Departament de Matemàtiques
http://hdl.handle.net/2117/3917
2016-05-26T04:46:54ZOn the Partition Dimension and the Twin Number of a Graph
http://hdl.handle.net/2117/87267
On the Partition Dimension and the Twin Number of a Graph
Hernando Martín, María del Carmen; Mora Giné, Mercè; Pelayo Melero, Ignacio Manuel
A partition of the vertex set of a connected graph G is a locating partition of G if every vertex is uniquely determined by its vector of distances to the elements of . The partition dimension of G is the minimum cardinality of a locating partition of G . A pair of vertices u;v of a graph G are called twins if they have exactly the same set of neighbors other than u and v . A twin class is a maximal set of pairwise twin vertices. The twin number of a graph G is the maximum cardinality of a twin class of G . In this paper we undertake the study of the partition dimension of a graph by also considering its twin number. This approach allows us to obtain the set of connected graphs of order n 9 having partition dimension n
2016-05-24T10:33:18ZHernando Martín, María del CarmenMora Giné, MercèPelayo Melero, Ignacio ManuelA partition of the vertex set of a connected graph G is a locating partition of G if every vertex is uniquely determined by its vector of distances to the elements of . The partition dimension of G is the minimum cardinality of a locating partition of G . A pair of vertices u;v of a graph G are called twins if they have exactly the same set of neighbors other than u and v . A twin class is a maximal set of pairwise twin vertices. The twin number of a graph G is the maximum cardinality of a twin class of G . In this paper we undertake the study of the partition dimension of a graph by also considering its twin number. This approach allows us to obtain the set of connected graphs of order n 9 having partition dimension nOn the one-phase reduction of the Stefan problem with a variable phase change temperature
http://hdl.handle.net/2117/87232
On the one-phase reduction of the Stefan problem with a variable phase change temperature
Myers, Timothy; Font, F
The one-phase reduction of the Stefan problem, where the phase change temperature is a variable, is analysed. It is shown that problems encountered in previous analyses may be traced back to an incorrectly formulated Stefan condition. Energy conserving reductions for Cartesian, cylindrically and spherically symmetric problems are presented and compared with solutions to the two-phase problem.
2016-05-20T16:56:59ZMyers, TimothyFont, FThe one-phase reduction of the Stefan problem, where the phase change temperature is a variable, is analysed. It is shown that problems encountered in previous analyses may be traced back to an incorrectly formulated Stefan condition. Energy conserving reductions for Cartesian, cylindrically and spherically symmetric problems are presented and compared with solutions to the two-phase problem.Boundary layer analysis and heat transfer of a nanofluid
http://hdl.handle.net/2117/87173
Boundary layer analysis and heat transfer of a nanofluid
MacDevette, M.M.; Myers, Timothy; Wetton, B.
A theoretical model for nanofluid flow, including Brownian motion and thermophoresis, is developed and analysed. Standard boundary layer theory is used to evaluate the heat transfer coefficient near a flat surface. The model is almost identical to previous models for nanofluid flow which have predicted an increase in the heat transfer with increasing particle concentration. In contrast our work shows a marked decrease indicating that under the assumptions of the model (and similar ones) nanofluids do not enhance heat transfer. It is proposed that the discrepancy between our results and previous ones is due to a loose definition of the heat transfer coefficient and various ad hoc assumptions.
