Matemática Aplicada I

URI permanente para esta comunidadhttps://hdl.handle.net/11441/10893

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0/1-Polytopes related to Latin squares autotopisms
(2008) Falcón Ganfornina, Raúl Manuel; Universidad de Sevilla. Departamento de Matemática Aplicada I (ETSII)
The set LS(n) of Latin squares of order n can be represented in Rn3 as a (n−1)3-dimensional 0/1-polytope. Given an autotopism Θ=(α,β,γ)∈An, we study in this paper the 0/1-polytope related to the subset of LS(n) having Θ in their autotopism group. Specifically, we prove that this polyhedral structure is generated by a polytope in R((nα−l1α)⋅n2+l1α⋅nβ⋅n)(l1α⋅l1β⋅(n−l1γ)+l1α⋅l1γ⋅(nβ−l1β)+l1β⋅l1γ⋅(nα−l1α)), where nα and nβ are the number of cycles of α and β, respectively, and l1δ is the number of fixed points of δ, for all δ∈{α,β,γ}. Moreover, we study the dimension of these two polytopes for Latin squares of order up to 9.
2D granular flows with the μ(I) rheology and side walls friction: A well-balanced multilayer discretization
(Elsevier Inc., 2018-03) Fernández Nieto, Enrique Domingo; Garres-Díaz, José; Mangeney, Anne; Narbona Reina, Gladys; Universidad de Sevilla. Departamento de Matemática Aplicada I (ETSII)
We present here numerical modelling of granular flows with the rheology in confined channels. The contribution is twofold: (i) a model to approximate the Navier–Stokes equations with the rheology through an asymptotic analysis; under the hypothesis of a one-dimensional flow, this model takes into account side walls friction; (ii) a multilayer discretization following Fernández-Nieto et al. (2016) [20]. In this new numerical scheme, we propose an appropriate treatment of the rheological terms through a hydrostatic reconstruction which allows this scheme to be well-balanced and therefore to deal with dry areas. Based on academic tests, we first evaluate the influence of the width of the channel on the normal profiles of the downslope velocity thanks to the multilayer approach that is intrinsically able to describe changes from Bagnold to S-shaped (and vice versa) velocity profiles. We also check the well-balanced property of the proposed numerical scheme. We show that approximating side walls friction using single-layer models may lead to strong errors. Secondly, we compare the numerical results with experimental data on granular collapses. We show that the proposed scheme allows us to qualitatively reproduce the deposit in the case of a rigid bed (i.e. dry area) and that the error made by replacing the dry area by a small layer of material may be large if this layer is not thin enough. The proposed model is also able to reproduce the time evolution of the free surface and of the flow/no-flow interface. In addition, it reproduces the effect of erosion for granular flows over initially static material lying on the bed. This is possible when using a variable friction coefficient but not with a constant friction coefficient.
3-color Schur numbers
(Elsevier, 2019) Boza Prieto, Luis; Marín Sánchez, Juan Manuel; Revuelta Marchena, María Pastora; Sanz Domínguez, María Isabel; Universidad de Sevilla. Departamento de Matemática Aplicada I (ETSII); Universidad de Sevilla. FQM-164: Matemática Discreta: Teoría de Grafos y Geometría Computacional
Let k ≥ 3 be an integer, the Schur number Sk(3) is the least positive integer, such that for every 3-coloring of the integer interval [1, Sk(3)] there exists a monochromatic solution to the equation x1+ · · · + xk= xk+1, where xi , i = 1, . . . , k need not be distinct. In 1966, a lower bound of Sk(3) was established by Znám (1966). In this paper, we determine the exact formula of Sk(3) = k 3 + 2k 2 − 2, finding an upper bound which coincides with the lower bound given by Znám (1966). This is shown in two different ways: in the first instance, by the exhaustive development of all possible cases and in the second instance translating the problem into a Boolean satisfiability problem, which can be handled by a SAT solver.
3-filiform Leibniz algebras of maximum length
(Springer, 2016) Camacho Santana, Luisa María; Cañete Molero, Elisa María; Gómez Martín, José Ramón; Omirov, Bakhrom Abdazovich; Universidad de Sevilla. Departamento de Matemática Aplicada I (ETSII)
This work completes the study of the solvable Leibniz algebras, more precisely, it completes the classi cation of the 3- liform Leibniz algebras of maximum length [4]. Moreover, due to the good structure of the algebras of maximum length, we also tackle some of their cohomological properties. Our main tools are the previous result of Cabezas and Pastor [3], the construction of appropriate homogeneous basis in the considered connected gradation and the computational support provided by the two programs implemented in the software Mathematica.
