5 papers
A computer-assisted counterexample to the planar Berenstein conjecture
Matthew J. Colbrook, Siavash Sadeghi, George Stepaniants
Recent work of Colbrook and Stepaniants produced the first counterexamples to the planar Pompeiu and Schiffer conjectures and introduced the conformal fixed-disc, disk-polynomial,…
A Proof of the Forsythe Conjecture for the Two-Step Restarted Conjugate Gradient Method
Matthew J. Colbrook, George Stepaniants, Alex Townsend
Forsythe conjectured in 1968 that the normalized residual directions of restarted conjugate gradients approach a two-cycle. We prove the conjecture for restart length two: unless t…
A computer-assisted counterexample to the planar Pompeiu and Schiffer conjectures
Matthew J. Colbrook, George Stepaniants
The planar Pompeiu problem, originating in 1929, and the associated Schiffer conjecture are long-standing rigidity questions linking rigid-motion integral transforms and Fourier ze…
A Spectral Theory of Scalar Volterra Equations
David Darrow, George Stepaniants
This work aims to bridge the gap between pure and applied research on scalar, linear Volterra equations by examining five major classes: integral and integro-differential equations…
Learning Memory and Material Dependent Constitutive Laws
Kaushik Bhattacharya, Lianghao Cao, George Stepaniants +2
We propose and study a neural operator framework for learning memory- and material microstructure-dependent constitutive laws for heterogeneous materials. We work in the two-scale…