20 citations · 48 across the 18 of their papers we have counts for
19 papers
Hypersphere-Based Restricting Conditions for Colorings of the Euclidean Space
Gabriel Istrate, Catalin Zara
We study colorings of the Euclidean space constrained by \emph{hypersphere forcing conditions}: if an admissible hypersphere, , centered at a point and of radius co…
Quantum dynamics of atoms in number-theory-inspired potentials
D. Cassettari, O. V. Marchukov, B. Carruthers +8
In this paper we study transitions of atoms between energy levels of several number-theory-inspired atom potentials, under the effect of time-dependent perturbations. First, we sim…
Polynomial Assignments for Bott-Samelson manifolds
Gouri Shankar Seal, Catalin Zara
Polynomial assignments for a torus -action on a smooth manifold were introduced by Ginzburg, Guillemin, and Karshon in 1999; they form a module over $\mathbb{S}(\mathfrak{t}…
Modeling how windfarm geometry affects bird mortality
Ethan D. Bolker, Jeremy J. Hatch, Catalin Zara
Birds flying across a region containing a windfarm risk death from turbine encounters. This paper describes a geometric model that helps estimate that risk and a spreadsheet that i…
The Prouhet-Tarry-Escott Problem and Generalized Thue-Morse Sequences
Ethan D. Bolker, Carl Offner, Robert Richman +1
We present new methods of generating Prouhet-Tarry-Escott partitions of arbitrarily large regularity. One of these methods generalizes the construction of the Thue-Morse sequence t…
Cardinality of -Segments and Genocchi Numbers
Catalin Zara
We prove that the Genocchi numbers of first and second kind give the cardinality of certain segments in permutation spaces, with respect to the -distance. Experimental data…