Instituto de Matemáticas

Permanent URI for this collectionhttps://hdl.handle.net/10347/34303

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Some Classes of Nilpotent Associative Algebras
(Springer, 2020-02-29) Karimjanov, Iqboljon A.; Ladra González, Manuel; Universidade de Santiago de Compostela. Departamento de Matemáticas
In this paper we classify filiform associative algebras of degree k over a field of characteristic zero. Moreover, we also classify naturally graded complex filiform and quasi-filiform nilpotent associative algebras which are described by the characteristic sequence C(A) = (n − 2, 1, 1) or C(A) = (n − 2, 2).
HNN-Extension of Lie Superalgebras
(Springer, 2020-06-03) Ladra González, Manuel; Páez Guillán, María Pilar; Zargeh, Chia; Universidade de Santiago de Compostela. Departamento de Matemáticas
We construct HNN-extensions of Lie superalgebras and prove that every Lie superalgebra embeds into any of its HNN-extensions. Then as an application we show that any Lie superalgebra with at most countable dimension embeds into a two-generator Lie superalgebra.
Rota-type operators on null-filiform associative algebras
(Taylor & Francis, 2020-01-26) Karimjanov, Iqboljon; Kaygorodov, Ivan; Ladra González, Manuel; Universidade de Santiago de Compostela. Departamento de Matemáticas
We give the description of homogeneous Rota–Baxter operators, Reynolds operators, Nijenhuis operators, Average operators and differential operator of weight 1 of null-filiform associative algebras of arbitrary dimension.
Transversality conditions for the existence of solutions of first–order discontinuous functional differential equations
(Juliusz Schauder University Center for Nonlinear Studies, 2021) López Pouso, Rodrigo; Márquez Albés, Ignacio; Rodríguez López, Jorge; Universidade de Santiago de Compostela. Departamento de Estatística, Análise Matemática e Optimización
We are concerned with the existence of extremal solutions to a large class of first–order functional differential problems under weak regularity assumptions. Our technique involves multivalued analysis and the method of lower and upper solutions in order to obtain a new existence result to a scalar Cauchy problem. As a consequence of this result and a monotone iterative method for discontinuous operators, we derive our main existence result which is illustrated by several examples concerning well–known models: a generalized logistic equation or second–order problems in the presence of dry friction.
Positive homoclinic solutions of n-th order difference equations with sign-changing Green's function
(Wiley, 2018-04-16) Cabada Fernández, Alberto; Dimitrov, Nikolay; Universidade de Santiago de Compostela. Departamento de Análise Matemática
In this paper we, consider an n-th order nonlinear difference equation with parameter dependence. An exhaustive study of the related Green's function is done. The exact expression of the function is given. The range of parameter for which either it has constant sign or it changes sign is obtained. Some existence results for the nonlinear problem are deduced by using the classical Krasnosel'skii's fixed point theorem on cones and fixed point index theory.
Existence of solutions for nth-order nonlinear differential boundary value problems by means of fixed point theorems
(Elsevier, 2018-08) Cabada Fernández, Alberto; Saavedra López, Lorena; Universidade de Santiago de Compostela. Departamento de Análise Matemática
This paper is devoted to prove the existence of one or multiple solutions of a wide range of nonlinear differential boundary value problems. To this end, we obtain some new fixed point theorems for a class of integral operators. We follow the well-known Krasnoselskiĭ’s fixed point Theorem together with two fixed point results of Leggett–Williams type. After obtaining a general existence result for a one parameter family of nonlinear differential equations, are proved, as particular cases, existence results for second and fourth order nonlinear boundary value problems.
Existence of solutions of integral equations with asymptotic conditions
(Elsevier, 2018-08) Cabada Fernández, Alberto; López Somoza, Lucía; Fernández Tojo, Fernando Adrián; Universidade de Santiago de Compostela. Departamento de Análise Matemática
In this work we will consider integral equations defined on the whole real line and look for solutions which satisfy some certain kind of asymptotic behavior. To do that, we will define a suitable Banach space which, to the best of our knowledge, has never been used before. In order to obtain fixed points of the integral operator, we will consider the fixed point index theory and apply it to this new Banach space.
