Spans of Spaces Contained in a Convex Disc Cross An Arc

2002 ◽  
Author(s):  
Thelma West
Keyword(s):  
2014 ◽  
Vol 46 (4) ◽  
pp. 899-918 ◽  
Author(s):  
F. Fodor ◽  
P. Kevei ◽  
V. Vígh

In this paper we generalize some of the classical results of Rényi and Sulanke (1963), (1964) in the context of spindle convexity. A planar convex disc S is spindle convex if it is the intersection of congruent closed circular discs. The intersection of finitely many congruent closed circular discs is called a disc polygon. We prove asymptotic formulae for the expectation of the number of vertices, missed area, and perimeter difference of uniform random disc polygons contained in a sufficiently smooth spindle convex disc.


1990 ◽  
Vol 23 (4) ◽  
pp. 280-280
Author(s):  
H. Nakayama ◽  
A. Kumel ◽  
M. Sakuuai ◽  
M. Takaoka

Author(s):  
Ferenc Fodor

AbstractEggleston (Approximation to plane convex curves. I. Dowker-type theorems. Proc. Lond. Math. Soc. 7, 351–377 (1957)) proved that in the Euclidean plane the best approximating convex n-gon to a convex disc K is always inscribed in K if we measure the distance by perimeter deviation. We prove that the analogue of Eggleston’s statement holds in the hyperbolic plane, and we give an example showing that it fails on the sphere.


10.14444/7041 ◽  
2020 ◽  
Vol 14 (3) ◽  
pp. 308-315
Author(s):  
CHRISTOPHER MIKHAIL ◽  
ROBERT BROCHIN ◽  
LILY EAKER ◽  
BARON S. LONNER

1989 ◽  
Vol 126 (6) ◽  
pp. 615-632 ◽  
Author(s):  
S. Conway Morris ◽  
Chen Menge

AbstractAnabaritids are a distinctive group of early skeletal fossils, with tri-radially symmetrical tubes. They occur in the earliest Cambrian deposits, and seem to be especially characteristic of the Tommotian strata and putative pre-Tommotian units (e.g. Manykay horizon). A detailed redescription ofAnabarites rotundusQian from near Kuanchuanpu, Shaanxi Province emphasizes the degree of morphological variation. New data on shell composition suggest a bilayered structure, the outer unit composed of fibres parallel to growth lines, overlying a distinctive inner lamella with a chevron ultrastructure. Tentative evidence for anabaritids possibly being operculate is presented, the putative operculum being a simple convex disc. More poorly preserved anabaritids from the Yangtze Gorges (Hubei Province) and Meishucun (Yunnan Province) are referred toA. trisulcatus. All these Chinese occurrences of anabaritids are consistent with a lower Tommotian age of the associated faunas, but reliable and precise correlations with other Precambrian-Cambrian boundary sections remain inconclusive.


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