Articles publicats (Matemàtica)

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Open Access
A blow-up method to prove formal integrability for some planar differential systems
(Shanghai Normal University & Wilmington Scientific Publisher, 2018) Fercec, Brigita; Giné, Jaume
In this work we provide an effective method to prove the formal integrability of the resonant saddles. The method is based on the use of a blow-up and the resolution of a recurrence differential equation using induction. Using the method some open integrability problems for certain resonant saddles are solved.
Open Access
A characterization of the generalized Liénard polynomial differential systems having invariant algebraic curves
(Elsevier, 2022) Giné, Jaume; Llibre, Jaume
The generalized Liénard polynomial differential systems are the differential systems of the form x′ = y, y′ = − f(x)y − g(x), where f and g are polynomials. We characterize all the generalized Liénard polynomial differential systems having an invariant algebraic curve. We show that the first four higher coefficients of the polynomial in the variable y, defining the invariant algebraic curve, determine completely the generalized Liénard polynomial differential system. This fact does not hold for arbitrary polynomial differential systems.
Open Access
A Chebyshev criterion for Abelian integrals
(American Mathematical Society, 2010) Grau Montaña, Maite; Mañosas, Francesc; Villadelprat, Jordi
We present a criterion that provides an easy sufficient condition in order that a collection of Abelian integrals has the Chebyshev property. This condition involves the functions in the integrand of the Abelian integrals and can be checked, in many cases, in a purely algebraic way. By using this criterion, several known results are obtained in a shorter way and some new results, which could not be tackled by the known standard methods, can also be deduced.
Open Access
A computational model approach to assess the effect of climate change on the growth and development of tadpoles
(Elsevier, 2021) Colomer, M. Àngels (Maria Àngels); Margalida, Antoni; Sanuy, Isabel; Llorente, Gustavo A.; Sanuy i Castells, Delfí; Pujol-Buixó, Eudal
All of the environmental conditions in nature act on an organism simultaneously. However, in experimental studies of the factors influencing metamorphosis, each factor needs to be examined individually in order to disentangle its specific effects. However, it is challenging to then build properly integrated models which include data on all of the different factors evaluated in different experiments. This study set out to develop a predictive model which could synthesize the results of several experiments on survival, development and growth of Natterjack toad (Epidalea calamita) tadpole guilds. The proposed Population Dynamic P System (PDP) model enables estimates of growth and development during the larval phase, under different environmental conditions, weather conditions, predator density, and pond characteristics and management. The architecture of the model allows the inclusion of an indefinite number of parameters and interactions, with all inputs interacting in parallel, and enables solutions to complex modeling approaches. Using the model with a range of field data, we found that the importance of predation pressure on Natterjack toad tadpole guilds exceeds the potential effects of variations in temperature and precipitation. The impact of introduced invasive predators therefore arguably poses the greatest threat to this species. This type of model holds promise as a reliable management and conservation tool for this and other species, especially where interactions between environmental factors make the impacts of individual factors difficult to predict.
Open Access
A Construction for Providing Reusability to Mobile Phone-Based e-Tickets
(IEEE, 2020) Borges Llorens, Ricard; Sebé Feixas, Francesc
Nowadays, the use of electronic tickets in public transport is a reality. Several mobile phone-based e-ticket systems have been proposed so far. Even so, very few of them include reusability in the sense that a single e-ticket allows to make several journeys. Although the identity of users is usually hidden behind a pseudonym, the existing proposals providing reusability allow the system to link all the journeys made with a given e-ticket. In this paper we present a privacy-preserving construction allowing to endow a mobile phone-based e-ticket system with reusability. The privacy of users is proven to be preserved even assuming an internal attacker with full access to all the information managed by the system servers. All the sensitive interactions of a user with the system keep anonymous and unlinkable. Further, as a result of an inspection, the system is only able to determine whether the inspected user is allowed to make the current journey.
Open Access
A counterexample to the composition condition conjecture for polynomial Abel differential equations
(Cambridge University Press, 2019) Giné, Jaume; Grau Montaña, Maite; Santallusia Esvert, Xavier
Polynomial Abel differential equations are considered a model problem for the classical Poincaré center–focus problem for planar polynomial systems of ordinary differential equations. In the last few decades, several works pointed out that all centers of the polynomial Abel differential equations satisfied the composition conditions (also called universal centers). In this work we provide a simple counterexample to this conjecture.