2016-05-18T17:53:49ZMacDevette, M.M.Myers, TimothyWetton, B.A theoretical model for nanofluid flow, including Brownian motion and thermophoresis, is developed and analysed. Standard boundary layer theory is used to evaluate the heat transfer coefficient near a flat surface. The model is almost identical to previous models for nanofluid flow which have predicted an increase in the heat transfer with increasing particle concentration. In contrast our work shows a marked decrease indicating that under the assumptions of the model (and similar ones) nanofluids do not enhance heat transfer. It is proposed that the discrepancy between our results and previous ones is due to a loose definition of the heat transfer coefficient and various ad hoc assumptions.Enumerating simplicial decompositions of surfaces with boundaries
http://hdl.handle.net/2117/87102
Enumerating simplicial decompositions of surfaces with boundaries
Bernardi, Olivier; Rué Perna, Juan José
It is well-known that the triangulations of the disc with n + 2 vertices on its boundary are counted by the nth Catalan number C(n) = 1 n+1 (2n n ) . This paper deals with the generalisation of this problem to any compact surface S with boundaries. We obtain the asymptotic number of simplicial decompositions of the surface S with n vertices on its boundary. More generally, we determine the asymptotic number of dissections of S when the faces are d-gons with d belonging to a set of admissible degrees ¿ ¿ {3, 4, 5, . . .}. We also give the limit laws for certain parameters of such dissections
2016-05-17T11:54:09ZBernardi, OlivierRué Perna, Juan JoséIt is well-known that the triangulations of the disc with n + 2 vertices on its boundary are counted by the nth Catalan number C(n) = 1 n+1 (2n n ) . This paper deals with the generalisation of this problem to any compact surface S with boundaries. We obtain the asymptotic number of simplicial decompositions of the surface S with n vertices on its boundary. More generally, we determine the asymptotic number of dissections of S when the faces are d-gons with d belonging to a set of admissible degrees ¿ ¿ {3, 4, 5, . . .}. We also give the limit laws for certain parameters of such dissectionsOn polynomial representation functions for multivariate linear forms
http://hdl.handle.net/2117/87101
On polynomial representation functions for multivariate linear forms
Rué Perna, Juan José
Given an infinite sequence of positive integers A, we prove that for every nonnegative integer k the number of solutions of the equation n = a1 +· · ·+ak, a1, . . . , ak ¿ A, is not constant for n large enough. This result is a corollary of our main theorem, which partially answers a question of S´ark¨ozy and S´os on representation functions for multivariate linear
forms. Additionally, we obtain an Erd¿os-Fuchs type result for a wide variety of representation functions.
2016-05-17T11:46:52ZRué Perna, Juan JoséGiven an infinite sequence of positive integers A, we prove that for every nonnegative integer k the number of solutions of the equation n = a1 +· · ·+ak, a1, . . . , ak ¿ A, is not constant for n large enough. This result is a corollary of our main theorem, which partially answers a question of S´ark¨ozy and S´os on representation functions for multivariate linear
forms. Additionally, we obtain an Erd¿os-Fuchs type result for a wide variety of representation functions.A sensor fault detection methodology in piezoelectric active systems used in structural health monitoring applications
http://hdl.handle.net/2117/87096
A sensor fault detection methodology in piezoelectric active systems used in structural health monitoring applications
Tibaduiza Burgos, Diego Alexander; Anaya Vejar, Maribel; Forero, Edwin; Castro, Rafael; Pozo Montero, Francesc
Damage detection is the basis of the damage identification task in Structural Health Monitoring. A good damage detection process can ensure the adequate work of a SHM System because allows to know early information about the presence of a damage in a structure under evaluation. However this process is based on the premise that all sensors are well installed and they are working properly, however, it is not true all the time. Problems such as debonding, cuts and the use of the sensors under different environmental and operational conditions result in changes in the vibrational response and a bad functioning in the SHM system. As a contribution to evaluate the state of the sensors in a SHM system, this paper describes a methodology for sensor fault detection in a piezoelectric active system. The methodology involves the use of PCA for multivariate analysis and some damage indices as pattern recognition technique and is tested in a blade from a wind turbine where different scenarios are evaluated including sensor cuts and debonding.
2016-05-17T10:27:28ZTibaduiza Burgos, Diego AlexanderAnaya Vejar, MaribelForero, EdwinCastro, RafaelPozo Montero, FrancescDamage detection is the basis of the damage identification task in Structural Health Monitoring. A good damage detection process can ensure the adequate work of a SHM System because allows to know early information about the presence of a damage in a structure under evaluation. However this process is based on the premise that all sensors are well installed and they are working properly, however, it is not true all the time. Problems such as debonding, cuts and the use of the sensors under different environmental and operational conditions result in changes in the vibrational response and a bad functioning in the SHM system. As a contribution to evaluate the state of the sensors in a SHM system, this paper describes a methodology for sensor fault detection in a piezoelectric active system. The methodology involves the use of PCA for multivariate analysis and some damage indices as pattern recognition technique and is tested in a blade from a wind turbine where different scenarios are evaluated including sensor cuts and debonding.Borane polyhedra as building blocks for unknown but potentially isolatable new molecules: extensions based on computations of the known B18H22 isomers
http://hdl.handle.net/2117/87093
Borane polyhedra as building blocks for unknown but potentially isolatable new molecules: extensions based on computations of the known B18H22 isomers
Oliva, Josep M.; Rué Perna, Juan José; Hnyk, Drahomír; Kennedy, John D.; Rosenfeld, Vladimir
Known borane polyhedral cluster characteristics can be used for predicting new architectural constructs. We propose additional structures derived from B18H22 : three positional isomers different from the well-known anti-B18H22 and syn-B18H22 boranes. We have also derived two new cyclic structures based on the condensation of borane pentagonal pyramids and bipyramids. Borane polyhedral concatenation of molecules is also considered from a mathematical point of view.
