UPCommons - E-prints UPC Universitat Politècnica de Catalunya
(2.036 recursos)
E-prints UPC cobreix dues finalitats: per una banda, és el dipòsit institucional de la UPC que recull els articles de revista, les comunicacions de congrés i els reports de recerca generats en les activitats de recerca del personal docent i investigador de la universitat; per l'altra, és una eina que permet accelerar la producció científica, allotjant versions de documents prèvies a la publicació en una revista o a les actes d’un congrés.
Mostrando recursos 1 - 20 de 444
1.
A pressure-stabilized formulation of incompressible flow problems on anisotropic finite-element meshes - Blasco Lorente, Jorge
We consider a pressure stabilized, finite element approximation of
incompressible flow problems in primitive velocity--pressure variables, which
is based on a projection of the gradient of the discrete pressure onto the space
of discrete functions. Equal order interpolation for the velocity and the pressure
can be employed with this formulation. The method introduced here is specially
developed to be used on anisotropic finite element meshes with large element aspect
ratios.
4.
Structural stability of (C,A)-marked and observable subspaces - Compta Creus, Albert; Peña Carrera, Marta
Given an observable pair of matrices (C;A) we consider the manifold
of (C;A)-invariant and observable subspaces having a fixed Brunovsky-
Kronecker structure. Using Arnold’s techniques we obtain the explicit
form of a miniversal deformation of a marked and observable (C;A)-
invariant subspace with regard to the usual equivalence relation. As an
application, we obtain the dimension of the orbit and we characterize
the structurally stable subspaces.
5.
Stability of (A,B)-invariant subspaces - Peña Carrera, Marta; Puerta Coll, Xavier; Puerta Sales, Fernando
Given a pair of matrices (A;B) we study the stability of their invariant subspaces from the geometry of the manifold of quadruples
(A;B; S; F) where S is an (A;B)-invariant subspace and F is such that (A + BF)S ½ S. In particular, we derive a su±cient computable condition of stability.
6.
On the scattering map and homoclinic connections between Lyapunov orbits - Cancalias Vila, Elisabet; Delshams, Amadeu; Masdemont Soler, Josep; Roldán González, Pablo
Homoclinic and heteroclinic connections between planar Lyapunov orbits of the
Sun-Earth and Earth-Moon models can be found by using their hyperbolic
invariant manifolds and Poincare section representations. These connections can
be classified in bifurcation families according to the range of values of the
associated Jacobi constant. In the formalism of invariant manifolds (as the
aforementioned Jacobi constant changes) the foliation of all Lyapunov orbits is
a Normally Hyperbolic Invariant Manifold. In this context, the homoclinic
connections correspond to the so called Scattering map of this NHIM into
itself.
In this work, the Scattering map is studied as a possible way to
formally describe the asymptotic connections arising from the...
9.
Entorn del desenvolupament històric de les equacions algebraiques - Magret Planas, Ma. Dolors (Maria Dolors); Massa Esteve, Ma. Rosa (Maria Rosa)
El conjunt dels nombres enters i el de polinomis amb coeficients en un cos són els exemples més bàsics d’anells commutatius, que constitueixen l’essència de l’àlgebra commutativa, branca de les matemàtiques estretament lligada a la geometria algebraica. És a finals del
segle XIX que, amb el desenvolupament de l’àlgebra abstracta, els anells de polinomis es van començar a estudiar des d’un nou enfocament.
L’estudi dels polinomis i de les equacions associades a ells, ha evolucionat molt al llarg del temps, i el seu recorregut històric és molt suggerent i instructiu. Aquí analitzem dos aspectes claus d’aquest desenvolupament. En l’apartat 1, ens ocupem...
10.
Familias diferenciables de inversas de Drazin - Clotet Juan, Josep; Magret Planas, Ma. Dolors (Maria Dolors)
Las inversas de Drazin son una clase de inversa generalizada entre cuyas aplicaciones
podemos mencionar la resoluci´on de ecuaciones diferenciales, ecuaciones en diferencias, estudio de
cadenas de Markov, etc. En esta presentaci´on se caracterizan las matrices cuyas inversas de Drazin
tienen misma forma reducida de Jordan y se estudia la partici´on del espacio de matrices cuadradas
correspondiente a la relaci´on de equivalencia derivada. Finalmente, se encuentra una condici´on sufi-
ciente para que una familia de inversas de Drazin de una familia diferenciable de matrices sea a su vez una familia diferenciable.
11.
Higher-Order Singular Systems and Polynomial Matrices - Magret Planas, Ma. Dolors (Maria Dolors)
There is a one-to-one correspondence between the set of quadruples of matrices defining
singular linear time-invariant dynamical systems and a subset of the set of polynomial matrices. This
correspondence preserves the equivalence relations introduced in both sets (feedback-similarity and
strict equivalence): two quadruples of matrices are feedback-equivalent if, and only if, the polynomial matrices associated to them are also strictly equivalent.
Los sistemas lineales singulares (DAEs) y su control han sido extensamente estudiados a
partir de la d´ecada de 1970 (v´eanse, por ejemplo, [1], [2], [3], [4], [6], [7], [8], [10], [11], [12], [15]). Estos sistemas aparecen de forma natural al proponer modelos para distintos...
