4 citations · 7 across the 9 of their papers we have counts for
5 papers · 1 filter
Energy on spheres and discreteness of minimizing measures
Dmitriy Bilyk, Alexey Glazyrin, Ryan Matzke +2
In the present paper we study the minimization of energy integrals on the sphere with a focus on an interesting clustering phenomenon: for certain types of potentials, optimal meas…
Optimal measures for p-frame energies on spheres
Dmitriy Bilyk, Alexey Glazyrin, Ryan Matzke +2
We provide new answers about the placement of mass on spheres so as to minimize energies of pairwise interactions. We find optimal measures for the -frame energies, i.e. energie…
Frame Potentials and Orthogonal Vectors
Josiah Park
An extension is given of a recent result of Glazyrin, showing that an orthonormal basis joined with the vectors , where min…
Lattices from tight frames and vertex transitive graphs
Lenny Fukshansky, Deanna Needell, Josiah Park +1
We show that real tight frames that generate lattices must be rational, and use this observation to describe a construction of lattices from vertex transitive graphs. In the case o…
Repeated minimizers of -frame energies
Alexey Glazyrin, Josiah Park
For a collection of unit vectors , define the -frame energy of as the quantity . In this…