A J Williams—a Tropical Veterinary Pioneer

THE TROPICAL j-INVARIANT

If (Q,A) is a marked polygon with one interior point, then a general polynomial f ∈ K[x, y] with support A defines an elliptic curve Cf on the toric surface XA. If K has a non-archimedean valuation into R we can tropicalize Cf to get a tropical curve Trop(Cf ). If the Newton subdivision induced by f is a triangulation, then Trop(Cf ) will be a graph of genus one and we show that the lattice len...

Veterinary Pharmacy, a Dismissed Necessity

Veterinary Pharmacy, a Dismissed Necessity

THE j-INVARIANT OF A PLANE TROPICAL CUBIC

Several results in tropical geometry have related the j-invariant of an algebraic plane curve of genus one to the cycle length of a tropical curve of genus one. In this paper, we prove that for a plane cubic over the field of Puiseux series the negative of the generic valuation of the j-invariant is equal to the cycle length of the tropicalization of the curve, if there is a cycle at all.

Transpiration efficiency of a tropical pioneer tree (Ficus insipida) in relation to soil fertility.

The response of whole-plant water-use efficiency, termed transpiration efficiency (TE), to variation in soil fertility was assessed in a tropical pioneer tree, Ficus insipida Willd. Measurements of stable isotope ratios (delta(13)C, delta(18)O, delta(15)N), elemental concentrations (C, N, P), plant growth, instantaneous leaf gas exchange, and whole-plant water use were used to analyse the mecha...