Nicholas Matteo

University of Colorado Boulder | CUB · Department of Mathematics

Any convex polytope whose combinatorial automorphism group has two orbits on the flags is isomorphic to one whose group of Euclidean symmetries has two orbits on the flags (equivalently, to one whose automorphism group and symmetry group coincide.) Hence, a combinatorially two-orbit convex polytope is isomorphic to one of a known finite list, all o...

We classify the convex polytopes whose symmetry groups have two orbits on the flags. These exist only in two or three dimensions, and the only ones whose combinatorial automorphism group is also two-orbit are the cuboctahedron, the icosidodecahedron, and their duals. The combinatorially regular two-orbit convex polytopes are certain 2n-gons for eac...

Suppose that we are given a family of choice functions on pairs from a given finite set. The set is considered as a set of alternatives (say candidates for an office) and the functions as potential “voters.” The question is, what choice functions agree, on every pair, with the majority of some finite subfamily of the voters? For the problem as stat...

The geomagnetic field is an important parameter in space physics. The International Geomagnetic Reference Field (IGRF) is a model of the Earth's main field. Current sources in the ionosphere, the interplanetary magnetic field, annual and diurnal variation, and other sporadic and unmodeled effects may alter the actual B field distribution. We invest...

1] The ionosphere is a dominant source of Global Positioning System receiver range measurement error. Although dual‐frequency receivers can eliminate the first‐order ionospheric error, most second‐ and third‐order errors remain in the range measurements. Higher‐order ionospheric error is a function of both electron density distribution and the magn...

Suppose we are given a family of choice functions on pairs from a given finite set. The set is considered as a set of alternatives (say candidates for an office) and the functions as potential "voters". The question is, what choice functions agree, on every pair, with the majority of some finite subfamily of the voters? For the problem as stated, a...

The ionosphere is a dominant source of GPS receiver range measurement errors. High accuracy positioning and navigation applications rely on the use of dual-frequency receivers to eliminate the first order ionosphere error. Range measurements generated by dual-frequency receivers, however, retain 72% of the second order error and 51% of the third or...