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Full-Text Articles in Physical Sciences and Mathematics
Balanced Biorthogonal Scaling Vectors Using Fractal Function Macroelements On [0,1], Bruce Kessler
Balanced Biorthogonal Scaling Vectors Using Fractal Function Macroelements On [0,1], Bruce Kessler
Mathematics Faculty Publications
Geronimo, Hardin, et al have previously constructed orthogonal and biorthogonal scaling vectors by extending a spline scaling vector with functions supported on $[0,1]$. Many of these constructions occurred before the concept of balanced scaling vectors was introduced. This paper will show that adding functions on $[0,1]$ is insufficient for extending spline scaling vectors to scaling vectors that are both orthogonal and balanced. We are able, however, to use this technique to extend spline scaling vectors to balanced, biorthogonal scaling vectors, and we provide two large classes of this type of scaling vector, with approximation order two and three, respectively, with …
On 4-Regular Planar Hamiltonian Graphs, David High
On 4-Regular Planar Hamiltonian Graphs, David High
Masters Theses & Specialist Projects
In order to research knots with large crossing numbers, one would like to be able to select a random knot from the set of all knots with n crossings with as close to uniform probability as possible. The underlying graph of a knot diagram can be viewed as a 4-regular planar graph. The existence of a Hamiltonian cycle in such a graph is necessary in order to use the graph to compute an upper bound on rope length for a given knot. The algorithm to generate such graphs is discussed and an exact count of the number of graphs is …