In this paper we study a special class of monodromy evolving deformations (MED), which represents Halphen’s quadratic system. In 1996, Chakravarty and Ablowitz [4] showed that a fifth-order equation (DH-V) ω 1 = ω2ω3 − ω1(ω2 + ω3) + φ , ω 2 = ω3ω1 − ω2(ω3 + ω1) + θ , ω 2 = ω3ω1 − ω2(ω3 + ω1)− φθ, (1) φ = ω1(θ − φ) − ω3(θ + φ), θ = −ω2(θ − φ)− ω3(θ + φ), which arises in complex Bianchi IX cosmol...

Multiresolution modelling of polygonal surface meshes has been presented as a solution for the interactive visualisation of scenes formed by hundreds of thousands of polygons. On the other hand, it has been shown that representing surfaces using sets of triangle strips or fans greatly reduces visualisation time and provides an important memory savings. In this paper we present a new method to m...

Recently the study and construction of quad/triangle subdivision schemes have attracted attention. The quad/triangle subdivision starts with a control net consisting of both quads and triangles and produces finer and finer meshes with quads and triangles. The use of the quad/triangle structure for surface design is motivated by the fact that in CAD modelling, the designers often want to model c...

Armed only with a triangle and a dream, Marion Walter, a professor of mathematics at the University of Oregon, embarked on a quest for mathematical enlightenment. She battled rough angles and contemplated numerous strategies to find answers. In the end, Walter discovered characteristics of a triangle when each of its sides is trisected. Okay, Walter’s “quest” was not that exciting or epic, but ...

Triangle algebras are equationally defined structures that are equivalent with certain residuated lattices on a set of intervals, which are called interval-valued residuated lattices (IVRLs). Triangle algebras have been used to construct Triangle Logic (TL), a formal fuzzy logic that is sound and complete w.r.t. the class of IVRLs. In this paper, we prove that the so-called pseudo-prelinear tri...

The triangle-free process begins with an empty graph on n vertices and iteratively adds edges chosen uniformly at random subject to the constraint that no triangle is formed. We determine the asymptotic number of edges in the maximal triangle-free graph at which the triangle-free process terminates. We also bound the independence number of this graph, which gives an improved lower bound on the ...

In computational geometry, packing problems ask whether a set of rigid pieces can be placed inside a target region such that no two pieces overlap. The triangle packing problem is a packing problem that involves triangular pieces, and it is crucial for algorithm design in many areas, including origami design, cutting industries, and warehousing. Previous works in packing algorithms have conject...

An overview of the ‘triangle’ method for estimating soil surface wetness and evapotranspiration fraction from satellite imagery is presented here. The method is insensitive to initial atmospheric and surface conditions, net radiation and atmospheric correction, yet can yield accuracies comparable to other methods. We describe the method first from the standpoint of the how the triangle is obser...