1 citations · 1 across the 7 of their papers we have counts for
7 papers
Analysis of Log-Weighted Quadrature Domains
Andrew Graven
This paper studies plane domains satisfying a quadrature identity with respect to the singular weight . These are referred to as log-weighted quadrature domains (L…
Quadrature Domains and the Faber Transform
Andrew J. Graven, Nikolai G. Makarov
We present a framework for reconstructing any simply connected, bounded or unbounded, quadrature domain from its quadrature function . Using the Faber transform, we derive f…
A Geometric Approach to Optimal Control of Hybrid and Impulsive Systems
William Clark, Maria Oprea, Andrew J. Graven
Hybrid dynamical systems are systems which undergo both continuous and discrete transitions. The Bolza problem from optimal control theory is applied to these systems and a hybrid…
An Elementary Proof of Poincaré's Last Geometric Theorem
Andrew J. Graven, John H. Hubbard
It is shown that the Poincaré-Birkhoff fixed point theorem may be proven by extending the geometric approach originally devised by Henri Poincaré himself, along with several result…
A Rapid Method For Orbital Coverage Statistics With Using Ergodic Theory
Andrew J. Graven, Alan H. Barr, Martin W. Lo
Quantifying long-term statistical properties of satellite trajectories typically entails time-consuming trajectory propagation. We present a fast, ergodic\cite{Arnold} method of an…
The Long-Term Forecast of Station View Periods for Elliptical Orbits
Andrew J. Graven, Martin W. Lo
In a previous paper, using ergodic theory, Lo [1] derived a simple definite integral that provided an estimate of the view periods of ground stations to satellites. This assumes th…
Density of States Graph Kernels
Leo Huang, Andrew Graven, David Bindel
A fundamental problem on graph-structured data is that of quantifying similarity between graphs. Graph kernels are an established technique for such tasks; in particular, those bas…