Reports de recerca
http://hdl.handle.net/2117/3919
Tue, 09 Feb 2016 14:00:12 GMT2016-02-09T14:00:12ZWeierstrass per ell mateix: alguns trets del seu pensament matemàtic
http://hdl.handle.net/2117/82230
Weierstrass per ell mateix: alguns trets del seu pensament matemàtic
Massa Esteve, Maria Rosa
El coneixement de Karl Weierstrass (1815-1897) a través dels teoremes que s’estudien a les classes de matemàtiques ens aporta una visió parcial del personatge.
En aquesta ponència es pretén enriquir aquesta visió apropant-nos tant a l’home com al matemàtic, des d’un altre vessant, a través de les seves paraules i dels seus deixebles.
Es reflexionarà sobre alguns trets característics de les contribucions de Weierstrass a la matemàtica, com ara la unitat del seu pensament matemàtic, la seva fonamentació aritmètica de l’Anàlisi i la seva cerca del rigor.
Presentació feta a la Jornada Weierstrass a l'FME: curs 2014-2015
Thu, 28 Jan 2016 15:45:06 GMThttp://hdl.handle.net/2117/822302016-01-28T15:45:06ZMassa Esteve, Maria RosaEl coneixement de Karl Weierstrass (1815-1897) a través dels teoremes que s’estudien a les classes de matemàtiques ens aporta una visió parcial del personatge.
En aquesta ponència es pretén enriquir aquesta visió apropant-nos tant a l’home com al matemàtic, des d’un altre vessant, a través de les seves paraules i dels seus deixebles.
Es reflexionarà sobre alguns trets característics de les contribucions de Weierstrass a la matemàtica, com ara la unitat del seu pensament matemàtic, la seva fonamentació aritmètica de l’Anàlisi i la seva cerca del rigor.Hamilton-Jacobi theory in multisymplectic classical field theories
http://hdl.handle.net/2117/81799
Hamilton-Jacobi theory in multisymplectic classical field theories
de León, Manuel; Prieto Martínez, Pedro Daniel; Román Roy, Narciso; Vilariño, Silvia
The geometric framework for the Hamilton-Jacobi theory developed in [14, 17, 39] is extended for multisymplectic first-order classical field theories. The Hamilton-Jacobi problema is stated for the Lagrangian and the Hamiltonian formalisms of these theories as a particular case of a more general problem, and the classical Hamilton-Jacobi equation for field theories is recovered from this geometrical setting. Particular and complete solutions to these problems are defined and characterized in several equivalent ways in both formalisms, and the equivalence between them is proved. The use of distributions in jet bundles that represent
the solutions to the field equations is the fundamental tool in this formulation. Some examples are analyzed and, in particular, the Hamilton-Jacobi equation for non-autonomous mechanical systems is obtained as a special case of our results.
Thu, 21 Jan 2016 11:19:16 GMThttp://hdl.handle.net/2117/817992016-01-21T11:19:16Zde León, ManuelPrieto Martínez, Pedro DanielRomán Roy, NarcisoVilariño, SilviaThe geometric framework for the Hamilton-Jacobi theory developed in [14, 17, 39] is extended for multisymplectic first-order classical field theories. The Hamilton-Jacobi problema is stated for the Lagrangian and the Hamiltonian formalisms of these theories as a particular case of a more general problem, and the classical Hamilton-Jacobi equation for field theories is recovered from this geometrical setting. Particular and complete solutions to these problems are defined and characterized in several equivalent ways in both formalisms, and the equivalence between them is proved. The use of distributions in jet bundles that represent
the solutions to the field equations is the fundamental tool in this formulation. Some examples are analyzed and, in particular, the Hamilton-Jacobi equation for non-autonomous mechanical systems is obtained as a special case of our results.Qüestions d'àlgebra lineal amb solucions
http://hdl.handle.net/2117/80910
Qüestions d'àlgebra lineal amb solucions
Cubarsí Morera, Rafael
Qüestions tipus test de l'assignatura d'Àlgebra Lineal de l'ETSETB (2015) amb solucions
Qüestions tipus test de l'assignatura d'Àlgebra Lineal amb solucions
