Browsing Articles publicats (Matemàtica) by Title
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The center problem and composition condition for Abel differential equations
(Elsevier, 2015)The classical Poincaré centerfocus problem for planar polynomial systems of ordinary differential equations can be transformed, in certain particular cases, to the center problem of a trigonometric Abel differential ... 
The center problem for a 2:3 resonant cubic Lotka–Volterra system
(Elsevier, 2013)In this paper we obtain conditions on the coefficients of a cubic Lotka–Volterra system of the form equation(1) x=x(2a20x2a11xya02y2), ẏ=y(3+b20x2+b11xy+b02y2), which fulfillment yields the existence in a ... 
The cubic polynomial differential systems with two circles as algebraic limit cycles
(Walter de Gruyter GmbH, 2018)In this paper we characterize all cubic polynomial differential systems in the plane having two circles as invariant algebraic limit cycles. 
The cyclicity of polynomial centers via the reduced bautin depth
(American Mathematical Society, 2016)We describe a method for bounding the cyclicity of the class of monodromic singularities of polyn omial planar families of vector fields X λ with an analytic Poincar e first return map having a polynomial Bautin ideal B ... 
The Degree/Diameter Problem for Mixed Abelian Cayley Graphs
(Elsevier, 20171120)This paper investigates the upper bounds for the number of vertices in mixed abelian Cayley graphs with given degree and diameter. Additionally, in the case when the undirected degree is equal to one, we give a construction ... 
The diameter of cyclic Kautz digraphs
(Faculty of Sciences and Mathematics, University of Nis, Serbia, 2017)We present a new kind of digraphs, called cyclic Kautz digraphs CK(d, ɭ), which are subdigraphs of the wellknown Kautz digraphs K(d,ɭ). The latter have the smallest diameter among all digraphs with their number of ... 
The Hopf cyclicity of the centers of a class of quintic polynomial vector fields
(Elsevier, 20150120)We consider families of planar polynomial vector fields having a singularity with purely imaginary eigenvalues for which a basis of its Bautin ideal B is known. We provide an algorithm for computing an upper bound of the ... 
The inverse integrating factor and the Poincaré map
(American Mathematical Society, 2010)This work is concerned with planar real analytic differential systems with an analytic inverse integrating factor defined in a neighborhood of a regular orbit. We show that the inverse integrating factor defines an ... 
The jumping knight and other (super) edgemagic constructions
(Springer, 2014)Let G be a graph of order p and size q with loops allowed. A bijective function f:V(G)∪E(G)→{i}p+qi=1 is an edgemagic labeling of G if the sum f(u)+f(uv)+f(v)=k is independent of the choice of the edge uv. The constant k ... 
The Manhattan Product of Digraphs
(Indonesian Combinatorial Society (InaCombS); Graph Theory and Applications (GTA) Research Centre; University of Newcastle, Australia; Institut Teknologi Bandung (ITB), Indonesia, 2013)We study the main properties of a new product of bipartite digraphs which we call Manhattan product. This product allows us to understand the subjacent product in the Manhattan street networks and can be used to built other ... 
The null divergence factor
(Universitat Autònoma de Barcelona. Departament de Matemàtiques, 1997)Let (P, Q) be a C 1 vector field defined in a open subset U ⊂ R2 . We call a null divergence factor a C 1 solution V (x, y) of the equation P ∂V + Q ∂V = ∂P + ∂Q V . In previous works ∂x ∂y ∂x ∂y it has been ... 
The power of digraph products applied to labelings
(Elsevier, 2012)The ⊗hproduct was introduced in 2008 by FigueroaCenteno et al. as a way to construct new families of (super) edgemagic graphs and to prove that some of those families admit an exponential number of (super) edgemagic ... 
The problem of distinguishing between a center and a focus for nilpotent and degenerate analytic systems
(Elsevier, 2006)In this work we study the centers of planar analytic vector fields which are limit of linear type centers. It is proved that all the nilpotent centers are limit of linear type centers and consequently the Poincaré–Liapunov ... 
The role of algebraic solutions in planar polynomial differential systems
(Cambridge University Press, 2007)We study a planar polynomial differential system, given by . We consider a function , where gi(x) are algebraic functions of with ak(x) and algebraic functions, A0(x,y) and A1(x,y) do not share any common factor, h2(x) is ... 
The spectra of lifted digraphs
(Springer, 20190102)We present a method to derive the complete spectrum of the lift Γα of a base digraph Γ , with voltage assignment α on a (finite) group G. The method is based on assigning to Γ a quotientlike matrix whose entries are ... 
The spectra of subKautz and cyclic Kautz digraphs
(Elsevier, 2017)Kautz digraphs K(d, `) are a wellknown family of dense digraphs, widely studied as a good model for interconnection networks. Closely related with these, the cyclic Kautz CK(d, `) and the subKautz sK(d, 2) digraphs were ... 
The spectral excess theorem for graphs with few eigenvalues whose distance 2 or distance1or2 graph is strongly regular
(Taylor & Francis, 20180713)We study regular graphs whose distance2 graph or distance1or2 graph is strongly regular. We provide a characterization of such graphs Γ (among regular graphs with few distinct eigenvalues) in terms of the spectrum and ... 
The threedimensional center problem for the zeroHopf singularity
(American Institute of Mathematical Sciences, 20160301)In this work we extend wellknown techniques for solving the Poincar\'eLyapunov nondegenerate analytic center problem in the plane to the 3dimensional center problem at the zeroHopf singularity. Thus we characterize the ... 
The unique mixed almost moore graph with parameters k = 2, r = 2 and z = 1
(World Scientific Publishing, 20171102)A natural upper bound for the maximum number of vertices in a mixed graph with maximum undirected degree r, maximum directed outdegree z and diameter k is given by the mixed Moore bound. Graphs with order attaining the ... 
Towards a quantum universe
(Springer Verlag, 2012)In this short review we study the state of the art of the great problems in cosmology and their interrelationships. The reconciliation of these problems passes undoubtedly through the idea of a quantum universe.