Barker–Larman Problem for Convex Polygons in the Hyperbolic Plane

Vasyl Gorkavyy; Dmytro Kalinin

doi:10.1007/s00025-015-0458-y

Barker–Larman Problem for Convex Polygons in the Hyperbolic Plane

Results in Mathematics ◽

10.1007/s00025-015-0458-y ◽

2015 ◽

Vol 68 (3-4) ◽

pp. 519-525 ◽

Cited By ~ 1

Author(s):

Vasyl Gorkavyy ◽

Dmytro Kalinin

Keyword(s):

Hyperbolic Plane ◽

Convex Polygons

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Aperiodic tilings of the hyperbolic plane by convex polygons

Israel Journal of Mathematics ◽

10.1007/bf02764015 ◽

1998 ◽

Vol 107 (1) ◽

pp. 319-325 ◽

Cited By ~ 12

Author(s):

G. A. Margulis ◽

S. Mozes

Keyword(s):

Hyperbolic Plane ◽

Convex Polygons ◽

Aperiodic Tilings

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Certain Two-Dimensional Local Limit Theorems with Applications to the Statistics of Convex Polygons

SSRN Electronic Journal ◽

10.2139/ssrn.3536633 ◽

2020 ◽

Author(s):

Sakhavet Zarbaliev

Keyword(s):

Limit Theorems ◽

Local Limit ◽

Two Dimensional ◽

Convex Polygons ◽

Local Limit Theorems

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Convex-Straight-Skeleton Voronoi Diagrams for Segments and Convex Polygons

Algorithmica ◽

10.1007/s00453-021-00824-9 ◽

2021 ◽

Author(s):

Gill Barequet ◽

Minati De ◽

Michael T. Goodrich

Keyword(s):

Voronoi Diagrams ◽

Convex Polygons

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Foraging range and habitat use by Cape Vulture Gyps coprotheres from the Msikaba colony, Eastern Cape province, South Africa

Koedoe ◽

10.4102/koedoe.v57i1.1240 ◽

2015 ◽

Vol 57 (1) ◽

Cited By ~ 14

Author(s):

Morgan B. Pfeiffer ◽

Jan A. Venter ◽

Colleen T. Downs

Keyword(s):

South Africa ◽

Protected Areas ◽

Breeding Season ◽

Movement Ecology ◽

Kernel Density ◽

Eastern Cape Province ◽

Eastern Cape ◽

Convex Polygons ◽

Density Estimates ◽

Kernel Density Estimates

Despite the extent of subsistence farmland in Africa, little is known about endangered species that persist within them. The Cape Vulture (Gyps coprotheres) is regionally endangered in southern Africa and at least 20% of the population breeds in the subsistence farmland area previously known as the Transkei in the Eastern Cape province of South Africa. To understand their movement ecology, adult Cape Vultures (n = 9) were captured and fitted with global positioning system/global system for mobile transmitters. Minimum convex polygons (MCPs),and 99% and 50% kernel density estimates (KDEs) were calculated for the breeding and non breeding seasons of the Cape Vulture. Land use maps were constructed for each 99% KDE and vulture locations were overlaid. During the non-breeding season, ranges were slightly larger(mean [± SE] MCP = 16 887 km2 ± 366 km2) than the breeding season (MCP = 14 707 km2 ± 2155 km2). Breeding and non-breeding season MCPs overlapped by a total of 92%. Kernel density estimates showed seasonal variability. During the breeding season, Cape Vultures used subsistence farmland, natural woodland and protected areas more than expected. In the non-breeding season, vultures used natural woodland and subsistence farmland more than expected, and protected areas less than expected. In both seasons, human-altered landscapes were used less, except for subsistence farmland.Conservation implications: These results highlight the importance of subsistence farm land to the survival of the Cape Vulture. Efforts should be made to minimise potential threats to vultures in the core areas outlined, through outreach programmes and mitigation measures.The conservation buffer of 40 km around Cape Vulture breeding colonies should be increased to 50 km.

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