3-Filiform Leibniz algebras of maximum length, whose naturally graded algebras are Lie algebras
(Taylor and Francis Ltd., 2011-09) Camacho Santana, Luisa María; Cañete, E. M.; Gómez, J. R.; Omirov, B. A.; Universidad de Sevilla. Departamento de Matemática Aplicada I (ETSII)
In this article we present the classification of the 3-filiform Leibniz algebras of maximum length, whose associated naturally graded algebras are Lie algebras. Our main tools are a previous existence result by Cabezas and Pastor [J.M. Cabezas and E. Pastor, Naturally graded p-filiform Lie algebras in arbitrary finite dimension, J. Lie Theory 15 (2005), pp. 379–391] and the construction of appropriate homogeneous bases in the connected gradation considered. This is a continuation of the work done in Ref. [J.M. Cabezas, L.M. Camacho, and I.M. Rodrı´guez, On filiform and 2-filiform Leibniz algebras of maximum length, J. Lie Theory 18 (2008), pp. 335–350].
3-filiform Lie algebras of dimension 8
(L'université Blaise Pascal, 1999) Camacho Santana, Luisa María; Gómez Martín, José Ramón; Navarro, R.M.; Universidad de Sevilla. Departamento de Matemática Aplicada I (ETSII); Junta de Andalucía
We give, up to isomorphism and in dimension 8, all the 3-filiform Lie algebras (whose Goze’s invariant is (n - 3,1,1,1))..
3D well-composed polyhedral complexes
(2015) González Díaz, Rocío; Jiménez Rodríguez, María José; Medrano Garfia, Belén; Universidad de Sevilla. Departamento de Matemática Aplicada I
A binary three-dimensional (3D) image II is well-composed if the boundary surface of its continuous analog is a 2D manifold. In this paper, we present a method to locally “repair” the cubical complex Q(I)Q(I) (embedded in R3R3) associated to II to obtain a polyhedral complex P(I)P(I) homotopy equivalent to Q(I)Q(I) such that the boundary surface of P(I)P(I) is a 2D manifold (and, hence, P(I)P(I) is a well-composed polyhedral complex). For this aim, we develop a new codification system for a complex KK, called ExtendedCubeMap (ECM) representation of KK, that codifies: (1) the information of the cells of KK (including geometric information), under the form of a 3D grayscale image gPgP; and (2) the boundary face relations between the cells of KK, under the form of a set BPBP of structuring elements that can be stored as indexes in a look-up table. We describe a procedure to locally modify the ECM representation EQEQ of the cubical complex Q(I)Q(I) to obtain an ECM representation of a well-composed polyhedral complex P(I)P(I) that is homotopy equivalent to Q(I)Q(I). The construction of the polyhedral complex P(I)P(I) is accomplished for proving the results though it is not necessary to be done in practice, since the image gPgP (obtained by the repairing process on EQEQ) together with the set BPBP codify all the geometric and topological information of P(I)P(I).
3D-Dynamical geometry in building construction
(2010) Falcón Ganfornina, Raúl Manuel; Universidad de Sevilla. Departamento de Matemática Aplicada I (ETSII)
In Architecture and Technical Architecture Degrees, students use CAD tools (ComputerAided Design) which are not capable, in general, of representing graphically curves orsurfaces starting from its corresponding equations. To get it, users have to definespecific macros or they have to create a table of points in order to convert a set of nodesinto polylines. CAS tools used in Math classes allow this graphical representation of curves and surfaces starting from their parametric equations. However, they lack the dynamical development given by CAD tools, which plays a main role in the mentioned degrees. Inthis sense, the complementation of the algebraic and geometric tools included in the software of dynamic geometry, GeoGebra, is an attractive alternative to design and model, from a mathematical point of view, curves and rigid objects in the space. Theuse of sliders related to the Euler’s angles and the possibility of generating tools which project 3D into 2D, makes easier this kind of modeling. In the current workshop, we will show how to construct 3D-models of several architectonical constructions which have been made in the context of the subject called Mathematics for Building Construction II, corresponding to the Building Construction Engineering of the University of Seville, which has been implemented this academicyear 2009-10.
4-semirredes asociadas a cuadros latinos parciales regularmente auto-ortogonales
(2012-07) Falcón Ganfornina, Raúl Manuel; Universidad de Sevilla. Departamento de Matemática Aplicada I (ETSII)
El presente artículo se centra en la enumeración y clasificación de 4- semirredes asociadas al conjunto Sn,s de cuadrados latinos parciales de orden n y tamaño s, regularmente auto-ortogonales, regulares y no compresibles. Los elementos de dicho conjunto pueden identificarse con los ceros de un ideal polinomial Booleano, cuya base reducida de Gröbner permite determinar de forma explícita este tipo de estructuras. Se muestra en particular, para n ≤ 4, las clases principales de Sn,s y las de aquellas 4-semirredes con estructura de grafo asociadas a Sn,2n .