2016-05-17T09:55:33ZOliva, Josep M.Rué Perna, Juan JoséHnyk, DrahomírKennedy, John D.Rosenfeld, VladimirKnown borane polyhedral cluster characteristics can be used for predicting new architectural constructs. We propose additional structures derived from B18H22 : three positional isomers different from the well-known anti-B18H22 and syn-B18H22 boranes. We have also derived two new cyclic structures based on the condensation of borane pentagonal pyramids and bipyramids. Borane polyhedral concatenation of molecules is also considered from a mathematical point of view.Juan Navarro Loidi , Don Pedro Giannini o las matemáticas de los artilleros del siglo xviii , Segovia: Biblioteca de Ciencia y Artillería.
http://hdl.handle.net/2117/87090
Juan Navarro Loidi , Don Pedro Giannini o las matemáticas de los artilleros del siglo xviii , Segovia: Biblioteca de Ciencia y Artillería.
Massa Esteve, Maria Rosa
2016-05-17T09:22:16ZMassa Esteve, Maria RosaExtending Brickell-Davenport theorem to non-perfect secret sharing schemes
http://hdl.handle.net/2117/86923
Extending Brickell-Davenport theorem to non-perfect secret sharing schemes
Farràs Ventura, Oriol; Padró Laimon, Carles
One important result in secret sharing is the Brickell-Davenport Theorem: every ideal perfect secret sharing scheme de nes a matroid that is uniquely determined by the access structure. Even though a few attempts have been made, there is no satisfactory de nition of ideal secret sharing scheme for the general case, in which non-perfect schemes are considered as well. Without providing another unsatisfactory de nition of ideal non-perfect secret sharing scheme, we present a generalization of the Brickell-Davenport Theorem to the general case. After analyzing that result under a new point of view and identifying its combinatorial nature, we present a characterization of the (not necessarily perfect) secret sharing schemes that are associated to matroids. Some optimality properties of such schemes are discussed.
2016-05-11T10:34:11ZFarràs Ventura, OriolPadró Laimon, CarlesOne important result in secret sharing is the Brickell-Davenport Theorem: every ideal perfect secret sharing scheme de nes a matroid that is uniquely determined by the access structure. Even though a few attempts have been made, there is no satisfactory de nition of ideal secret sharing scheme for the general case, in which non-perfect schemes are considered as well. Without providing another unsatisfactory de nition of ideal non-perfect secret sharing scheme, we present a generalization of the Brickell-Davenport Theorem to the general case. After analyzing that result under a new point of view and identifying its combinatorial nature, we present a characterization of the (not necessarily perfect) secret sharing schemes that are associated to matroids. Some optimality properties of such schemes are discussed.On secret sharing with nonlinear product reconstruction
http://hdl.handle.net/2117/86921
On secret sharing with nonlinear product reconstruction
Cascudo, Ignacio; Cramer, Ronald; Mirandola, Diego; Padró Laimon, Carles; Xing, Chaoping
Multiplicative linear secret sharing is a fundamental notion in the area of secure multi- party computation (MPC) and, since recently, in the area of two-party cryptography as well. In a nutshell, this notion guarantees that \the product of two secrets is obtained as a linear function of the vector consisting of the coordinate-wise product of two respective share-vectors
2016-05-11T10:22:41ZCascudo, IgnacioCramer, RonaldMirandola, DiegoPadró Laimon, CarlesXing, ChaopingMultiplicative linear secret sharing is a fundamental notion in the area of secure multi- party computation (MPC) and, since recently, in the area of two-party cryptography as well. In a nutshell, this notion guarantees that \the product of two secrets is obtained as a linear function of the vector consisting of the coordinate-wise product of two respective share-vectors