Estatística, Análise Matemática e Optimización

Permanent URI for this collectionhttps://hdl.handle.net/10347/34390

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Numerical reconstruction of the kernel function in generalized non-convolutional fractional operators
(Elsevier, 2026-05-15) Al-Shdaifat, Hamza; Rodríguez López, Rosana
This paper deals with the numerical reconstruction of the kernel function 𝜅(𝑡,𝑧) for a new class of generalized non-convolutional fractional operators. These operators are defined in integral form of Volterra type and the general kernel is not always reducible to classical convolutiontype expressions. The work focuses on the reconstruction of the kernel starting from the generalized Sonin condition, which connects the kernel of the integral operator with that of the corresponding differential operator. Taking the generalized Sonin condition as the starting point, we propose a constructive numerical method by approximating the functional identity obtained from the integration of the product of both kernels, operation that is achieved by proper integration on segment lines of the domain. By casting the theoretical requirements as one-dimensional integral estimations on parameterized trajectories (segment lines), the problem becomes a nonlinear inverse problem for the determination of one of the kernels, 𝜅, provided that the other one is known. Our approach is based on the selection of a proper partition of the domain, and the consideration of the auxiliary functions 𝜑𝑡,𝑧 and 𝜙𝑡,𝑧, which are combined in such a way that it is possible to compute the unknown functions 𝜓𝑡,𝑧 and 𝛹𝑡,𝑧, provided that the given restrictions on the integrals in the generalized Sonin condition are fulfilled. The feasibility of reconstructing the kernel in some chosen test examples is illustrated by some numerical procedures, as a first step toward the implementation of generalized fractional models in numerical simulations, and also as a tool for the selection of proper kernels in the definition of generalized fractional operators.
Effect of fear and refuge in eco-epidemiological model with predator supported by additional food
(Springer, 2026-02-24) Kar, Raktim; Biswas, Santosh; Pal, Amit Kumar; Nieto Roig, Juan José; Universidade de Santiago de Compostela. Departamento de Estatística, Análise Matemática e Optimización
We propose a three-compartment eco-epidemiological model in which prey experience fear from susceptible predators and may seek refuge, predator follows a modified Leslie–Gower growth. The predator population is divided into susceptible and infected class, with disease transmission occurring horizontally together with saturated treatment of infected class. We analyze positivity and boundedness, compute biologically feasible equilibria, and derive the basic reproduction number (R0) along with conditions for local and global stability. Sensitivity is explored by partial rank correlation coefficient (PRCC) method; bifurcation behaviours are illustrated analytically and numerically. Furthermore, we formulate and numerically solve an optimal control problem aimed at minimizing infected predator biomass and treatment cost using the forward–backward sweep method. The results reveal that larger refuge size and stronger treatment efforts effectively reduce infection prevalence, while fear on prey species control by the refuge. Additionally, the system exhibits parameter-dependent bi-stability and multi-stability, as demonstrated through bifurcation diagrams.
Un proyecto para mejorar la visualización espacial a través de las TIC
(Dykinson, 2024) Diz Pita, Erika; Castiñeira Veiga, Gonzalo; Universidade de Santiago de Compostela. Departamento de Didácticas Aplicadas; Universidade de Santiago de Compostela. Departamento de Estatística, Análise Matemática e Optimización
El aprendizaje de la geometría suele resultar especialmente difícil para el alumnado debido, sobre todo, al alto nivel de abstracción y a problemas de visualización y comprensión de relaciones espaciales. Estas dificultades se agravan cuando no se incorporan recursos manipulativos y tecnológicos que permitan representar y explorar figuras, especialmente en 3D. En este contexto, el currículo actual refuerza la necesidad de integrar las TIC en la enseñanza de matemáticas. Por ello, el capítulo presenta una propuesta didáctica para 2º de ESO que combina TIC y materiales manipulativos con el fin de facilitar la comprensión geométrica y mejorar la motivación y la percepción del alumnado hacia las matemáticas. Finalmente, se plantea evaluar el impacto de la propuesta en la afectividad mediante cuestionarios, dado que una actitud más positiva se asocia con mejores resultados académicos.
