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- Christopher J. Hillar, Darren L. Rhea
- The American Mathematical Monthly
- 2007

Much less known, however, is that there is a description of Aut(G), the automorphism group of G. The first compete characterization that we are aware of is contained in a paper by Ranum [1] near the turn of the last century. Beyond this, however, there are few other expositions. Our goal is to fill this gap, thereby providing a much needed accessible and… (More)

- Daniel Urbán, Hu Zhu, +12 authors Bryan L. Roth
- Neuropsychopharmacology : official publication of…
- 2016

Elucidating how the brain's serotonergic network mediates diverse behavioral actions over both relatively short (minutes-hours) and long period of time (days-weeks) remains a major challenge for neuroscience. Our relative ignorance is largely due to the lack of technologies with robustness, reversibility, and spatio-temporal control. Recently, we have… (More)

- Christopher J. Hillar, Darren L. Rhea
- Comput. Geom.
- 2006

Let S be a finite set of points in the plane and let T (S) be the set of intersection points between pairs of lines passing through any two points in S. We characterize all configurations of points S such that iteration of the above operation produces a dense set. We also discuss partial results on the characterization of those finite point-sets with… (More)

We study equations in groups G with unique m-th roots for each positive integer m. A word equation in two letters is an expression of the form w(X,A) = B, where w is a finite word in the alphabet {X,A}. We think of A,B ∈ G as fixed coefficients, and X ∈ G as the unknown. Certain word equations, such as XAXAX = B, have solutions in terms of radicals: X =… (More)

We study equations in groups G with unique m-th roots for each positive integer m. A word equation in two letters is an expression of the form w(X,A) = B, where w is a finite word in the alphabet {X,A}. We think of A,B ∈ G as fixed coefficients, and X ∈ G as the unknown. Certain word equations, such as XAXAX = B, have solutions in terms of radicals: X =… (More)

- Christopher J. Hillar, Darren L. Rhea
- The American Mathematical Monthly
- 2004

- Christopher J. Hillar, Darren L. Rhea, Godfrey L. Isaacs
- The American Mathematical Monthly
- 2006

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