We describe a general method of constructing nonlocal recursion operators for symmetries PDEs. As an example, the cotangent equation to 3D rdDym $$u_{yt} = u_xu_{xy} - u_yu_{xx}$$ is considered which two mutually inverse are found. The exposition includes rigorous criterion check hereditary property operators.

We study the Masur-Veech volumes $MV_{g,n}$ of principal stratum moduli space quadratic differentials unit area on curves genus $g$ with $n$ punctures. show that are constant terms a family polynomials in variables governed by topological recursion/Virasoro constraints. This is equivalent to formula giving these as sum over stable graphs, and retrieves result \cite{Delecroix} proved combinatori...

We describe a second-order calculus of objects. The calculus supports object subsumption, method override, and the type Self. It is constructed as an extension of System F with subtyping, recursion, and first-order object types.

It is shown that the two-loop recursion for computing the search direction of a limited memory method for optimization can be derived by means of the reverse mode of automatic differentiation applied to an auxiliary function.