In this paper, we study how a stochastic model can be used to determine optimal levels of exploitation of the North-East Arctic Cod (NEAC, Gadus morhua). A non-critical depensation growth model is developed for this species in order to examine both deterministic and stochastic cases. Estimation of the biological and the noise term parameters in the stochastic biomass dynamics is based on simulation and use of empirical NEAC data sets for the years 1985–2001. The Kolmogorov– Smirnov criterion-based method is used to estimate both drift and diffusion parameters simultaneously. The estimates turn out to be reasonable and the model is able to capture the salient features of the NEAC dynamics. The model is used to derive optimal levels of exploitation with different diffusion functions in the stochastic case and various discount rates in the deterministic case. Optimal catches are compared to the historical catch records. A striking feature of our modeling results is that these records fit surprisingly well with the infinite discounting tracks, i.e., the bliss solution. Our general results indicate that over fishing has resulted from lack of long-term planning as well as inadequate response to uncertainty. Copyright Springer 2006Kolmogorov–Smirnov statistics, optimal control, parameter estimation, stochastic bioeconomic model, C10, C14, Q20, Q22,

A stability analysis for a diffuse high β, l=1 helical system is presented. It is shown that there exists a gross m=1 mode whose properties are very similar to those predicted by sharp boundary theory. In addidion, two new classes of m=1 modes are found. One is a set of interior localized modes and the other a set of modes localized exterior to the plasma. The growth rate of these modes is quite small. The internal mode exists for any monotonic pressure profile and cannot be wall stabilized. Its effect on experimental plasmas is as yet unknown.

It is well known that mechanical systems in an unstable equilibrium position can be stabilized by dynamic techniques. Dynamic stabilization has also been applied to unstable plasma equilibria. This review paper attempts to give a general introduction to these problems. A number of special cases within the framework of MHD are discussed.

A method is presented for dynamically stabilizing the m = 1 mode in a screw pinch

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