Regular polygons and transfinite diameter

Grandcolas, Michel

doi:10.1017/s0004972700018487

Cited by 3 publications

(3 citation statements)

References 7 publications

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“…Further generalizations of this concept were made by them and by F. Leja. Finally E. Hille summarized and unified the previous generalizations (see [14]; but for some recent related result, see, e.g., [7], [13] and [18]).…”

Section: Ess Diam(a) := Inf{diam(b)|b Is µ-Measurable B ⊆ a µ(B) = mentioning

confidence: 59%

Strongly mixing transformations and geometric diameters

Fatkić¹,

Brkić²

2012

SJM

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In this paper, we investigate metric properties and dispersive effects of strongly mixing transformations on general metric spaces endowed with a finite measure; in particular, we investigate their connections with the theory of generalized (geometric) diameters on general metric spaces. We first show that the known result by Rice [17,Theorem 2] (motivated by some physical phenomena and offer some clarifications of these phenomena), which is a substantial improvement of Theorems 1 and 2 due to Erber, Schweizer and Sklar [4], can be generalized in such a way that this result remains valid when "ordinary diameter" is replaced by "geometric diameter of any finite order". Next we show that "ordinary essential diameter" in the mentioned Rice's result can be replaced by "essential geometric diameter of any finite order". These results also complement the previous results of Fatkić [ 6,8,10], Saff [18] and Sempi [20].

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Section: Ess Diam(a) := Inf{diam(b)|b Is µ-Measurable B ⊆ a µ(B) = mentioning

confidence: 59%

Strongly mixing transformations and geometric diameters

Fatkić¹,

Brkić²

2012

SJM

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“…It is related to the notions of logarithmic capacity and the Chebysheff constant [Ahlfors 1973;Hille 1962;Tsuji 1959]. Some extremal problems involving the transfinite diameter and n-diameter of planar sets were studied in [Burckel et al 2008;Dubinin 1986;Duren and Schiffer 1991;Grandcolas 2000;Grandcolas 2002;Reich and Schiffer 1964].…”

Section: Extremal Problem For N-diametermentioning

confidence: 99%

Untitled

2012

Involve

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The steady states of a mathematical model for the dynamics of Chagas disease, developed by Spagnuolo et al., are studied and numerically simulated. The model consists of a system of four nonlinear ordinary differential equations for the total number of domestic carrier insects, and the infected insects, infected humans, and infected domestic animals. The equation for the vector dynamics has a growth rate of the blowfly type with a delay. In the parameter range of interest, the model has two unstable disease-free equilibria and a globally asymptotically stable (GAS) endemic equilibrium. Numerical simulations, based on the fourth-order Adams-Bashforth predictor corrector scheme for ODEs, depict the various cases.

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