Does a low solar cycle minimum hint at a weak upcoming cycle?

The maximum amplitude (Rm) of a solar cycle, in the term of mean sunspot numbers, is well-known to be positively correlated with the preceding minimum (Rmin). So far as the long term trend is concerned, a low level of Rmin tends to be followed by a weak Rm, and vice versa. In this paper, we found that the evidence is insufficient to infer a very weak Cycle 24 from the very low Rmin in the preceding cycle. This is concluded by analyzing the correlation in the temporal variations of parameters for two successive cycles.Comment: 5 pages, 2 figures. Accepted by RA

On solvability of an indefinite Riccati equation

This note concerns a class of matrix Riccati equations associated with stochastic linear-quadratic optimal control problems with indefinite state and control weighting costs. A novel sufficient condition of solvability of such equations is derived, based on a monotonicity property of a newly defined set. Such a set is used to describe a family of solvable equations.Comment: 11 page