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Abstrakty
Ellipses will be considered as subsets of suitably defined Minkowski planes in such a way that, additionally to the well-known area content property A(r) = Π (a,b) r 2, the number Π (a,b) = abΠ reflects a generalized circumference property U (a,b)(r) = 2Π (a,b) r of the ellipses E (a,b)(r) with main axes of lengths 2ra and 2rb, respectively. In this sense, the number Π (a,b) is an ellipse number w.r.t. the Minkowski functional r of the reference set E (a,b)(1). This approach is closely connected with a generalization of the method of indivisibles and avoids elliptical integrals. Further, several properties of both a generalized arc-length measure and the ellipses numbers will be discussed, e.g. disintegration of the Lebesgue measure and an elliptically contoured Gaussian measure indivisiblen representation, wherein the ellipses numbers occur in a natural way as norming constants.
Słowa kluczowe
ellipse number
generalized arc-length
generalized perimeter
generalized method of indivisibles
isoperimetric constant
Minkowski plane
geometric measure representation
intersection-percentage function
generalized uniform distribution on the ellipse
generalized trigonometric functions
generalized elliptical coordinates
disintegration of Lebesgue measure
elliptically contoured Gaussian measure representation
stochastic representation
Wydawca
Czasopismo
Rocznik
Tom
Strony
165--179
Opis fizyczny
Bibliogr. 3 poz.
Twórcy
autor
- University of Rostock, Ulmenstr. 69, Haus 3, 18057 Rostock, Germany, wolf-dieter.richter@uni-rostock.de
Bibliografia
- [1] H. Busemann, The isoperimetric problem in the Minkowski plane, Amer. J. Math. 69 (1947), 863-871.
- [2] W.-D. Richter, Generalized spherical and simplicial coordinates, J. Math. Anal. Appl. 336(2007), 1187-1202.
- [3] W.-D. Richter, On l2,p-circle numbers, Lith. Math. J. 48 (2008), no. 2, 228-234.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-LOD7-0033-0021