Improved bound for the disk-packing constant

1973 ◽  
Vol 9 (1) ◽  
pp. 115-116
Author(s):  
David W. Boyd
Keyword(s):  
Disk Packing

scholarly journals PROPERTIES OF THE INVARIANT DISK PACKING IN A MODEL BANDPASS SIGMA–DELTA MODULATOR

2003 ◽  
Vol 13 (03) ◽  
pp. 631-641 ◽  
Author(s):  
PETER ASHWIN ◽  
XIN-CHU FU ◽  
JONATHAN DEANE
Keyword(s):  
Phase Space ◽  
Analytic Functions ◽  
Parameter Family ◽  
Sigma Delta Modulator ◽  
Sigma Delta ◽  
Disk Packing ◽  
Piecewise Isometries ◽  
Map Operations ◽  
Countably Infinite ◽  
Parameter Values

In this paper we discuss the packing properties of invariant disks defined by periodic behavior of a model for a bandpass Σ–Δ modulator. The periodically coded regions form a packing of the forward invariant phase space by invariant disks. For this one-parameter family of PWIs, by introducing codings underlying the map operations we give explicit expressions for the centers of the disks by analytic functions of the parameters, and then show that tangencies between disks in the packings are very rare; more precisely they occur on parameter values that are at most countably infinite. We indicate how similar results can be obtained for other plane maps that are piecewise isometries.

Improved bounds for the disk-packing constant

1973 ◽  
Vol 9 (1) ◽  
pp. 99-106 ◽  
Author(s):  
David W. Boyd
Keyword(s):  
Disk Packing

The disk-packing constant

1971 ◽  
Vol 7 (2-3) ◽  
pp. 182-193 ◽  
Author(s):  
David W. Boyd
Keyword(s):  
Disk Packing

scholarly journals Poisson disk sampling through disk packing

2015 ◽  
Vol 1 (1) ◽  
pp. 17-26 ◽  
Author(s):  
Guanghui Liang ◽  
Lin Lu ◽  
Zhonggui Chen ◽  
Chenglei Yang
Keyword(s):  
Disk Packing ◽  
Poisson Disk Sampling

The disk-packing constant

1971 ◽  
Vol 7 (1) ◽  
pp. 113-114
Author(s):  
David W. Boyd
Keyword(s):  
Disk Packing

scholarly journals A LOWER BOUND ON THE AREA OF A 3-COLOURED DISK PACKING

2010 ◽  
Vol 20 (03) ◽  
pp. 341-360 ◽  
Author(s):  
PETER BRASS ◽  
FERRAN HURTADO ◽  
BENJAMIN LAFRENIERE ◽  
ANNA LUBIW
Keyword(s):  
Lower Bound ◽  
Pairwise Disjoint ◽  
Channel Assignment ◽  
Wireless Access ◽  
Disjoint Subset ◽  
Standard Practice ◽  
Disk Packing ◽  
Pairwise Disjoint Subset ◽  
Selected Subset ◽  
Unit Disks

Given a set of unit disks in the plane with union area A, what fraction of A can be covered by selecting a pairwise disjoint subset of the disks? Rado conjectured 1/4 and proved 1/4.41. Motivated by the problem of channel assignment for wireless access points, in which use of 3 channels is a standard practice, we consider a variant where the selected subset of disks must be 3-colourable with disks of the same colour pairwise-disjoint. For this variant of the problem, we conjecture that it is always possible to cover at least 1/1.41 of the union area and prove 1/2.09. We also provide an O(n2) algorithm to select a subset achieving a 1/2.77 bound. Finally, we discuss some results for other numbers of colours.

Air purification in disk-packing regenerators

1981 ◽  
Vol 17 (12) ◽  
pp. 645-648
Author(s):  
V. P. Alekseev ◽  
L. P. Danilenko ◽  
N. K. Polivalin
Keyword(s):  
Air Purification ◽  
Disk Packing
Sign in / Sign up

Export Citation Format

Share Document