Browsing Articles publicats (Matemàtica) by Title
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New MooreLike Bounds and Some Optimal Families of Abelian Cayley Mixed Graphs
(20200606)Mixed graphs can be seen as digraphs that have both arcs and edges (or digons, that is, two opposite arcs). In this paper, we consider the case where such graphs are Cayley graphs of abelian groups. Such groups can be ... 
New problems related to the valences of (super) edgemagic labelings
(2013)A graph G of order p and size q is edgemagic if there is a bijective function f : V (G) ∪ E(G) −→ {i} p+q i=1 such that f(x) + f(xy) + f(y) = k , for all xy ∈ E(G) . The function f is an edgemagic labeling of G and the ... 
New results for the Mondrian art problem
(Elsevier, 2021)The Mondrian problem consists of dissecting a square of side length n ∈ N into noncongruent rectangles with natural length sides such that the difference d(n) between the largest and the smallest areas of the rectangles ... 
Nilpotent centres via inverse integrating factors
(Cambridge University Press, 201610)In this paper we are interested in the nilpotent center problem of planar analytic monodromic vector fields. It is known that the formal integrability is not enough to characterize such centers. More general objects are ... 
Non existence of almost Moore digraphs of diameter three
(Electronic Journal of Combinatorics, 2008)Almost Moore digraphs appear in the context of the degree/diameter problem as a class of extremal directed graphs, in the sense that their order is one less than the unattainable Moore bound M(d; k) = 1 + d + + dk, where ... 
Nonexistence of limit cycles for planar vector fields
(Texas State University. Department of Mathematics, 2014)This article presents sufficient conditions for the nonexistence of limit cycles for planar vector fields. Classical methods for the nonexistence of limit cycles are connected with the theory developed here. 
Nonsmooth quadratic centers defined in two arbitrary sectors
(Elsevier, 20161125)In this paper we analyze the centerfocus problem of some families of piecewise planar quadratic vector fields on two zones of R2. The zones we consider are two unbounded sectors defined by an arbitrary angle α and a fixed ... 
Nondegenerate centers for Abel polynomial differential equations of second kind
(Elsevier, 2017)In this paper we study the center problem for Abel polynomial differential equations of second kind. Computing the focal values and using modular arithmetics and Gröbner bases we find the center conditions for such systems ... 
Numerical Simulation of NonLinear Models of Reaction—Diffusion for a DGT Sensor
(MDPI, 20200420)In this work, we present a novel strategy for the numerical solution of a coupled system of partial differential equations that describe reaction–diffusion processes of a mixture of metals and ligands that can be absorbed ... 
On bipartitemixed graphs
(Wiley, 20180404)Mixed graphs can be seen as digraphs that have both arcs and edges (or digons, that is, two opposite arcs). In this arti cle, we consider the case where such graphs are bipartite. As main results, we show that in this ... 
On Middle Cube Graphs
(Indonesian Combinatorial Society (InaCombS); Graph Theory and Applications (GTA) Research Centre; University of Newcastle, Australia; Institut Teknologi Bandung (ITB), Indonesia, 2015)We study a family of graphs related to the $n$cube. The middle cube graph of parameter k is the subgraph of $Q_{2k1}$ induced by the set of vertices whose binary representation has either $k1$ or $k$ number of ones. The ... 
On mixed almost Moore graphs of diameter two
(Electronic Journal of Combinatorics, 20160401)Mixed almost Moore graphs appear in the context of the Degree/Diameter problem as a class of extremal mixed graphs, in the sense that their order is one less than the Moore bound for mixed graphs. The problem of their ... 
On super edgemagic decomposable graphs
(Springer, 2012)Let G be any graph and let {Hi}i∈I be a family of graphs such that E(Hi) ∩ E(Hj ) = ∅ when i 6= j, ∪i∈IE(Hi) = E(G) and E(Hi) 6= ∅ for all i ∈ I. In this paper we introduce the concept of {Hi}i∈I super edgemagic decomposable ... 
On the ℓadic valuation of the cardinality of elliptic curves over finite extensions of Fq
(Springer Verlag, 2015)Let E be an elliptic curve defined over a finite field Fq of odd characteristic. Let l≠2 be a prime number different from the characteristic and dividing #E(Fq). We describe how the ladic valuation of the number of points ... 
On the betanumber of forests with isomorphic components
(De Gruyter Open, 2018)The betanumber, β (G), of a graph G is defined to be either the smallest positive integer n for which there exists an injective function f : V (G) → {0, 1, . . . , n} such that each uv ∈ E (G) is labeled f (u) − f (v) ... 
On the center conditions for analytic monodromic degenerate singularities
(World Scientific Publishing, 2012)In this paper we present two methods for detecting centers of monodromic degenerate singularities of planar analytic vector fields. These methods use auxiliary symmetric vector fields can be applied independently that the ... 
On the extensions of the Darboux theory of integrability
(IOP Publishing, 2013)Recently some extensions of the classical Darboux integrability theory to autonomous and nonautonomous polynomial vector fields were completed. The classical Darboux integrability theory and its recent extensions are based ... 
On the Formal Integrability Problem for Planar Differential Systems
(Hindawi Publishing Corporation, 2013)We study the analytic integrability problem through the formal integrability problem and we show its connection, in some cases, with the existence of invariant analytic (sometimes algebraic) curves. From the results ... 
On the Integrability of Liénard systems with a strong saddle
(Elsevier, 2017)We study the local analytic integrability for real Li\'{e}nard systems, $\dot x=yF(x),$ $\dot y= x$, with $F(0)=0$ but $F'(0)\ne0,$ which implies that it has a strong saddle at the origin. First we prove that this problem ... 
On the multiple zeros of a real analytic function with applications to the averaging theory of differential equations
(IOP Publishing, 20181121)In this work we consider real analytic functions $d(z,\la,\e)$, where $d : \Omega \times \mathbb{R}^p \times I \to \Omega$, $\Omega$ is a bounded open subset of $\R$, $I \subset \mathbb{R}$ is an interval containing the ...