12.
The characteristic numbers of the variety of P3 - Hernández, Xavier; Miret Biosca, Josep M; Xambó Descamps, Sebastián
In this note we obtain, phrased in present day geometric and computational frameworks,
the characteristic numbers of the family Unod of non–degenerate nodal plane
cubics in P3, first obtained by Schubert in his Kalk¨ul der abz¨ahlenden Geometrie.
The main geometric contribution is a detailed study of a variety Xnod, which is a
compactification of the family Unod, including the boundary components (degenerations)
and a generalization to P3 of a formula of Zeuthen for nodal cubics in P2.
The computations have been carried out with the OmegaMath intersection theory
module WIT.
13.
Mathematical interactive content: what, why and how - Caprotti, Olga; Seppälä, Mika; Xambó Descamps, Sebastián
The real challenge of e-Learning is to produce content that
brings a general improvement in the way students learn and teachers
teach. For that, “intelligent” interactivity is the single most important
feature that such content should have. But the design and production
of content with this kind of interactivity has turned out to be harder
than expected, the main reason being that it requires the convergence
of many kinds of experts in parallel to the convergence of the several
technologies involved. In the case of mathematics, the least amount of
expertise asks for the presence of professional mathematicians,
software engineers, publishers, and perhaps learning theorists, that
can productively talk to...
14.
Using Web Technologies to Teach Mathematics - Seppälä, Mika; Caprotti, Olga; Xambó Descamps, Sebastián
The technical barriers hindering the development of on-line learning in the
sciences have disappeared in 2005. It is now possible and practical to teach on-line via
videoconferencing supported by systems like Festoon. Students are ready to embrace
synchronous and asynchronous on-line learning at the university level. Instructors are still
largely either against teaching on-line or, at best, hesitant about the effectiveness of online learning. This paper reports on the recent experiments at the University of Helsinki
and at Florida State University. We also discuss the enhancements that the WebALT
Project will bring to on-line learning. The experiences gathered at the University of
Helsinki and at Florida State...
15.
Geometric Hamilton–Jacobi Theory - Cariñena, José F.; Gràcia Sabaté, Xavier; Marmo, Giuseppe; Martínez, Eduardo; Muñoz Lecanda, Miguel Carlos; Román Roy, Narciso
The Hamilton–Jacobi problem is revisited bearing in mind the consequences arising from a possible bi-Hamiltonian structure. The problem is formulated on the tangent bundle for Lagrangian systems in order to avoid the bias of the existence of a natural symplectic structure on the cotangent bundle. First it is developed for systems described by regular Lagrangians and then extended to systems described by singular Lagrangians with no secondary constraints. We also consider the example of the free relativistic particle, the rigid body and the electron-monopole system.
16.
k-cosymplectic formalism in classical field theory: the Skinner–Rusk approach - Rey, Angel M.; Román Roy, Narciso; Salgado, Modesto
The k-cosymplectic Lagrangian and Hamiltonian formalisms of first-order field theories are
reviewed and completed. In particular they are stated for singular almost-regular systems. After that, both formalisms are unified by giving an extension of the Skinner-Rusk formulation on classical mechanics for first-order field theories.
17.
Hamiltonian Systems in Multisymplectic Field Theories - Echeverría Enríquez, Arturo; León, Manuel de; Muñoz Lecanda, Miguel Carlos; Román Roy, Narciso
We consider Hamiltonian systems in first-order multisymplectic field theories. First we review the construction and properties of Hamiltonian systems in the so-called restricted multimomentum bundle using Hamiltonian sections, including the variational principle which leads to the Hamiltonian field equations. Then, we introduce Hamiltonian systems in the extended multimomentum bundle, in an analogous way to how these systems are defined in non-autonomous (symplectic) mechanics or in the so-called extended (symplectic) formulation of autonomous mechanics. The corresponding variational principle is also stated for these extended Hamiltonian systems and, after studying the geometric properties of these systems, we establish the relation
between the extended...
18.
Multisymplectic Lagrangian and Hamiltonian formalisms of First-order Classical Field theories - Román Roy, Narciso
This review paper is devoted to presenting the standard multisymplectic formulation for
describing geometrically first-order classical field theories, both the regular and singular cases. First, the main features of the Lagrangian formalism are revisited and, second, the Hamiltonian formalism is constructed using Hamiltonian sections. In both cases, the variational principles
leading to the Euler-Lagrange and the Hamilton-De Donder-Weyl equations, respectively, are stated, and these field equations are given in different but equivalent geometrical ways in each formalism. Finally, both are unified in a new formulation (which has been recently developed),
following the original ideas of Rusk and Skinner for mechanical systems.
19.
Some topics concerning the theory of singular dynamical systems - Román Roy, Narciso
Some subjects related to the geometric theory of singular dynamical systems are reviewed in this paper. In particular, the following two
matters are considered: the theory of canonical transformations for presymplectic Hamiltonian systems, and the Lagrangian and Hamiltonian constraint algorithms and the time-evolution operator.
1.