Positive Solutions of a Discontinuous One-Dimensional Beam Equation
(Springer, 2021) Rodríguez López, Jorge; Universidade de Santiago de Compostela. Departamento de Estatística, Análise Matemática e Optimización
We provide sufficient conditions for the existence of one positive solution for a fourth-order beam equation with a discontinuous nonlinear term. Also a multiplicity result is established. They are based on a recent generalization of the Krasnosel’skiĭ fixed point theorem in cones.
Existence and uniqueness of solutions for systems of discontinuous differential equations under localized Bressan-Shen transversality conditions
(Elsevier, 2020) López Pouso, Rodrigo; Rodríguez López, Jorge
We present new results on existence and uniqueness of absolutely continuous solutions for systems of discontinuous ordinary differential equations. Our existence result complements an earlier theorem by Bressan and Shen. Basically, we show that a global transversality condition assumed by Bressan and Shen need only be imposed on the sets where the nonlinear part is discontinuous. Our proof, completely different to the one given by Bressan and Shen, uses Krasovskij solutions as a first step. We illustrate the applicability of our result with several examples not covered by the previous literature. The second part of this paper concerns uniqueness. Specifically, we prove uniqueness of solutions for discontinuous systems of differential equations with piecewise Lipschitz continuous nonlinearities and assuming localized Bressan–Shen transversality conditions on the boundaries between different Lipschitz continuity domains. Our uniqueness result appears to be new even in the classical case of continuous nonlinearities.
Fixed point index theory for decomposable multivalued maps and applications to discontinuous ϕ-Laplacian problems
(Elsevier, 2020) Precup, Radu; Rodríguez López, Jorge; Universidade de Santiago de Compostela. Departamento de Estatística, Análise Matemática e Optimización
In this paper, we develop a fixed point index theory for decomposable multivalued maps, that is, compositions of two multivalued nonlinear upper semicontinuous maps. As an application, this fixed point index theory is combined with the method of lower and upper solutions in order to obtain new existence, localization and multiplicity results for ϕ-Laplacian problems with discontinuous nonlinearities and nonlinear functional boundary conditions.
Multiplicity Results for Operator Systems via Fixed Point Index
(Springer, 2019) Precup, Radu; Rodríguez López, Jorge; Universidade de Santiago de Compostela. Departamento de Estatística, Análise Matemática e Optimización
We establish existence, localization and multiplicity results of positive solutions for general operator systems in ordered Banach spaces. Our main tool is the fixed point index in cones which we compute in suitable relatively open sets. In this context, each component of the fixed point operator can satisfy either the expansion condition or the compression condition. If some component of the operator is expansive, then we obtain multiplicity results. As an application, new results concerning systems of Hammerstein equations and systems of -Laplace equations are deduced.
Positive solutions for discontinuous problems with applications to φ-Laplacian equations
(Springer, 2018) Precup, Radu; Rodríguez López, Jorge; Universidade de Santiago de Compostela. Departamento de Estatística, Análise Matemática e Optimización
We establish existence and localization of positive solutions for general discontinuous problems for which a Harnack-type inequality holds. In this way, a wide range of ordinary differential problems such as higher order boundary value problems or -Laplacian equations can be treated. In particular, we study the Dirichlet–Neumann problem involving the -Laplacian. Our results rely on Bohnenblust–Karlin fixed point theorem which is applied to a multivalued operator defined in a product space.
Índices de pobreza en Galicia
(Instituto de Matemáticas. Universidade de Santiago de Compostela, 2011) Ginzo Villamayor, María José; Universidade de Santiago de Compostela. Departamento de Estatística, Análise Matemática e Optimización
En este estudio se analiza el perfil de la pobreza de la población gallega. Se han utilizado los microdatos de la “Encuesta de Condiciones de Vida”(ECV) del Instituto Gallego de Estadística (IGE), año 2006. La ECV es una encuesta dirigida a los hogares gallegos cuyo objetivo es obtener información sobre sus características socioeconómicas. Se estiman índices de la familia Foster, Greer y Thorbecke, (véase en Foster, Greer and Thorbecke (1984)). Para analizar la pobreza, se utilizó la inferencia estadística para estimar los niveles de pobreza de cada provincia y de Galicia en su conjunto. Concretamente, se determinaron los intervalos de confianza (IC) para distintos indicadores usando inferencia clásica basada en distribuciones asintóticas y metodología Bootstrap. Se obtiene un mapa de la distribución provincial de la pobreza en Galicia y compara la precisión de las técnicas.
