Departament de Matemàtiques
http://hdl.handle.net/2117/3917
2015-11-27T08:37:00ZThe 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.
2015-11-26T18:18:08ZMartino, 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.The automorphism group of a free-by-cyclic group in rank 2
http://hdl.handle.net/2117/79983
The automorphism group of a free-by-cyclic group in rank 2
Bogopolski, Oleg; Martino, Armando; Ventura Capell, Enric
Let
¡
be an automorphism of a free group
F
2
of rank
2 and let
M
¡
=
F
2
o
¡
Z
be the corresponding mapping torus of
¡
.
We prove that the group
Out
(
M
¡
) is usually virtually cyclic. More-
over, we classify the cases when this group is Ønite depending on the
conjugacy class of the image of
¡
in
GL
2
(
Z
)
2015-11-26T17:54:44ZBogopolski, OlegMartino, ArmandoVentura Capell, EnricLet
¡
be an automorphism of a free group
F
2
of rank
2 and let
M
¡
=
F
2
o
¡
Z
be the corresponding mapping torus of
¡
.
We prove that the group
Out
(
M
¡
) is usually virtually cyclic. More-
over, we classify the cases when this group is Ønite depending on the
conjugacy class of the image of
¡
in
GL
2
(
Z
)Absolute-type shaft encoding using LFSR sequences with a prescribed length
http://hdl.handle.net/2117/79981
Absolute-type shaft encoding using LFSR sequences with a prescribed length
Fuertes Armengol, José Mª; Balle Pigem, Borja de; Ventura Capell, Enric
Maximal-length binary sequences have existed for a long time. They have many interesting properties, and one of them is that, when taken in blocks of n consecutive positions, they form 2n - 1 different codes in a closed circular sequence. This property can be used to measure absolute angular positions as the circle can be divided into as many parts as different codes can be retrieved. This paper describes how a closed binary sequence with an arbitrary length can be effectively designed with the minimal possible block length using linear feedback shift registers. Such sequences can be used to measure a specified exact number of angular positions using the minimal possible number of sensors that linear methods allow.
2015-11-26T17:41:12ZFuertes Armengol, José MªBalle Pigem, Borja deVentura Capell, EnricMaximal-length binary sequences have existed for a long time. They have many interesting properties, and one of them is that, when taken in blocks of n consecutive positions, they form 2n - 1 different codes in a closed circular sequence. This property can be used to measure absolute angular positions as the circle can be divided into as many parts as different codes can be retrieved. This paper describes how a closed binary sequence with an arbitrary length can be effectively designed with the minimal possible block length using linear feedback shift registers. Such sequences can be used to measure a specified exact number of angular positions using the minimal possible number of sensors that linear methods allow.Absolute type shaft encoding using LFSR sequences with prescribed length
http://hdl.handle.net/2117/79980
Absolute type shaft encoding using LFSR sequences with prescribed length
Fuertes Armengol, José Mª; Balle, Borja; Ventura Capell, Enric
Maximal-length binary sequences have been known for
a long time. They have many interesting properties, one of them
is that when taken in blocks of
n
consecutive positions they form
2
n
°
1 diÆerent codes in a closed circular sequence. This property
can be used for measuring absolute angular positions as the circle
can be divided in as many parts as diÆerent codes can be retrieved.
This paper describes how can a closed binary sequence with arbitrary
length be eÆectively designed with the minimal possible block-length,
using
linear feedback shift registers
(LFSR). Such sequences can be
used for measuring a speciØed exact number of angular positions,
using the minimal possible number of sensors that linear methods
allow
2015-11-26T17:28:19ZFuertes Armengol, José MªBalle, BorjaVentura Capell, EnricMaximal-length binary sequences have been known for
a long time. They have many interesting properties, one of them
is that when taken in blocks of
n
consecutive positions they form
2
n
°
1 diÆerent codes in a closed circular sequence. This property
can be used for measuring absolute angular positions as the circle
can be divided in as many parts as diÆerent codes can be retrieved.
