICIN). España
A cooperative game with a coalition structure is formed by a TU-game and a partition of the agent set. For this class of games, the Owen value is computed as a two-step procedure where the relevant coalitions are those formed by the union of some elements of the partition and a coalition of another element of the partition. In this paper, we consider a broader class of games where the partition is replaced by a collection of (not necessarily pairwise disjoint) coalitions over the agent set and where, in each element of this collection, cooperation among the agents is restricted. Agents then organize themselves into a profile of feasible coalitions. This class of games can be applied to several situations such as the problem of allocating aircraft landing fees in the presence of airlines and codeshare flights. We begin by defining and axiomatically characterizing the class of flow methods, which are marginal values whose coefficients induce a unit flow on the graph of feasible coalition profiles. We then define Owen-type values constructed from flow methods. We show that these values are flow methods whose flow is decomposable into two flows. Finally, we introduce two axioms from which we characterize the flows that can be decomposed in this way, and hence the flow methods constructed by our Owen-type procedure. The last part of the paper studies some special cases.
A new kind of T-point in the Lorenz system with a different bifurcation set
(Elsevier, 2025-10) Algaba Durán, Antonio; Fernández Sánchez, Fernando; Merlino Morlesín, Manuel; Rodríguez Luis, Alejandro José; Matemática Aplicada II (ETSI); Ministerio de Ciencia, Innovación y Universidades (MICIU). España; TIC130: Investigación en Sistemas Dinámicos en Ingeniería
In this work we find a new kind of T-point (or Bykov point) in the Lorenz system. At this codimension-two degeneracy, a heteroclinic cycle connects the origin (when it is a real saddle) and non-trivial equilibria (when they are saddle-focus). We observe that it presents a noteworthy geometric difference from the “classical” T-point, known since the 1980s in the Lorenz system. Because the dominant eigenvalue of the two-dimensional manifold at the origin changes, a variation in the direction of the corresponding heteroclinic orbit occurs near this equilibrium. Simultaneously, there is an important change in the bifurcation set, not previously found in the literature. While at the classical T-point the homoclinic and heteroclinic curves of non-trivial equilibria arise as half-lines in the same direction (as predicted by the well-known model of Glendinning and Sparrow), now these global bifurcation curves emerge in opposite directions. To justify this change we build a theoretical model with suitable Poincaré sections in a tubular environment of the heteroclinic cycle. Finally, by introducing a fourth parameter into the Lorenz system (a new quadratic term in its third equation), we show how the classical T-point can also lead to the new bifurcation set. This transition through a nongeneric situation (which occurs when the Jacobian matrix at the origin has a double eigenvalue) implies the existence of a codimension-three degenerate T-point. We find this bifurcation in the Lorenz-like system considered and illustrate how the bifurcation sets evolve by analyzing parallel parameter planes on both sides of the degeneracy.
Interface logistic problems: Large diffusion and singular perturbation results
(Elsevier, 2025-06) Álvarez Caudevilla, Pedro; Brändle, Cristina; Molina Becerra, Mónica; Suárez Fernández, Antonio; Matemática Aplicada II (ETSI); Ecuaciones Diferenciales y Análisis Numérico; Ministerio de Economía y Competitividad (MINECO). España; Ministerio de Ciencia, Innovación y Universidades (MICIU). España; TIC130: Investigación en Sistemas Dinámicos en Ingeniería; FQM131: Ecuaciones diferenciales, Simulación Num. y Desarrollo Software
In this work we consider an interface logistic problem where two populations live in two different regions, separated by a membrane or interface where it happens an interchange of flux. Thus, the two populations only interact or are coupled through such a membrane where we impose the so-called Kedem–Katchalsky boundary conditions. For this particular scenario we analyse the existence and uniqueness of positive solutions depending on the parameters involved in the system, obtaining interesting results where one can see for the first time the effect of the membrane under such boundary conditions. To do so, we first ascertain the asymptotic behaviour of several linear and nonlinear problems for which we include a diffusion coefficient and analyse the behaviour of the solutions when such a diffusion parameter goes to zero or infinity. Despite their own interest, since these asymptotic results have never been studied before, they will be crucial in analysing the existence and uniqueness for the main interface logistic problems under analysis. Finally, we apply such an asymptotic analysis to characterize the existence of solutions in terms of the growth rate of the populations, when both populations possess the same growth rate and, also, when they depend on different parameters.