Fri, 18 Dec 2015 13:12:19 GMThttp://hdl.handle.net/2117/809102015-12-18T13:12:19ZCubarsí Morera, RafaelQüestions tipus test de l'assignatura d'Àlgebra Lineal de l'ETSETB (2015) amb solucionsSynthetic events description, generation and characterization report
http://hdl.handle.net/2117/80907
Synthetic events description, generation and characterization report
González Casado, Guillermo; Juan Zornoza, José Miguel; Sanz Subirana, Jaume
Fri, 18 Dec 2015 12:47:15 GMThttp://hdl.handle.net/2117/809072015-12-18T12:47:15ZGonzález Casado, GuillermoJuan Zornoza, José MiguelSanz Subirana, JaumeProblemes de matrius
http://hdl.handle.net/2117/80904
Problemes de matrius
Cubarsí Morera, Rafael
Problemes test de matrius
Fri, 18 Dec 2015 12:05:42 GMThttp://hdl.handle.net/2117/809042015-12-18T12:05:42ZCubarsí Morera, RafaelProblemes test de matriusOn cyclic Kautz digraphs
http://hdl.handle.net/2117/80848
On cyclic Kautz digraphs
Böhmová, Katerina; Dalfó Simó, Cristina; Huemer, Clemens
A prominent problem in Graph Theory is to find extremal graphs or digraphs with restrictions in their diameter, degree and number of vertices. Here we obtain a new family of digraphs with minimal diameter, that is, given the number of vertices and out-degree there is no other digraph with a smaller diameter. This new family is called modified cyclic digraphs MCK(d, `) and it is derived from the Kautz digraphs K(d, `). It is well-known that the Kautz digraphs K(d, `) have the smallest diameter among all digraphs with their number of vertices and degree. We define the cyclic Kautz digraphs
CK(d, `), whose vertices are labeled by all possible sequences a1 . . . a` of length `, such that each character ai is chosen from an alphabet containing d + 1 distinct symbols, where the consecutive characters in the sequence are different (as in Kautz digraphs), and now also requiring that a1 6= a`. The cyclic Kautz digraphs CK(d, `) have arcs between vertices a1a2 . . . a` and a2 . . . a`a`+1, with a1 6= a` and a2 6= a`+1. Unlike in Kautz digraphs K(d, `), any label of a vertex of CK(d, `) can be cyclically shifted to form again a label of a vertex of CK(d, `).
We give the main parameters of CK(d, `): number of vertices, number of arcs, and diameter.
Moreover, we construct the modified cyclic Kautz digraphs MCK(d, `) to obtain the same diameter as in the Kautz digraphs, and we show that MCK(d, `) are d-out-regular.
Finally, we compute the number of vertices of the iterated line digraphs of CK(d, `).
Thu, 17 Dec 2015 10:58:24 GMThttp://hdl.handle.net/2117/808482015-12-17T10:58:24ZBöhmová, KaterinaDalfó Simó, CristinaHuemer, ClemensA prominent problem in Graph Theory is to find extremal graphs or digraphs with restrictions in their diameter, degree and number of vertices. Here we obtain a new family of digraphs with minimal diameter, that is, given the number of vertices and out-degree there is no other digraph with a smaller diameter. This new family is called modified cyclic digraphs MCK(d, `) and it is derived from the Kautz digraphs K(d, `). It is well-known that the Kautz digraphs K(d, `) have the smallest diameter among all digraphs with their number of vertices and degree. We define the cyclic Kautz digraphs
CK(d, `), whose vertices are labeled by all possible sequences a1 . . . a` of length `, such that each character ai is chosen from an alphabet containing d + 1 distinct symbols, where the consecutive characters in the sequence are different (as in Kautz digraphs), and now also requiring that a1 6= a`. The cyclic Kautz digraphs CK(d, `) have arcs between vertices a1a2 . . . a` and a2 . . . a`a`+1, with a1 6= a` and a2 6= a`+1. Unlike in Kautz digraphs K(d, `), any label of a vertex of CK(d, `) can be cyclically shifted to form again a label of a vertex of CK(d, `).
We give the main parameters of CK(d, `): number of vertices, number of arcs, and diameter.
Moreover, we construct the modified cyclic Kautz digraphs MCK(d, `) to obtain the same diameter as in the Kautz digraphs, and we show that MCK(d, `) are d-out-regular.
Finally, we compute the number of vertices of the iterated line digraphs of CK(d, `).Continua of periodic points for planar integrable rational maps.
http://hdl.handle.net/2117/80625
Continua of periodic points for planar integrable rational maps.
