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There exists no distance-regular graph with intersection array {56,36,9;1,3,48}
distance-regular graph intersection array
2010/11/23
We prove that a distance-regular graph with intersection array {56,36,9;1,3,48} does not exist. This intersection array is from the table of feasible parameters for distance-regular graphs in "Distanc...
Fock Spaces, Landau Operators and the Regular Solutions of time-harmonic Maxwell equations
Fock Spaces Landau Operators time-harmonic Maxwell equations
2010/11/24
We investigate the solution representation for Maxwell equations based on the combination of hypercomplex function-theoretical methods with quantum mechanical methods. This gives a characterization f...
Vertex subsets with minimal width and dual width in $Q$-polynomial distance-regular graphs
Vertex subsets $Q$-polynomial distance-regular graphs
2010/11/15
We study $Q$-polynomial distance-regular graphs from the point of view of what we call descendents, that is to say, those vertex subsets with the property that the width $w$ and dual width $w^*$ sati...
Vandermonde factorizations of a regular Hankel matrix and their application on the computation of Bézier curves
Vandermonde factorizations regular Hankel matrix Bézier curves
2010/11/17
In this paper, a new method to compute a B\'ezier curve of degree n = 2m-1 is introduced, here formulated as a set of points whose coordinates are calculated from two Hankel forms in $\C^m$. From Van...
The threshold-two contact process on a random r-regular graph has a first order phase transition
The threshold-two contact process r-regular graph phase transition
2010/11/12
We consider the discrete time threshold-two contact process on a random $r$-regular graph on $n$ vertices. In this process, a vertex with at least two occupied neighbors at time $t$ will be occupied ...