A discrete optimality system for an optimal harvesting problem

In this paper, we obtain the discrete optimality system of an optimal harvesting problem. While maximizing a combination of the total expected utility of the consumption and of the terminal size of a population, as a dynamic constraint, we assume that the density of the population is modeled by a stochastic quasi-linear heat equation. Finite-difference and symplectic partitioned Runge–Kutta (SPRK) schemes are used for space and time discretizations, respectively. It is the first time that a SPRK scheme is employed for the optimal control of stochastic partial differential equations. Monte-Carlo simulation is applied to handle expectation appearing in the cost functional. We present our results together with a numerical example. The paper ends with a conclusion and an outlook to future studies, on further research questions and applications.     

Decade fluctuations in the Earth's rate of rotation and long-term librations in polar motion

Summary An investigation into long series of astronomical latitude and time observations is presented in order to analyse their long-term variations. Decade fluctuations in the Earth's rate of rotation and long-term librations in polar motion (secular drift and Markowitz wobble) are discussed. Available data show a good correlation between observed rotational acceleration of the Earth and the motion of the mean pole over periods of about thirty years.