A 4D counter-example showing that DWCness does not imply CWCness in n-D
(Springer, 2020) Boutry, Nicolas; González Díaz, Rocío; Najman, Laurent; Géraud, Thierry; Universidad de Sevilla. Departamento de Matemática Aplicada I (ETSII)
In this paper, we prove that the two avours of well-compo- sedness called Continuous Well-Composedness (shortly CWCness), stat- ing that the boundary of the continuous analog of a discrete set is a manifold, and Digital Well-Composedness (shortly DWCness), stating that a discrete set does not contain any critical con guration, are not equivalent in dimension 4. To prove this, we exhibit the example of a con- guration of 8 tesseracts (4D cubes) sharing a common corner (vertex), which is DWC but not CWC. This result is surprising since we know that CWCness and DWCness are equivalent in 2D and 3D. To reach our goal, we use local homology.
A bed pressure correction of the friction term for depth-averaged granular flow models
(Elsevier, 2022) Bouchut, François; Delgado Sánchez, Juan Manuel; Fernández Nieto, Enrique Domingo; Mangeney, Anne; Narbona Reina, Gladys; Universidad de Sevilla. Departamento de Matemática Aplicada I (ETSII); Ministerio de Ciencia, Innovación y Universidades (MICINN). España; European Research Council (ERC)
Depth-averaged models, such as the Savage-Hutter model with Coulomb or Pouliquen fric tion laws, do not in some cases preserve the physical threshold of motion. In particular, the simulated granular mass can start to flow (or stay at rest) even if the slope angle of its free surface is lower (or higher) than the repose angle of the granular material involved. The problem is related to the hydrostatic pressure assumption, associated with the direction of integration, which is orthogonal to a reference plane or a reference bottom. We propose here an initial method to correct this misleading behavior. Firstly, we define a correction of the friction term that accounts for the Jacobian of a change of coordinates, making it possible to reproduce the physical threshold of motion and thus the solutions at rest. Sec ondly, we observe that the 3D model presented in [F. Bouchut, I. Ionescu, and A. Mangeney. An analytic approach for the evolution of the static-flowing interface in viscoplastic granular flows. Commun, Math. Sci., 14(8):2101–2126, 2016] verifies the physical thresholds of mo tion because it is based on a second order correction of the pressure valid for slow granu lar flows. The correction proposed here ensures that the model preserves, up to the second order, the physical threshold of motion defined by the repose angle of the material. Sev eral numerical tests are presented to illustrate certain problems related to classical depth averaged models and the remedial effect of the proposed correction, in particular through comparisons with experimental data. We finally show that this correction is not exact far from the starting and stopping phases of the granular avalanche and should be improved by adding other second order terms in the pressure approximation
A bio-inspired software for segmenting digital images.
(2010) Díaz Pernil, Daniel; Molina Abril, Helena; Real Jurado, Pedro; Gutiérrez Naranjo, Miguel Ángel; Universidad de Sevilla. Departamento de Matemática Aplicada I (ETSII); Universidad de Sevilla. Departamento de Ciencias de la Computación e Inteligencia Artificial; Universidad de Sevilla. FQM296: Topología Computacional y Matemática Aplicada; Universidad de Sevilla. TIC193: Computación Natural
Segmentation in computer vision refers to the process of partitioning a digital image into multiple segments (sets of pixels). It has several features which make it suitable for techniques inspired by nature. It can be parallelized, locally solved and the input data can be easily encoded by bio-inspired representations. In this paper, we present a new software for performing a segmentation of 2D digital images based on Membrane Computing techniques.
A Bochev-Dohrmann-Gunzburger stabilization method for the primitive equations of the ocean
(Elsevier, 2013-04) Chacón Rebollo, Tomás; Gómez Mármol, María Macarena; Sánchez Muñoz, Isabel María; Universidad de Sevilla. Departamento de Ecuaciones Diferenciales y Análisis Numérico; Ministerio de Ciencia e Innovación (MICIN). España; European Commission (EC). Fondo Europeo de Desarrollo Regional (FEDER)
We introduce a low-order stabilized discretization of the Primitive Equations of the Ocean, with a highly reduced computational complexity. We prove stability through a specific inf-sup condition, and weak convergence to a weak solution. We also perform some numerical test for relevant flows.
A Cellular Way to Obtain Homology Groups in Binary 2D Images
(Fénix Editora, 2010) Díaz Pernil, Daniel; Gutiérrez Naranjo, Miguel Ángel; Real Jurado, Pedro; Sánchez Canales, Vanesa; Universidad de Sevilla. Departamento de Ciencias de la Computación e Inteligencia Artificial; Universidad de Sevilla. Departamento de Matemática Aplicada I (ETSII); Universidad de Sevilla. TIC193: Computación Natural; Universidad de Sevilla. FQM296: Topología Computacional y Matemática Aplicada
In this paper we present a P systems-based solution for the Homology Groups of Binary 2D Image (HGB2I) Problem, a classical problem in Homology Theory. To this aim, we present a family of P systems which solves all the instances of the problem in the framework of Tissue-like P systems with catalysts. This new framework combines the membrane structure and symport-antiport communication rules of tissue-like P systems with the power of catalysts and inhibitors.