Open Access
A differential approach for bounding the index of graphs under perturbations
(Electronic Journal of Combinatorics, 2011-09-02) Dalfó, Cristina; Fiol Mora, Miguel Ángel; Garriga, Ernest
This paper presents bounds for the variation of the spectralradiusλ(G) ofa graphGafter some perturbations or local vertex/edge modifications ofG. Theperturbations considered here are the connection of a new vertex with, say,gverticesofG, the addition of a pendant edge (the previous case withg= 1) and the additionof an edge. The method proposed here is based on continuous perturbations andthe study of their differential inequalities associated. Within rather economicalinformation (namely, the degrees of the vertices involved in the perturbation), thebest possible inequalities are obtained. In addition, the cases when equalities areattained are characterized. The asymptotic behavior of thebounds obtained isalso discussed. For instance, ifGis a connected graph andGudenotes the graphobtained fromGby adding a pendant edge at vertexuwith degreeδu, then,λ(Gu)≤λ(G) +δuλ3(G)+ o(1λ3(G))
Open Access
A Digital Cash Paradigm with Valued and No-Valued e-Coins
(MDPI, 2021) Borges Llorens, Ricard; Sebé Feixas, Francesc
Digital cash is a form of money that is stored digitally. Its main advantage when compared to traditional credit or debit cards is the possibility of carrying out anonymous transactions. Diverse digital cash paradigms have been proposed during the last decades, providing different approaches to avoid the double-spending fraud, or features like divisibility or transferability. This paper presents a new digital cash paradigm that includes the so-called no-valued e-coins, which are e-coins that can be generated free of charge by customers. A vendor receiving a payment cannot distinguish whether the received e-coin is valued or not, but the customer will receive the requested digital item only in the former case. A straightforward application of bogus transactions involving no-valued e-coins is the masking of consumption patterns. This new paradigm has also proven its validity in the scope of privacy-preserving pay-by-phone parking systems, and we believe it can become a very versatile building block in the design of privacy-preserving protocols in other areas of research. This paper provides a formal description of the new paradigm, including the features required for each of its components together with a formal analysis of its security.
Open Access
A general method to obtain the spectrum and local spectra of a graph from its regular partitions
(International Linear Algebra Society, 2020-07-12) Dalfó, Cristina; Fiol Mora, Miguel Ángel
It is well known that, in general, part of the spectrum of a graph can be obtained from the adjacency matrix of its quotient graph given by a regular partition. In this paper, a method that gives all the spectrum, and also the local spectra, of a graph from the quotient matrices of some of its regular partitions, is proposed. Moreover, from such partitions, the C-local multiplicities of any class of vertices C is also determined, and some applications of these parameters in the characterization of completely regular codes and their inner distributions are described. As examples, it is shown how to find the eigenvalues and (local) multiplicities of walk-regular, distance-regular, and distance-biregular graphs.
Open Access
A Green Strategy for Federated and Heterogeneous Clouds with Communicating Workloads
(Hindawi Publishing Corporation, 2014-07) Mateo Fornés, Jordi; Vilaplana Mayoral, Jordi; Solsona Tehàs, Francesc; Pla Aragonés, Lluís Miquel; Lérida Monsó, Josep Lluís
Providers of cloud environments must tackle the challenge of configuring their system to provide maximal performance while minimizing the cost of resources used. However, at the same time, they must guarantee an SLA (service-level agreement) to the users. The SLA is usually associated with a certain level of QoS (quality of service). As response time is perhaps the most widely used QoS metric, it was also the one chosen in this work. This paper presents a green strategy (GS) model for heterogeneous cloud systems. We provide a solution for heterogeneous job-communicating tasks and heterogeneous VMs that make up the nodes of the cloud. In addition to guaranteeing the SLA, the main goal is to optimize energy savings. The solution results in an equation that must be solved by a solver with nonlinear capabilities. The results obtained from modelling the policies to be executed by a solver demonstrate the applicability of our proposal for saving energy and guaranteeing the SLA.
Open Access
A method for characterizing nilpotent centers
(Elsevier, 2014) Giné, Jaume; Llibre, Jaume
To characterize when a nilpotent singular point of an analytic differential system is a center is of particular interest, first for the problem of distinguishing between a focus and a center, and after for studying the bifurcation of limit cycles from it or from its period annulus. We give an effective algorithm in the search of necessary conditions for detecting nilpotent centers based in recent developments. Moreover we survey the last results on this problem and illustrate our approach by means of examples.
