In: Bulletin of the Brazilian Mathematical Society, New Series, 2004, vol. 35, no. 1, p. 83-122
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In: Journal of Mathematical Analysis and Applications, 2010, p. -
In this paper we consider the two species competitive delay plankton allelopathy stimulatory model system. We show the existence and uniqueness of the solution of the deterministic model. Moreover, we study the persistence of the model and the stability properties of its equilibrium points. We illustrate the theoretical results by some numerical simulations.
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In: Journal of Scientific Computing, 2018, vol. 75, no. 3, p. 1757-1775
A method for solving delay Volterra integro-differential equations is introduced. It is based on two applications of linear barycentric rational interpolation, barycentric rational quadrature and barycentric rational finite differences. Its zero–stability and convergence are studied. Numerical tests demonstrate the excellent agreement of our implementation with the predicted convergence...
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In: Annali di Matematica Pura ed Applicata (1923 -), 2020, vol. 199, no. 1, p. 147–186
We prove a Koebe distortion theorem for the average derivative of a quasiconformal mapping between domains in the sub-Riemannian Heisenberg group H1. Several auxiliary properties of quasiconformal mappings between subdomains of H1 are proven, including BMO estimates for the logarithm of the Jacobian. Applications of the Koebe theorem include diameter bounds for images of curves, comparison of...
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In: Mathematische Annalen, 2019, vol. 373, no. 1, p. 237–251
The goal of this note is to affirm a local version of conjecture of Nisse–Sottile [19] on higher convexity of complements of tropical varieties, while providing a family of counter-examples for the global Nisse–Sottle conjecture in any codimension and dimension higher than one. Moreover, it is shown that, surprisingly, this family also provides a family of counter-examples for the...
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In: Annali di Matematica Pura ed Applicata (1923 -), 2017, vol. 196, no. 1, p. 65–83
In this paper, we consider mappings on uniform domains with exponentially integrable distortion whose Jacobian determinants are integrable. We show that such mappings can be extended to the boundary, and moreover, these extensions are exponentially integrable with quantitative bounds. This extends previous results of Chang and Marshall (Am J Math 107(5):1015–1033, 1985) on analytic...
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In: Bulletin of the London Mathematical Society, 2019, p. blms.12276
The Regge symmetry is a set of remarkable relations between two tetrahedra whose edge lengths are related in a simple fashion. It was first discovered as a consequence of an asymptotic formula in mathematical physics. Here, we give a simple geometric proof of Regge symmetries in Euclidean, spherical, and hyperbolic geometry.
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In: Monatshefte für Mathematik, 2016, vol. 179, no. 2, p. 165–189
This paper is about surfaces of infinite topological type. Unlike the case of surfaces of finite type, there are several deformation spaces associated with a surface S of infinite topological type. Such spaces depend on the choice of a basepoint (that is, the choice of a fixed conformal structure or hyperbolic structure on S) and they also depend on the choice of a distance on the set of...
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In: Comptes rendus Mathematique
We construct simply connected smooth manifolds M of dimension 4k ≤ 8 with the following properties: the second homotopy group π₂(M) is finite, M admits a smooth action by the circle S¹ and the Â-genus Â(M) is non-zero.
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In: Topology and its Applications, 2011, vol. 158, no. 1, p. 84-92
We show that the asymptotic growth rate for the minimal cardinality of a set of simple closed curves on a closed surface of genus g which fill and pairwise intersect at most Kgreater-or-equal, slanted1 times is View the MathML source as g→∞. We then bound from below the cardinality of a filling set of systoles by g/log(g). This illustrates that the topological condition that a set of curves...
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