A census of critical sets based on non-trivial autotopisms of Latin squares of order up to five
(AIMS Press, 2020) Falcón Ganfornina, Raúl Manuel; Johnson, Laura; Perkins, Stephanie; Universidad de Sevilla. Departamento de Matemática Aplicada I (ETSII); Junta de Andalucía
This paper delves into the study of critical sets of Latin squares having a given isotopism in their autotopism group. Particularly, we prove that the sizes of these critical sets only depend on both the main class of the Latin square and the cycle structure of the isotopism under consideration. Keeping then in mind that the autotopism group of a Latin square acts faithfully on the set of entries of the latter, we enumerate all the critical sets based on autotopisms of Latin squares of order up to five.
A characterization of constant mean curvature surfaces in homogeneous 3-manifolds
(Elsevier, 2007) Fernández Delgado, Isabel; Mira, Pablo; Universidad de Sevilla. Departamento de Matemática Aplicada I (ETSII); Ministerio de Educación y Ciencia (MEC). España
It has been recently shown by Abresch and Rosenberg that a cer- tain Hopf differential is holomorphic on every constant mean curvature surface in a Riemannian homogeneous 3-manifold with isometry group of dimension 4. In this paper we describe all the surfaces with holomorphic Hopf differential in the homogeneous 3-manifolds isometric to H2 ×R or having isometry group isomorphic either to the one of the universal cover of PSL(2, R), or to the one of a certain class of Berger spheres. It turns out that, except for the case of these Berger spheres, there exist some exceptional surfaces with holomorphic Hopf differential and non-constant mean curvature.
A characterization of operators with p-summing adjoint via p-limited sets
(Tartu Ülikool, 2013) Delgado Sánchez, Juan Manuel; Piñeiro Gómez, Cándido; Departamento de Matemática Aplicada I
A Class of Computationally Fast First Order Finite Volume Solvers: PVM Methods
(Society for Industrial and Applied Mathematics, 2012) Castro Díaz, Manuel Jesús; Fernández Nieto, Enrique Domingo; Universidad de Sevilla. Departamento de Matemática Aplicada I (ETSII)
In this work, we present a class of fast first order finite volume solvers, named as PVM (Polynomial Viscosity Matrix), for balance laws or, more generally, for nonconservative hyperbolic systems. They are defined in terms of viscosity matrices computed by a suitable polynomial evaluation of a Roe matrix. These methods have the advantage that they only need some information about the eigenvalues of the system to be defined, and no spectral decomposition of Roe Matrix is needed. As consequence, they are faster than Roe method. These methods can be seen as a generalization of the schemes introduced by Degond et al. in [12] for balance laws and nonconservative systems. The first-order path conservative methods to be designed here are intended to be used as the basis for higher order methods for multi-dimensional problems. In this work, some well known solvers as Rusanov, Lax-Friedrichs, FORCE (see [30], [8]), GFORCE (see [31], [8]) or HLL (see [18]) are redefined under this form, and then some new solvers are proposed. Finally, some numerical tests are presented and the performance of the numerical schemes are compared among them and with Roe scheme
A class of nilpotent lie algebras
(Taylor and Francis, 2000) Cabezas, J. M.; Camacho Santana, Luisa María; Gómez Martín, José Ramón; Navarro, R.M.; Universidad de Sevilla. Departamento de Matemática Aplicada I (ETSII); Junta de Andalucía; Universidad del País Vasco
A p-filiform Lie algebra g is a nilpotent Lie algebra for which Goze’s invariant is (n–p,1,…,1). These Lie algebras are well known for P ≥ n-4n = dim(g). In this paper we describe the p-filiform Lie algebras, for p = n-5 and we gjive their classification when the derived subalgebra is maximal
A combinatorial method for computing Steenrod squares
(Elsevier, 1999) González Díaz, Rocío; Real Jurado, Pedro; Universidad de Sevilla. Departamento de Matemática Aplicada I (ETSII); Junta de Andalucía; Ministerio de Educación y Ciencia (MEC). España
We present here a combinatorial method for computing Steenrod squares of a simplicial set X. This method is essentially based on the determination of explicit formulae for the component morphisms of a higher diagonal approximation (i.e., a family of morphisms measuring the lack of commutativity of the cup product on the cochain level) in terms of face operators of X. A generalization of this method to Steenrod reduced powers is sketched

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