Modelización onomástica
(Instituto de Matemáticas. Universidade de Santiago de Compostela, 2016) Ginzo Villamayor, María José; Universidade de Santiago de Compostela. Departamento de Estatística e Investigación Operativa
Os apelidos poden ser utilizados como unha fonte de información para caracterizar a poboación dunha rexión, dado que a an´alise dos patróns que se observan na distribución dos apelidos reflicte aspectos importantes dos movementos poboacionais. As investigacións desenvolvidas no contexto de estudo, ata a data, non teñen en conta a dimensión espacial e espazo–temporal da evolución dos apelidos; por iso, este traballo céntrase na introdución de métodos estatísticos para o procesamento de datos e o modelado en xeolinguística, especificamente, nos apelidos de Galicia.
Numerical simulation of the transient heat transfer in a blast furnace main trough during its complete campaign cycle
(Elsevier, 2022) Barral Rodiño, Patricia; Pérez Pérez, Luis Javier; Quintela Estévez, Peregrina; Universidade de Santiago de Compostela. Departamento de Matemática Aplicada; Universidade de Santiago de Compostela. Instituto de Matemáticas
To achieve higher blast furnace (BF) main trough availability and to minimize the frequency of reparations is a key concern in the steelmaking industry. For this purpose, strategies to assess refractory wear are required, which is heavily influenced by the temperature in the refractory linings. In this work, a mathematical model to assess the transient behaviour of the temperature in a cross-section of a BF main trough during a complete campaign is presented. The scope is to investigate the effect that the casting stops have on the temperature in the trough. A sequence of problems corresponding to each BF tapping and the subsequent stop is determined using process data of a BF. The open-source finite element computing platform FEniCS is employed to solve the model. The discretization and the numerical algorithm have been presented and validated with a manufactured solution test in a previous work. The numerical results show that the effect of the stops during these campaign cycles is non-negligible, preventing the bulk of the solid layers from reaching a steady state. Qualitative agreement with temperature measurements obtained with thermocouples embedded in the trough is observed. Since there is a significant degree of uncertainty concerning the placement of the devices, a minimization problem to adjust their positions within the corresponding feasible regions is proposed. At the identified positions, good levels of fit between the measured and the computed temperatures are achieved. The agreement decreases towards the end of the campaign cycle, being suggestive of severe refractory wear, especially at the laterals of the trough
A numerical approach for heat flux estimation in thin slabs continuous casting molds using data assimilation
(Wiley, 2021) Stabile, Giovanni; Morelli, Umberto Emil; Barral Rodiño, Patricia; Quintela Estévez, Peregrina; Rozza, Gianluigi; Stabile, Giovanni; Universidade de Santiago de Compostela. Departamento de Matemática Aplicada; Universidade de Santiago de Compostela. Instituto de Matemáticas
In the present work, we consider the industrial problem of estimating in real-time the mold-steel heat flux in continuous casting mold. We approach this problem by first considering the mold modeling problem (direct problem). Then, we plant the heat flux estimation problem as the inverse problem of estimating a Neumann boundary condition having as data pointwise temperature measurements in the interior of the mold domain. We also consider the case of having a total heat flux measurement together with the temperature measurements. We develop two methodologies for solving this inverse problem. The first one is the traditional Alifanov's regularization, the second one exploits the parameterization of the heat flux. We develop the latter method to have an offline–online decomposition with a computationally efficient online part to be performed in real-time. In the last part of this work, we test these methods on academic and industrial benchmarks. The results show that the parameterization method outclasses Alifanov's regularization both in performance and computational cost. Moreover, it proves to be robust with respect to the measurements noise. Finally, the tests confirm that the computational cost is suitable for real-time estimation of the heat flux
One Year of the COVID-19 Pandemic in Galicia: A Global View of Age-Group Statistics during Three Waves
(MDPI, 2021) Area Carracedo, Iván Carlos; Lorenzo, Henrique; Marcos, Pedro J; Nieto Roig, Juan José; Universidade de Santiago de Compostela. Departamento de Estatística, Análise Matemática e Optimización; Universidade de Santiago de Compostela. Instituto de Matemáticas
