13 citations · 13 across the 6 of their papers we have counts for
6 papers
Sparks of Quantum Advantage and Rapid Retraining in Machine Learning
William Troy
The advent of quantum computing holds the potential to revolutionize various fields by solving complex problems more efficiently than classical computers. Despite this promise, pra…
Zero Energy Self-Similar Solutions Describing Singularity Formation In The Nonlinear Schrodinger Equation In Dimension N=3
William C. Troy
In dimension N=3 the cubic nonlinear Schrodinger equation has solutions which become singular, i.e. at a spatial point they blow up to infinity in finite time. In 1972 Zakharov fam…
On -Harmonic Measures in Half Spaces
J. G. Llorente, J. J. Manfredi, W. C. Troy +1
For all and we prove that there is a constant such that the -harmonic measure in of a ball of radius in is bou…
There are Asymmetric Minimizers for the One-Dimensional Ginzburg-Landau Model of Superconductivity
S. P. Hastings, W. C. Troy
We study a boundary value problem associated with a system of two second order differential equations with cubic nonlinearity which model a film of superconductor material subjecte…
On the solutions of the one dimensional Ginzburg-Landau equations for superconductivity
Amandine Aftalion, William C. Troy
This paper gives a complete description of the solutions of the one dimensional Ginzburg-Landau equations which model superconductivity phenomena in infinite slabs. We investigate…
A shooting approach to the Lorenz equations
Stuart P. Hastings, William C. Troy
We announce and outline a proof of the existence of a homoclinic orbit of the Lorenz equations. In addition, we develop a shooting technique and two key conditions, which lead to t…