Nevanlinna theory of meromorphic functions on annuli

In this survey paper, we discuss the recent development of Nevanlinna theory of meromorphic functions on annuli, which extends results in Nevanlinna theory in the complex plane or in a disk. In particular, we show that the approach taken on annuli is a unified treatment of functions meromorphic in the complex plane, a disk and an annulus. It allows one to obtain many results in the complex plane and in a disk as corollaries of our results in annuli.     

WHY INCREASED UNCERTAINTY MAY LEAD TO MORE RISKY BEHAVIOR

The purpose of this article is to investigate circumstances under which it may be optimal to deliberately harvest a fish stock to extinction applying a stochastic surplus growth model. It is known from the literature that deliberate extinction may result when there is critical depensation or when the discount rate is high compared to the intrinsic growth rate. Here it is shown that deliberate extinction may also be optimal when the degree of stochasticitry is high even with zero discounting. A high degree of stochasticity may have the same effect as critical depensation even though it is not present in the biological model. In other words, high uncertainty, instead of leading to more conservative harvesting as is usually expected, in this model result in more aggressive harvesting and more risky behavior. The main message is therefore always to try to keep the stock well above any critical limit.     

INFERRING A BIOPOLITICAL CONSENSUS VIEW OF STOCHASTIC DYNAMICS FOR MANAGEMENT OF A TRANSBOUNDARY FISHERY

ABSTRACT. Management of trans‐boundary fisheries is a complicated problem with biological, legal, economic and political implications. We propose a simple stochastic differential‐equation model to describe a biopolitical consensus view of fish stock dynamics. Estimates of the drift and diffusion terms of three stochastic differential equations are obtained using data from the southern bluefin tuna (SBT) fishery with a method based on the Kolmogorov‐Smirnov statistic. We refer to these estimated equations as alternative biopolitical consensus views of SBT stock dynamics. Each of these is used to generate a time series of optimal harvest that achieves the objective of maximizing the present value of expected fishery returns. These time series of optimal harvests are then compared to actual harvests for the period 1981 1997.     

A Sine-Collocation Method for the Computation of the Eigenvalues of the Radial Schr?dinger Equation

A collocation scheme using sine function basis elements is developedand used to approximate the eigenvalues of the radial Schr?dingerequation. The method is shown to apply to problems with singulareigensolutions and error bounds for the approximate eigenvaluesare given. The method is applied to a few test examples to indicateboth the accuracy and the implementation of the method.