Semiparametric regression for circular responsewith application in ecology
(Wiley, 2025) Ameijeiras Alonso, José; Gijbels, Irène
A regression model for a circular response variabledepending on a linear or a circular predictor is pre-sented in this paper. The conditional density belongsto a parametric flexible family that allows for asymme-try and varying peakedness around the modal direction.The modal direction and concentration depend on thecovariate and are nonparametrically modeled via localpolynomial fitting with a kernel weight. The asymp-totic normality of the estimators for the conditionalmodal direction and concentration is established. Fur-thermore, from these theoretical results, the expressionof the optimal smoothing parameter and a proposeddata-driven estimator are derived. An application con-cerns the orientation of migratory birds according to theflight altitude and the wind direction.
The Peano–Sard theorem for fractional operators with Mittag-Leffler kernel and application in classical numerical approximation
(Elsevier, 2025-03-15) Jornet, Marc; Nieto Roig, Juan José; Universidade de Santiago de Compostela. Departamento de Estatística, Análise Matemática e Optimización
We investigate fractional Peano kernels for continuous linear functionals, in the context of differintegral operators with Mittag-Leffler kernel. New bounds for polynomial interpolation are obtained and numerical computations are shown, indicating improvements.
A goodness-of-fit test for functional time series with applications to Ornstein-Uhlenbeck processes
(Elsevier, 2024) Álvarez-Liébana, Javier; López Pérez, Alejandra; González Manteiga, Wenceslao; Febrero Bande, Manuel; Universidade de Santiago de Compostela. Departamento de Estatística, Análise Matemática e Optimización
High-frequency financial data can be collected as a sequence of time-ordered curves, such as intraday prices. The Functional Data Analysis (FDA) framework offers a powerful approach to uncover information embedded in the shape of the daily paths, often unavailable from classical statistical methods. A novel goodness-of-fit test for autoregressive Hilbertian (ARH) models is introduced, imposing only the Hilbert-Schmidt condition on the autocorrelation operator. The test statistic is formulated in terms of a Cramér–von Mises norm, with calibration achieved via a wild bootstrap resampling procedure. A simulation study examines the test's finite-sample performance in terms of power and size. Furthermore, a new specification test for diffusion models, including Ornstein-Uhlenbeck processes, is proposed, illustrated with an application to intraday currency exchange rates. Specifically, a two-stage methodology is proffered: firstly, the relationship between functional samples and their lagged values is assessed using an ARH(1) model; second, under linearity, a functional F-test is conducted.
Representation and inequalities involving continuous linear functionals and fractional derivatives
(Springer, 2024-10-29) Jornet, Marc; Nieto Roig, Juan José; Universidade de Santiago de Compostela. Departamento de Estatística, Análise Matemática e Optimización
We investigate how continuous linear functionals can be represented in terms of generic operators and certain kernels (Peano kernels), and we study lower bounds for the operators as a consequence, in the space of square-integrable functions. We apply and develop the theory for the Riemann–Liouville fractional derivative (an inverse of the Riemann–Liouville integral), where inequalities are derived with the Gaussian hypergeometric function. This work is inspired by the recent contributions by Fernandez and Buranay (J Comput Appl Math 441:115705, 2024) and Jornet (Arch Math, 2024).
Displacement Lipschitz Spaces and Rectifiability
(Springer, 2024-12-13) Fernández Tojo, Fernando Adrián; Universidade de Santiago de Compostela. Departamento de Estatística, Análise Matemática e Optimización
In this article, we introduce the notion of displacement Lipschitz spaces based on a divided difference approach. After studying rectifiability and arc length in displacement spaces, we apply Lipschitz functions to the study of convexity by measuring the allowed curvature of paths.
