4 citations · 9 across the 6 of their papers we have counts for
10 papers
Abstract art generated by Thue-Morse correlation functions
Darren C. Ong
The Thue-Morse sequence is an aperiodically ordered infinite binary sequence. It is used as a one-dimensional way to model the structure of a quasicrystal. For example, taking auto…
On Simon's Hausdorff Dimension Conjecture
David Damanik, Jake Fillman, Shuzheng Guo +1
Barry Simon conjectured in 2005 that the Szegő matrices, associated with Verblunsky coefficients obeying for…
Simon's OPUC Hausdorff Dimension Conjecture
David Damanik, Shuzheng Guo, Darren C. Ong
We show that the Szegő matrices, associated with Verblunsky coefficients obeying for some , are b…
Quasiperiodic Music
Darren C. Ong
Using the definition of quasiperiodic function as a motivation, we introduce the idea of quasiperiodic music and detail the composition process of a quasiperiodic music piece, Rain…
Restrictions on the existence of a canonical system flow hierarchy
Injo Hur, Darren C. Ong
The KdV hierarchy is a family of evolutions on a Schrödinger operator that preserves its spectrum. Canonical systems are a generalization of Schrödinger operators, that nevertheles…
Sharp spectral transition for eigenvalues embedded into the spectral bands of perturbed periodic Jacobi operators
Wencai Liu, Darren C. Ong
We are interested in diagonal perturbations of a periodic Jacobi operator that introduce embedded eigenvalues in its essential spectrum. Embedding multiple points in the essential…