scholarly journals An Extremum Problem for Convex Polygons

2010 ◽  
Vol 1 ◽  
pp. SBII-173-SBII-176
Author(s):  
Gerhard Larcher
Keyword(s):  
Extremum Problem ◽  
Convex Polygons

Solution of inverse coefficient problem for fractional anomalous diffusion equation

2012 ◽  
Vol 9 (2) ◽  
pp. 65-70
Author(s):  
E.V. Karachurina ◽  
S.Yu. Lukashchuk
Keyword(s):  
Anomalous Diffusion ◽  
Fractional Derivatives ◽  
Descent Method ◽  
Extremum Problem ◽  
Steepest Descent Method ◽  
Coefficient Problem ◽  
Caputo Fractional Derivatives ◽  
Inverse Coefficient Problem ◽  
Residual Functional ◽  
Inverse Coefficient

An inverse coefficient problem is considered for time-fractional anomalous diffusion equations with the Riemann-Liouville and Caputo fractional derivatives. A numerical algorithm is proposed for identification of anomalous diffusivity which is considered as a function of concentration. The algorithm is based on transformation of inverse coefficient problem to extremum problem for the residual functional. The steepest descent method is used for numerical solving of this extremum problem. Necessary expressions for calculating gradient of residual functional are presented. The efficiency of the proposed algorithm is illustrated by several test examples.

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

Algorithmica ◽  
2021 ◽  
Author(s):  
Gill Barequet ◽  
Minati De ◽  
Michael T. Goodrich
Keyword(s):  
Voronoi Diagrams ◽  
Convex Polygons

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

Koedoe ◽  
2015 ◽  
Vol 57 (1) ◽  
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.

scholarly journals Small distances in convex polygons

2013 ◽  
Vol 313 (18) ◽  
pp. 1767-1782 ◽  
Author(s):  
Filip Morić
Keyword(s):  
Convex Polygons

AN APPROXIMATION ALGORITHM FOR LOCATING MAXIMAL DISKS WITHIN CONVEX POLYGONS

2011 ◽  
Vol 21 (06) ◽  
pp. 661-684
Author(s):  
HIROFUMI AOTA ◽  
TAKURO FUKUNAGA ◽  
HIROSHI NAGAMOCHI
Keyword(s):  
Approximation Algorithm ◽  
Convex Polygon ◽  
Computation Time ◽  
Approximation Ratio ◽  
Convex Polygons ◽  
The Given

This paper considers a problem of locating the given number of disks into a container so that the area covered by the disks is maximized. In the problem, the radii of the disks can be changed arbitrarily unless they overlap outside of the container, and the disks are allowed to overlap with each other. We present an approximation algorithm for this problem assuming that the container is a convex polygon. Our algorithm achieves approximation ratio (0.78 - ϵ) for any small ϵ > 0. Since the computation time of our algorithm depends on the number of corners of the convex polygon exponentially, we also give a heuristic to reduce the number of corners.

An extremum problem for the power moment of a convex polygon contained in a disc

2021 ◽  
Vol 21 (4) ◽  
pp. 599-609
Author(s):  
Irmina Herburt ◽  
Shigehiro Sakata
Keyword(s):  
Convex Polygon ◽  
Extremum Problem ◽  
Classical Theorem ◽  
Power Moment ◽  
Area Functional ◽  
The Mean

Abstract In this paper, we investigate an extremum problem for the power moment of a convex polygon contained in a disc. Our result is a generalization of a classical theorem: among all convex n-gons contained in a given disc, the regular n-gon inscribed in the circle (up to rotation) uniquely maximizes the area functional. It also implies that, among all convex n-gons contained in a given disc and containing the center in those interiors, the regular n-gon inscribed in the circle (up to rotation) uniquely maximizes the mean of the length of the chords passing through the center of the disc.

An Algorithm for a Near Optimal NC Path Generation in Staircase (Lase) Traversal of Convex Polygonal Surfaces

1999 ◽  
Vol 122 (1) ◽  
pp. 182-190 ◽  
Author(s):  
S. V. Kamarthi ◽  
S. T. S. Bukkapatnam ◽  
S. Hsieh
Keyword(s):  
Rapid Prototyping ◽  
Path Length ◽  
Tool Path ◽  
Path Generation ◽  
Convex Polygons ◽  
Sweep Angle ◽  
Pocket Milling ◽  
Different Shapes ◽  
Path Lengths ◽  
Better Than

This paper presents an analytical model of the tool path for staircase traversal of convex polygonal surfaces, and an algorithm—referred to as OPTPATH—developed based on the model to find the sweep angle that gives a near optimal tool path length. The OPTPATH algorithm can be used for staircase traversal with or without (i) overlaps between successive sweep passes, and (ii) rapid traversal along edge passes. This flexibility of OPTPATH renders it applicable not only to conventional operations such as face and pocket milling, but also to other processes such as robotic deburring, rapid prototyping, and robotic spray painting. The effective tool path lengths provided by OPTPATH are compared with those given by the following two algorithms: (i) a common industrial heuristic—referred to as the IH algorithm—and (ii) an algorithm proposed by Prabhu et al. (Prabhu, P. V., Gramopadhye, A. K., and Wang, H. P., 1990, Int. J. Prod. Res., 28, No. 1, pp. 101–130) referred to as PGW algorithm. This comparison is conducted using 100 randomly generated convex polygons of different shapes and a set of seven different tool diameters. It is found that OPTPATH performs better than both the IH as well as PGW algorithms. The superiority of OPTPATH over the two algorithms becomes more pronounced for large tool diameters. [S1087-1357(00)71501-2]

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