Open Access
A Moore-like bound for mixed abelian Cayley graphs
(Elsevier B.V., 2016-09-26) López Lorenzo, Ignacio; Pérez Rosés, Hebert; Pujolàs Boix, Jordi
We give an upper bound for the number of vertices in mixed abelian Cayley graphs with given degree and diameter.
Open Access
A new approach to gross error detection for GPS networks
(Elsevier, 2019) Dalfó, Cristina; Fiol Mora, Miguel Ángel
We present a new matrix-based approach to detect and correct gross errors in GPS geodetic control networks. The study is carried out by introducing a new matrix, whose entries are powers of a (real or complex) variable, which fully represents the network.
Open Access
A new general family of mixed graphs
(Elsevier, 2018) Dalfó, Cristina
A new general family of mixed graphs is presented, which generalizes both the pancake graphs and the cycle prefix digraphs. The obtained graphs are vertex transitive and, for some values of the parameters, they constitute the best infinite families with asymptotically optimal (or quasi-optimal) number of vertices for their diameter.
Open Access
A new labeling construction from the ⊗h-product
(Elsevier, 2017) López Masip, Susana-Clara; Muntaner Batle, Francesc Antoni; Prabu, M.
The -product that is referred in the title was introduced in 2008 as a generalization of the Kronecker product of digraphs. Many relations among labelings have been obtained since then, always using as a second factor a family of super edge-magic graphs with equal order and size. In this paper, we introduce a new labeling construction by changing the role of the factors. Using this new construction the range of applications grows up considerably. In particular, we can increase the information about magic sums of cycles and crowns.
Open Access
A New Normal Form for Monodromic Nilpotent Singularities of Planar Vector Fields
(Springer, 2021) Algaba, Antonio; García, Cristóbal; Giné, Jaume
In this work, we present a new technique for solving the center problem for nilpotent singularities which consists of determining a new normal form conveniently adapted to study the center problem for this singularity. In fact, it is a pre-normal form with respect to classical Bogdanov–Takens normal formal and it allows to approach the center problem more efficiently. The new normal form is applied to several examples.
Open Access
A new sufficient condition in order that the real Jacobian conjecture in R2 holds
(Elsevier, 2021) Giné, Jaume; Llibre, Jaume
Let F = (f, g) : R2 → R2 be a polynomial map such that det(DF (x, y)) is nowhere zero and F (0, 0) = (0, 0). In this work we give a new sufficient condition for the injectivity of F . We also state a conjecture when det(DF (x, y)) = constant = 0 and F (0, 0) = (0, 0) equivalent to the Jacobian conjecture.
Open Access
A note on a new general family of deterministic hierarchical networks
(World Scientific Publishing, 2019) Dalfó, Cristina; Fiol Mora, Miguel Ángel
It is known that many networks modeling real-life complex systems are small-word (large local clustering and small diameter) and scale-free (power law of the degree distribution), and very often they are also hierarchical. Although most of the models are based on stochastic methods, some deterministic constructions have been recently proposed, because this allows a better computation of their properties. Here a new deterministic family of hierarchical networks is presented, which generalizes most of the previous proposals, such as the so-called binomial tree. The obtained graphs can be seen as graphs on alphabets (where vertices are labeled with words of a given alphabet, and the edges are defined by a specific rule relating different words). This allows us the characterization of their main distance-related parameters, such as the radius and diameter. Moreover, as a by-product, an efficient shortest-path local algorithm is proposed.
Open Access
A note on Liouvillian first integrals and invariant algebraic curves
(Elsevier, 2013-02) Giné, Jaume; Grau Montaña, Maite; Llibre, Jaume
In this work we study the existence and non-existence of finite invariant algebraic curves for a complex planar polynomial differential system having a Liouvillian first integral.
Open Access
A note on the order of iterated line digraphs
(Wiley Periodicals Inc., 2016-06) Dalfó, Cristina; Fiol Mora, Miguel Ángel
Given a digraph G, we propose a new method to find therecurrence equation for the number of vertices nk of the k-iterated linedigraph Lk(G), for k≥0, where L0(G)=G. We obtain this result by usingthe minimal polynomial of a quotient digraph π(G) of G