This paper describes how can a closed binary sequence with arbitrary
length be eÆectively designed with the minimal possible block-length,
using
linear feedback shift registers
(LFSR). Such sequences can be
used for measuring a speciØed exact number of angular positions,
using the minimal possible number of sensors that linear methods
allowIonospheric and plasmaspheric electron contents inferred from radio occultations and global ionospheric maps
http://hdl.handle.net/2117/79027
Ionospheric and plasmaspheric electron contents inferred from radio occultations and global ionospheric maps
González Casado, Guillermo; Juan Zornoza, José Miguel; Sanz Subirana, Jaume; Rovira Garcia, Adrià; Aragón Angel, Angela
We introduce a methodology to extract the separate contributions of the ionosphere and the plasmasphere to the vertical total electron content, without relying on a fixed altitude to perform that separation. The method combines two previously developed and tested techniques, namely, the retrieval of electron density profiles from radio occultations using an improved Abel inversion technique and a two-component model for the topside ionosphere plus protonosphere. Taking measurements of the total electron content from global ionospheric maps and radio occultations from the Constellation Observing System for Meteorology, Ionosphere, and Climate/FORMOSAT-3 constellation, the ionospheric and plasmaspheric electron contents are calculated for a sample of observations covering 2007, a period of low solar and geomagnetic activity. The results obtained are shown to be consistent with previous studies for the last solar minimum period and with model calculations, confirming the reversal of the winter anomaly, the hemispheric asymmetry of the semiannual anomaly, and the existence in the plasmasphere of an annual anomaly in the South American sector of longitudes. The analysis of the respective fractional contributions from the ionosphere and the plasmasphere to the total electron content shows quantitatively that during the night the plasmasphere makes the largest contribution, peaking just before sunrise and during winter. On the other hand, the fractional contribution from the ionosphere reaches a maximum value around noon, which is nearly independent of season and geomagnetic latitude.
2015-11-11T13:07:44ZGonzález Casado, GuillermoJuan Zornoza, José MiguelSanz Subirana, JaumeRovira Garcia, AdriàAragón Angel, AngelaWe introduce a methodology to extract the separate contributions of the ionosphere and the plasmasphere to the vertical total electron content, without relying on a fixed altitude to perform that separation. The method combines two previously developed and tested techniques, namely, the retrieval of electron density profiles from radio occultations using an improved Abel inversion technique and a two-component model for the topside ionosphere plus protonosphere. Taking measurements of the total electron content from global ionospheric maps and radio occultations from the Constellation Observing System for Meteorology, Ionosphere, and Climate/FORMOSAT-3 constellation, the ionospheric and plasmaspheric electron contents are calculated for a sample of observations covering 2007, a period of low solar and geomagnetic activity. The results obtained are shown to be consistent with previous studies for the last solar minimum period and with model calculations, confirming the reversal of the winter anomaly, the hemispheric asymmetry of the semiannual anomaly, and the existence in the plasmasphere of an annual anomaly in the South American sector of longitudes. The analysis of the respective fractional contributions from the ionosphere and the plasmasphere to the total electron content shows quantitatively that during the night the plasmasphere makes the largest contribution, peaking just before sunrise and during winter. On the other hand, the fractional contribution from the ionosphere reaches a maximum value around noon, which is nearly independent of season and geomagnetic latitude.Identifying optimal components in a reliability system
http://hdl.handle.net/2117/78945
Identifying optimal components in a reliability system
Freixas Bosch, Josep; Pons Vallès, Montserrat
The first step in a reliability optimization process is to
make a reliability assessment for each component in the system. If
this assessment is made in a qualitative way, by grouping together
components with the same reliability, and establishing a prevalence
order among groups, is there a way to decide which components
have the greatest Birnbaum measure without computing the exact
value of this measure? In this paper, three relations between com-
ponents are introduced and studied, and it is proved that they are
useful for selecting the components that have the biggest effect on
the system reliability in the sense of Birnbaum. An algorithm that
uses the results in the paper to select these important components
is also provided.
2015-11-09T17:12:18ZFreixas Bosch, JosepPons Vallès, MontserratThe first step in a reliability optimization process is to
make a reliability assessment for each component in the system. If
this assessment is made in a qualitative way, by grouping together
components with the same reliability, and establishing a prevalence
order among groups, is there a way to decide which components
have the greatest Birnbaum measure without computing the exact
value of this measure? In this paper, three relations between com-
ponents are introduced and studied, and it is proved that they are
useful for selecting the components that have the biggest effect on
the system reliability in the sense of Birnbaum. An algorithm that
uses the results in the paper to select these important components
is also provided.Dynamics of the parabolic restricted three-body problem
http://hdl.handle.net/2117/78941
Dynamics of the parabolic restricted three-body problem
Barrabés Vera, Esther; Cors Iglesias, Josep Maria; Ollé Torner, Mercè
The main purpose of the paper is the study of the motion of a massless body attracted, under the Newton's law of gravitation, by two equal masses moving in parabolic orbits all over in the same plane, the planar parabolic restricted three body problem. We consider the system relative to a rotating and pulsating frame where the equal masses (primaries) remain at rest. The system is gradient like and has exactly ten hyperbolic equilibrium points lying on the boundary invariant manifolds corresponding to escape of the primaries in past and future time. The global flow of the system is described in terms of the final evolution (forwards and backwards in time) of the solutions. The invariant manifolds of the equilibrium points play a key role in the dynamics. We study the connections, restricted to the invariant boundaries, between the invariant manifolds associated to the equilibrium points. Finally we study numerically the connections in the whole phase space, paying special attention to capture and escape orbits. (C) 2015 Elsevier B.V. All rights reserved.
