Parallel MLFMA based on curvilinear triangle patch discretization

2007 ◽  
Author(s):  
Huapeng Zhao ◽  
Jun Hu ◽  
Zaiping Nie
Keyword(s):  
Curvilinear Triangle

A new proof for the residual set dimension of the apollonian packing

1984 ◽  
Vol 96 (3) ◽  
pp. 413-423 ◽  
Author(s):  
Claude Tricot
Keyword(s):  
Hausdorff Dimension ◽  
Density Theorem ◽  
Residual Set ◽  
Curvilinear Triangle

AbstractLet (Dn) be the apollonian packing of a curvilinear triangle T, ρn the radius of Dn, E = T—U Dn the residual set, dim (E) its Hausdorff dimension. In this paper we give a new proof of the equality dim proved by Boyd [2]. Our technique is to construct a sequence of regular triangles covering E, and suitable measures μkcarried by E which allow us to apply a density theorem.

scholarly journals Hyperbolic Cosines and Sines Theorems for the Triangle Formed by Arcs of Intersecting Semicircles on Euclidean Plane

2013 ◽  
Vol 2013 ◽  
pp. 1-10 ◽  
Author(s):  
Robert M. Yamaleev
Keyword(s):  
Exponential Function ◽  
Euclidean Plane ◽  
Cross Ratio ◽  
Curvilinear Triangle ◽  
Circular Arcs ◽  
General Complex ◽  
The Cross

The hyperbolic cosines and sines theorems for the curvilinear triangle bounded by circular arcs of three intersecting circles are formulated and proved by using the general complex calculus. The method is based on a key formula establishing a relationship between exponential function and the cross-ratio. The proofs are carried out on Euclidean plane.

scholarly journals Outer billiard around a curvilinear triangle with a fixed diameter

2014 ◽  
Vol EXTRA ◽  
pp. 179-194
Author(s):  
N. Dobbs ◽  
T. Nowicki ◽  
G. Świrszcz
Keyword(s):  
Curvilinear Triangle
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