In this work we look at the past in order to analyze four key variables after one year of the COVID-19 pandemic in Galicia (NW Spain): new infected, hospital admissions, intensive care unit admissions and deceased. The analysis is presented by age group, comparing at each stage the percentage of the corresponding group with its representation in the society. The time period analyzed covers 1 March 2020 to 1 April 2021, and includes the influence of the B.1.1.7 lineage of COVID-19 which in April 2021 was behind 90% of new cases in Galicia. It is numerically shown how the pandemic affects the age groups 80+, 70+ and 60+, and therefore we give information about how the vaccination process could be scheduled and hints at why the pandemic had different effects in different territories
Optimal control of the COVID-19 pandemic: controlled sanitary deconfinement in Portugal
(Springer Nature, 2021) Silva, Cristiana; Cruz, Carla; Torres, Delfim F. M.; Pérez Muñuzuri, Alberto; Carballosa Calleja, Alejandro; Area Carracedo, Iván Carlos; Nieto Roig, Juan José; Fonseca-Pinto, Rui; Passadouro da Fonseca, Rui; Soares dos Santos, Estevão; Abreu, Wilson; Mira Pérez, Jorge; Universidade de Santiago de Compostela. Departamento de Física Aplicada; Universidade de Santiago de Compostela. Departamento de Física de Partículas; Universidade de Santiago de Compostela. Instituto Interdisciplinar de Tecnoloxías Ambientais (CRETUS); Universidade de Santiago de Compostela. Departamento de Estatística, Análise Matemática e Optimización; Universidade de Santiago de Compostela. Instituto de Matemáticas
The COVID-19 pandemic has forced policy makers to decree urgent confinements to stop a rapid and massive contagion. However, after that stage, societies are being forced to find an equilibrium between the need to reduce contagion rates and the need to reopen their economies. The experience hitherto lived has provided data on the evolution of the pandemic, in particular the population dynamics as a result of the public health measures enacted. This allows the formulation of forecasting mathematical models to anticipate the consequences of political decisions. Here we propose a model to do so and apply it to the case of Portugal. With a mathematical deterministic model, described by a system of ordinary differential equations, we fit the real evolution of COVID-19 in this country. After identification of the population readiness to follow social restrictions, by analyzing the social media, we incorporate this effect in a version of the model that allow us to check different scenarios. This is realized by considering a Monte Carlo discrete version of the previous model coupled via a complex network. Then, we apply optimal control theory to maximize the number of people returning to “normal life” and minimizing the number of active infected individuals with minimal economical costs while warranting a low level of hospitalizations. This work allows testing various scenarios of pandemic management (closure of sectors of the economy, partial/total compliance with protection measures by citizens, number of beds in intensive care units, etc.), ensuring the responsiveness of the health system, thus being a public health decision support tool
First order differential systems with a nonlinear boundary condition via the method of solution-regions
(Springer Nature, 2021) Frigon, Marlène; Tella Álvarez, Marcos; Fernández Tojo, Fernando Adrián; Universidade de Santiago de Compostela. Departamento de Estatística, Análise Matemática e Optimización
In this article we extend the known theory of solution regions to encompass nonlinear boundary conditions. We both provide results for new boundary conditions and recover some known results for the linear case
Resolution methods for mathematical models based on differential equations with Stieltjes derivates
(University of Szeged, 2019) López Pouso, Rodrigo; Márquez Albés, Ignacio; Universidade de Santiago de Compostela. Departamento de Estatística, Análise Matemática e Optimización; Universidade de Santiago de Compostela. Instituto de Matemáticas
Stieltjes differential equations, i.e. differential equations with usual derivatives replaced by derivatives with respect to given functions (derivators), are useful to model processes which exhibit dead times and/or sudden changes. These advantages of Stieltjes equations are exploited in this paper in the analysis of two real life models: first, the frictionless motion of a vehicle equipped with an electric engine and, second, the evolution of populations of cyanobacteria Spirullina plantensis in semicontinuous cultivation processes. Furthermore, this is not only a paper on applications of known results. For the adequate analysis of our mathematical models we first deduce the solution formula for Stieltjes equations with separate variables. Finally, we show that differential equations with Stieltjes derivatives reduce to ODEs when the derivator is continuous, thus obtaining another resolution method for more general cases.

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