How many ways can a chess Rook or Queen move from a corner cell to the opposite corner cell of an arbitrary size, arbitrary dimensional chessboard, assuming that the piece moves closer to the goalâ€¦ (More)

Plantâ€“microbe interactions play crucial roles in species invasions but are rarely investigated at the intraspecific level. Here, we study these interactions in three lineages of a globallyâ€¦ (More)

Let Hm(z) be a sequence of polynomials whose generating function âˆ‘âˆž m=0 Hm(z)t m is the reciprocal of a bivariate polynomial D(t, z). We show that in the three cases D(t, z) = 1 + B(z)t + A(z)t, D(t,â€¦ (More)

In his paper of 2000, Kenneth B. Stolarsky made various observations and conjectures about discriminants and generating functions of certain types of Chebyshev-like polynomials. We prove several ofâ€¦ (More)

Nicotine has been shown to cause appetite suppressing effects in humans. Studies have shown that nicotine has a similar effect on C. elegans as it does to mammals thanks to a common receptor toâ€¦ (More)

In this short note, we give simple proofs of several results and conjectures formulated by Stolarsky and Tran concerning generating functions of some families of Chebyshev-like polynomials.

For any fixed positive integer n, we study the root distribution of a sequence of polynomials Hm(z) satisfying the rational generating function âˆž âˆ‘ m=0 Hm(z)t m = 1 1 +B(z)t+A(z)tn where A(z) andâ€¦ (More)

We report on the discovery of stellar occultations, observed with Kepler, which recur periodically at 15.685 hr intervals, but which vary in depth from a maximum of 1.3% to a minimum that can be lessâ€¦ (More)