Criteria for extension of commutativity to fractional iterates of holomorphic self-maps in the unit disc
(Wiley, 2025-02-17) Contreras Márquez, Manuel Domingo; Díaz Madrigal, Santiago; Gumenyuk, Pavel; Matemática Aplicada II (ETSI); Ministerio de Ciencia e Innovación (MICIN). España; FQM133: Grupo de Investigación en Análisis Funcional
Let 𝜑 be a univalent non-elliptic self-map of the unit disc 𝔻 and let (𝜓𝑡) be a continuous one-parameter semigroup of holomorphic functions in 𝔻 such that 𝜓1 ≠ 𝗂𝖽𝔻 commutes with 𝜑. This assumption does not imply that all elements of the semigroup (𝜓𝑡) commute with 𝜑. In this paper, we provide a number of sufficient conditions that guarantee that 𝜓𝑡 ◦𝜑 = 𝜑 ◦ 𝜓𝑡 for all 𝑡 > 0: This holds, for example, if 𝜑 and 𝜓1 have a common boundary (regular or irregular) fixed point different from their common Denjoy–Wolff point 𝜏, orwhen 𝜓1 has a boundary regular fixed point 𝜎 ≠ 𝜏 at which 𝜑 is isogonal, or when (𝜑 − 𝗂𝖽𝔻)∕(𝜓1 − 𝗂𝖽𝔻) has an unrestricted limit at 𝜏. In addition, we analyze how 𝜑 behaves in the petals of the semigroup (𝜓𝑡).
Optimal Bounds for POD Approximations of Infinite Horizon Control Problems Based on Time Derivatives
(Springer, 2025) De Frutos, Javier; García-Archilla, Bosco; Novo, Julia; 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.; Matemática Aplicada II (ETSI); Ministerio de Ciencia, Innovación y Universidades (MICIU). España; Junta de Andalucía; 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; Matemática Aplicada II (ETSI); Ministerio de Ciencia e Innovación (MICIN). España; European Union (UE); 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.; Matemática Aplicada I (ETSII); 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; Matemática Aplicada II (ETSI); 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; Matemática Aplicada II (ETSI); Ecuaciones Diferenciales y Análisis Numérico; TIC130: Investigación en Sistemas Dinámicos en Ingeniería; 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; 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; Matemática Aplicada II (ETSI); Ministerio de Ciencia, Innovación y Universidades (MICIU). España; 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; Matemática Aplicada II (ETSI); Ministerio de Ciencia, Innovación y Universidades (MICIU). España; Junta de Andalucía,; 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.; Ingeniería Aeroespacial y Mecánica de Fluidos; 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; Matemática Aplicada II (ETSI); Ministerio de Economía y Competitividad (MINECO). España; Junta de Andalucía; European Commission (EC). Fondo Europeo de Desarrollo Regional (FEDER); 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; Matemática Aplicada II (ETSI); Ministerio de Economia y Competitividad; Junta de Andalucía; European Commission (EC). Fondo Europeo de Desarrollo Regional (FEDER); FQM262: Teoría de la Aproximación; 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. ⃝
Fixed Points and Common Fixed Points for Orbit-Nonexpansive Mappings in Metric Spaces
(Springer, 2023-03-31) Espínola García, Rafael; Japón Pineda, María de los Ángeles; Souza, Daniel Parasio Sobreira de; Análisis Matemático; FQM127: Análisis Funcional no Lineal
In this paper, we introduce an interlacing condition on the elements of a family of operators that allows us to gather together a number of results on fixed points and common fixed points for single and families of mappings defined on metric spaces. The innovative concept studied here deals with nonexpansivity conditions with respect to orbits and under assumptions that only depend on the features of the closed balls of the metric space.
Time-and-band limiting for matrix orthogonal polynomials of Jacobi type
(World Scientific Publishing, 2017-10) Castro Smirnova, Mirta María; Grünbaum, Francisco Alberto; 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; 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; 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).

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