Gasull Embid, Armengol; Llorens, Mireia; Mañosa Fernández, Víctor
We present three alternative methodologies to find continua of periodic points with a prescribed period for rational maps having rational first integrals. The first two have been already used for other authors and apply when the maps are birational and the generic level sets of the corresponding first integrals have either genus 0 or 1. As far as we know, the third one is new and it works for rational maps without imposing topological properties to the invariant level sets. It is based on a computational point of view, and relies on the use of resultants in a suitable setting. We apply them to several examples, including the 2-periodic Lyness composition maps and some of the celebrated McMillan-Gumowski-Mira maps.
Prepublicació
Wed, 16 Dec 2015 09:04:48 GMThttp://hdl.handle.net/2117/806252015-12-16T09:04:48ZGasull Embid, ArmengolLlorens, MireiaMañosa Fernández, VíctorWe present three alternative methodologies to find continua of periodic points with a prescribed period for rational maps having rational first integrals. The first two have been already used for other authors and apply when the maps are birational and the generic level sets of the corresponding first integrals have either genus 0 or 1. As far as we know, the third one is new and it works for rational maps without imposing topological properties to the invariant level sets. It is based on a computational point of view, and relies on the use of resultants in a suitable setting. We apply them to several examples, including the 2-periodic Lyness composition maps and some of the celebrated McMillan-Gumowski-Mira maps.Problemes d'espais vectorials
http://hdl.handle.net/2117/80005
Problemes d'espais vectorials
Cubarsí Morera, Rafael
Problemes test d'espais vectorials
Problemes test d'espais vectorials
Fri, 27 Nov 2015 12:08:37 GMThttp://hdl.handle.net/2117/800052015-11-27T12:08:37ZCubarsí Morera, RafaelProblemes test d'espais vectorialsThe conjugacy problem for free-by-cyclic groups
http://hdl.handle.net/2117/79985
The conjugacy problem for free-by-cyclic groups
Martino, Armando; Ventura Capell, Enric
We show that the conjugacy problem is solvable in [finitely
generated free]-by-cyclic groups, by using a result of O. Maslakova
that one can algorithmically find generating sets for the fixed sub-
groups of free group automorphisms, and one of P. Brinkmann that
one can determine whether two cyclic words in a free group are
mapped to each other by some power of a given automorphism. The
algorithm effectively computes a conjugating element, if it exists. We
also solve the power conjugacy problem and give an algorithm to rec-
ognize if two given elements of a finitely generated free group are
Reidemeister equivalent with respect to a given automorphism.
Thu, 26 Nov 2015 18:18:08 GMThttp://hdl.handle.net/2117/799852015-11-26T18:18:08ZMartino, ArmandoVentura Capell, EnricWe show that the conjugacy problem is solvable in [finitely
generated free]-by-cyclic groups, by using a result of O. Maslakova
that one can algorithmically find generating sets for the fixed sub-
groups of free group automorphisms, and one of P. Brinkmann that
one can determine whether two cyclic words in a free group are
mapped to each other by some power of a given automorphism. The
algorithm effectively computes a conjugating element, if it exists. We
also solve the power conjugacy problem and give an algorithm to rec-
ognize if two given elements of a finitely generated free group are
Reidemeister equivalent with respect to a given automorphism.Bisemivalues, binomial bisemivalues and multilinear extension for bicooperative games
http://hdl.handle.net/2117/78354
Bisemivalues, binomial bisemivalues and multilinear extension for bicooperative games
Domènech Blázquez, Margarita; Giménez Pradales, José Miguel; Puente del Campo, María Albina
We introduce bisemivalues for bicooperative games and we also provide an interesting characterization of this kind of values by means of weighting coefficients in a similar way than given for semivalues in the context of cooperative games. Moreover, the notion of induced bisemivalues on lower cardinalities also makes sense and an adaptation of Dragan’s recurrence formula is obtained. Besides its characterization, a computational procedure in terms of the multilinear extension of the game is given.
Tue, 27 Oct 2015 14:22:43 GMThttp://hdl.handle.net/2117/783542015-10-27T14:22:43ZDomènech Blázquez, MargaritaGiménez Pradales, José MiguelPuente del Campo, María AlbinaWe introduce bisemivalues for bicooperative games and we also provide an interesting characterization of this kind of values by means of weighting coefficients in a similar way than given for semivalues in the context of cooperative games. Moreover, the notion of induced bisemivalues on lower cardinalities also makes sense and an adaptation of Dragan’s recurrence formula is obtained. Besides its characterization, a computational procedure in terms of the multilinear extension of the game is given.