Influence of Abutment Shape on Implant Marginal Bone Remodeling: A Double-Blind, Randomized 24-Month Clinical Study
(Wiley, 2025-12-30) Seijas Naya, Flavio; Bernabeu Mira, Juan C.; Pérez Jardón, Alba; Conde Amboage, Mercedes; Peñarrocha Oltra, David; Camacho Alonso, Fabio; Pérez-Sayáns García, Mario; Universidade de Santiago de Compostela. Departamento de Estatística, Análise Matemática e Optimización; Universidade de Santiago de Compostela. Instituto de Materiais (iMATUS); Universidade de Santiago de Compostela. Departamento de Cirurxía e Especialidades Médico-Cirúrxicas
Objective This study follows a 2-year evaluation to verify marginal bone remodeling (MBR) trends associated with different abutment designs. Methods A balanced, randomised, double-blind clinical trial with two parallel experimental arms. 68 implants were placed in 9 men and 12 women, 48.5% using the straight abutment and 51.5% the concave abutment. The primary variable was peri-implant tissue stability, measured by marginal bone loss (MBL) or gain (MBG) through digital radiology. Mixed linear regression models and Additive Generalized Additive Models were constructed to estimate MBR, simultaneously considering the variables abutment height, group, and time. Results At 24 months, linear mixed-effects regression models revealed that the concave abutment group exhibited significantly less MBL than the straight abutment group across mesial, distal, and average measurements (p = 0.006–0.026). Significant interactions between abutment type and time at 8 weeks and 6 months suggest early and sustained benefits of the concave design. At 24 months, this effect remained significant except in the mesial model (p = 0.072). Abutment height was positively associated with MBL, particularly in the straight group; however, in the concave group, greater height mitigated bone loss (p < 0.01). Conclusion Concave abutments demonstrated a potential advantage in reducing early marginal bone loss and promoting mid-term bone stability compared to straight abutments. Their design may enhance soft tissue adaptation, contributing to improved peri-implant bone preservation. While increased abutment height showed a protective effect in the concave group, these findings require confirmation. Further long-term studies are warranted to validate these results and clarify their clinical relevance.
On the connection between Stieltjes differential equations and ordinary differential equations
(Elsevier, 2025-06-01) Fernández Tojo, Fernando Adrián; Universidade de Santiago de Compostela. Departamento de Estatística, Análise Matemática e Optimización
In this work, we establish a link between Stieltjes differential equations and ordinary differential equations, allowing for the transformation of one into the other. As applications, we prove Binding's theorem for the equation xg′=f∘x, as well as a topological result used in the theory of differential equations.
Bootstrap in functional linear regression
(Elsevier, 2010-07-01) González Manteiga, Wenceslao; Martínez Calvo, Adela; Universidade de Santiago de Compostela. Departamento de Estatística e Investigación Operativa; Universidade de Santiago de Compostela. Facultade de Matemáticas
We have considered the functional linear model with scalar response and functional explanatory variable. One of the most popular methodologies for estimating the model parameter is based on functional principal components analysis (FPCA). In recent literature, weak convergence for a wide class of FPCA-type estimates has been proved, and consequently asymptotic confidence sets can be built. In this paper, we have proposed an alternative approach in order to obtain pointwise confidence intervals by means of a bootstrap procedure, for which we have obtained its asymptotic validity. Besides, a simulation study allows us to compare the practical behaviour of asymptotic and bootstrap confidence intervals in terms of coverage rates for different sample sizes.
Solutions of the first order linear equation with reflection and general linear conditions
(IFNA Publishers, Inc., 2013) Cabada Fernández, Alberto; Fernández Tojo, Fernando Adrián; Universidade de Santiago de Compostela. Departamento de Estatística, Análise Matemática e Optimización
This work is devoted to the study of first order linear problems with involution and general linear conditions. We first study the problem in the case of antiperiodic boundary conditions, giving an explicit Green's function for it. Then we move forward to more general linear boundary conditions, focusing on sufficient conditions for existence and uniqueness of solution. At the end of the paper we give estimates that ensure the positivity of the solution in the general problems and illustrate these applications with examples
The system of Kaup equations with a self-consistent source in the class of periodic functions
(National Academy of Sciences of Ukraine, B.Verkin Institute for Low Temperature Physics and Engineering, 2013) Cabada Fernández, Alberto; Yakhshimuratov, Alisher; Universidade de Santiago de Compostela. Departamento de Estatística, Análise Matemática e Optimización
