12,191 research outputs found
Optimal Flood Control
A mathematical model for optimal control of the water levels in a chain of
reservoirs is studied. Some remarks regarding sensitivity with respect to the time horizon, terminal cost and forecast of inflow are made
Open -spin theory II: The analogue of Witten's conjecture for -spin disks
We conclude the construction of -spin theory in genus zero for Riemann
surfaces with boundary. In particular, we define open -spin intersection
numbers, and we prove that their generating function is closely related to the
wave function of the th Gelfand--Dickey integrable hierarchy. This provides
an analogue of Witten's -spin conjecture in the open setting and a first
step toward the construction of an open version of Fan--Jarvis--Ruan--Witten
theory. As an unexpected consequence, we establish a mysterious relationship
between open -spin theory and an extension of Witten's closed theory.Comment: The more foundational parts of the previous version, v3, were moved
to the article arXiv:2003.01082. These include the description of objects,
constructions of moduli spaces and bundles and proofs of orientations
theorems. The name of the paper and the abstract were changed accordingl
- âŚ