We use piecewise polynomials to define tropical cocycles generalising the well-known notion of Cartier divisors to higher codimensions. We also introduce an intersection product of cocycles with tropical cycles and prove that this gives rise to a Poincaré duality in some cases.
A Rota–Baxter algebra, also known as a Baxter algebra, is an algebra with a linear operator satisfying a relation, called the Rota–Baxter relation, that generalizes the integration by parts formula. Most of the studies on Rota–Baxter algebras have been for commutative algebras. Two constructions of free commutative Rota–Baxter algebras were obtained by Rota and Cartier in the 1970s and a third ...
Let $Y_{1}, \ldots , Y_{q}$ be closed subschemes in $\ell $-subgeneral position with index $\kappa $ a complex projective variety $X$ of dimension $n.$ $A$ an ample Cartier divisor on $X.$ We show that if holomorphic curve $f:\mathbb C \to X$