2015-11-09T15:11:24ZBarrabés Vera, EstherCors Iglesias, Josep MariaOllé Torner, MercèThe main purpose of the paper is the study of the motion of a massless body attracted, under the Newton's law of gravitation, by two equal masses moving in parabolic orbits all over in the same plane, the planar parabolic restricted three body problem. We consider the system relative to a rotating and pulsating frame where the equal masses (primaries) remain at rest. The system is gradient like and has exactly ten hyperbolic equilibrium points lying on the boundary invariant manifolds corresponding to escape of the primaries in past and future time. The global flow of the system is described in terms of the final evolution (forwards and backwards in time) of the solutions. The invariant manifolds of the equilibrium points play a key role in the dynamics. We study the connections, restricted to the invariant boundaries, between the invariant manifolds associated to the equilibrium points. Finally we study numerically the connections in the whole phase space, paying special attention to capture and escape orbits. (C) 2015 Elsevier B.V. All rights reserved.Overconvergent generalised eigenforms of weight one and class fields of real quadratic fields
http://hdl.handle.net/2117/78762
Overconvergent generalised eigenforms of weight one and class fields of real quadratic fields
Darmon, Henri; Lauder, Alan; Rotger Cerdà, Víctor
This article examines the Fourier expansions of certain non-classical p-adic modular forms of weight one: the eponymous generalised eigertforms of the title, so called because they lie in a generalised eigenspace for the Hecke operators. When this generalised eigenspace contains the theta series attached to a character of a real quadratic field K in which the prime p splits, the coefficients of the attendant generalised eigenform are expressed as p-adic logarithms of algebraic numbers belonging to an idoneous ring class field of K. This suggests an approach to
2015-11-04T11:14:19ZDarmon, HenriLauder, AlanRotger Cerdà, VíctorThis article examines the Fourier expansions of certain non-classical p-adic modular forms of weight one: the eponymous generalised eigertforms of the title, so called because they lie in a generalised eigenspace for the Hecke operators. When this generalised eigenspace contains the theta series attached to a character of a real quadratic field K in which the prime p splits, the coefficients of the attendant generalised eigenform are expressed as p-adic logarithms of algebraic numbers belonging to an idoneous ring class field of K. This suggests an approach toVariational principles for multisymplectic second-order classical field theories
http://hdl.handle.net/2117/78759
Variational principles for multisymplectic second-order classical field theories
Román Roy, Narciso; Prieto Martínez, Pedro Daniel
We state a unified geometrical version of the variational principles for second-order classical field theories. The standard Lagrangian and Hamiltonian variational principles and the corresponding field equations are recovered from this unified framework.
2015-11-04T11:07:30ZRomán Roy, NarcisoPrieto Martínez, Pedro DanielWe state a unified geometrical version of the variational principles for second-order classical field theories. The standard Lagrangian and Hamiltonian variational principles and the corresponding field equations are recovered from this unified framework.Algorithms for chow-heegner points via iterated integrals
http://hdl.handle.net/2117/78758
Algorithms for chow-heegner points via iterated integrals
Darmon, Henri; Daub, Michael; Lichtenstein, Sam; Rotger Cerdà, Víctor
Let E/Q be an elliptic curve of conductor N and let f be the weight 2 newform on G0(N) associated to it by modularity. Building on an idea of S. Zhang, an article by Darmon, Rotger, and Sols describes the construction of so-called Chow-Heegner points, PT,f ¿ E(Q), indexed by algebraic correspondences T ¿ X0(N) × X0(N). It also gives an analytic formula, depending only on the image of T in cohomology under the complex cycle class map, for calculating PT,f numerically via Chen's theory of iterated integrals. The present work describes an algorithm based on this formula for computing the Chow-Heegner points to arbitrarily high complex accuracy, carries out the computation for all elliptic curves of rank 1 and conductor N < 100 when the cycles T arise from Hecke correspondences, and discusses several important variants of the basic construction.
2015-11-04T10:59:38ZDarmon, HenriDaub, MichaelLichtenstein, SamRotger Cerdà, VíctorLet E/Q be an elliptic curve of conductor N and let f be the weight 2 newform on G0(N) associated to it by modularity. Building on an idea of S. Zhang, an article by Darmon, Rotger, and Sols describes the construction of so-called Chow-Heegner points, PT,f ¿ E(Q), indexed by algebraic correspondences T ¿ X0(N) × X0(N). It also gives an analytic formula, depending only on the image of T in cohomology under the complex cycle class map, for calculating PT,f numerically via Chen's theory of iterated integrals. The present work describes an algorithm based on this formula for computing the Chow-Heegner points to arbitrarily high complex accuracy, carries out the computation for all elliptic curves of rank 1 and conductor N < 100 when the cycles T arise from Hecke correspondences, and discusses several important variants of the basic construction.