In the paper, a method of the inverse spectral problem is used to integrate the system of Kaup equations with a self-consistent source in the class of periodic functions
New criteria for the existence of non-trivial fixed points in cones
(Springer, 2013-05-13) Cabada Fernández, Alberto; Cid Araújo, José Ángel; Infante, Gennaro; Universidade de Santiago de Compostela. Departamento de Estatística, Análise Matemática e Optimización
We give new criteria for the existence of nontrivial fixed points on cones assuming some monotonicity of the operator on a suitable conical shell. Moreover, we give an application to the existence of multiple solutions for a nonlocal boundary value problem that models the displacement of a beam subject to some feedback controllers
Multiplicity of solutions of a two point boundary value problem for a fourth-order equation
(Elsevier, 2013-01-15) Cabada Fernández, Alberto; Tersian, Stepan; Universidade de Santiago de Compostela. Departamento de Estatística, Análise Matemática e Optimización
We study the existence of multiple solutions for semi linear fourth-order differential equation describing elastic deflections. The proof of the main result is based on a three critical point theorem
Existence and multiplicity of solutions to boundary value problems for fourth-order impulsive differential equations
(Springer, 2014-05-08) Cabada Fernández, Alberto; Tersian, Stepan; Universidade de Santiago de Compostela. Departamento de Estatística, Análise Matemática e Optimización
In this paper we study the existence and the multiplicity of solutions for an impulsive boundary value problem for fourth-order differential equations. The notions of classical and weak solutions are introduced. Then the existence of at least one and infinitely many nonzero solutions is proved, using the minimization, the mountain-pass, and Clarke’s theorems
An integral boundary value problem for nonlinear differential equations of fractional order on an unbounded domain
(Rocky Mountain Mathematics Consortium, 2014) Wang, Guotao; Cabada Fernández, Alberto; Zhang, Lihong; Universidade de Santiago de Compostela. Departamento de Estatística, Análise Matemática e Optimización
This paper investigates the existence of solutions for nonlinear fractional diﬀerential equations with integral boundary conditions on an unbounded domain. An example illustrating how the theory can be applied in practice is also included
Existence results for a linear equation with reflection, non-constant coefficient and periodic boundary conditions
(Elsevier, 2014-04-01) Cabada Fernández, Alberto; Fernández Tojo, Fernando Adrián; Universidade de Santiago de Compostela. Departamento de Estatística, Análise Matemática e Optimización
This work is devoted to the study of first order linear problems with involution and periodic boundary value conditions. We first prove a correspondence between a large set of such problems with different involutions to later focus our attention to the case of the reflection. We study then different cases for which a Greenʼs function can be obtained explicitly and derive several results in order to obtain information about its sign. Once the sign is known, maximum and anti-maximum principles follow. We end this work with more general existence and uniqueness of solution results
A generalization of an extensible beam equation with critical growth in RN
(Elsevier, 2014-12) Cabada Fernández, Alberto; Figueiredo, Giovany M.; Universidade de Santiago de Compostela. Departamento de Estatística, Análise Matemática e Optimización
In this work we obtain an existence result for a generalized extensible beam equation with critical growth in $\mathbb{R}^{N}$ of the type $$\Delta^{2}u-M\biggl(\dis\int_{\mathbb{R}^{N}}|\nabla u|^{2} \ dx\ \biggl)\Delta u +u = \lambda f(u)+ |u|^{2^{**}-2}u \ \mbox{in} \ \ \mathbb{R}^{N}, $$ where $N\geq 5$ and $\lambda>0$. The functions $M:[0,+\infty)\rightarrow \mathbb{R}$ and $f:\mathbb{R}\rightarrow \mathbb{R}$ are continuous. Since there is a competition between the function $M$ and the critical exponent given by $2^{**}=\frac{2N}{N-4}$, we need to make a truncation on function $M$. Using the size of $\lambda$, we show that each solution of auxiliary problem is a solution of original problem. Our approach is variational and uses minimax point critical theorems
Existence of homoclinic constant sign solutions for a difference equation on the integers
(Elsevier, 2013-11-01) Cabada Fernández, Alberto; Iannizzotto, Antonio; Universidade de Santiago de Compostela. Departamento de Estatística, Análise Matemática e Optimización
We consider a difference equation involving the discrete $p$-Laplacian operator, depending on a positive real parameter $\lambda$. We prove, under convenient assumptions, that for $\lambda$ big enough the equations admits at least one homoclinic constant sign solution in $\Z$. Our method consists in two parts: first, we prove the existence of two Dirichlet-type solutions for the equation in the discrete interval $[-n,n]$, for all $n\in\N$ big enough; then, we show that such solutions converge to a homoclinic solution in $\Z$, as $n\to\infty$

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