Sliding and oscillations in fisheries with on–off harvesting and different switching times

In this paper, we propose a fishery model with a discontinuous on–off harvesting policy, based on a very simple and well known rule: stop fishing when the resource is too scarce, i.e. whenever fish biomass is lower than a given threshold. The dynamics of the one-dimensional continuous time model, represented by a discontinuous piecewise-smooth ordinary differential equation, converges to the Schaefer equilibrium or to the threshold through a sliding process. We also consider the model with discrete time impulsive on–off switching that shows oscillations around the threshold value. Finally, a discrete-time version of the model is considered, where on–off harvesting switchings are decided with the same discrete time scale of non overlapping reproduction seasons of the harvested fish species. In this case the border collision bifurcations leading to the creations and destruction of periodic oscillations of the fish biomass are studied.     

Persistent oscillations in a threshold adjustment model

In this paper we present a simple time-continuous behavioural model of habit formation. Addictive behaviour is damped by a threshold which adapts itself to the habit. This adaptive behaviour of the threshold may lead to periodic fluctuations of the consumption rate, the habit and the threshold. It turns out that both a low adjustment rate of the threshold as well as a steep consumption function favour oscillatory patterns.     

On filtering and estimation of a threshold stochastic volatility model

We derive a nonlinear filter and the corresponding filter-based estimates for a threshold autoregressive stochastic volatility (TARSV) model. Using the technique of a reference probability measure, we derive a nonlinear filter for the hidden volatility and related quantities. The filter-based estimates for the unknown parameters are then obtained from the EM algorithm.     

Elementary symmetric polynomials in Shamir's scheme

The concept of k-admissible tracks in Shamir's secret sharing scheme over a finite field was introduced by Schinzel et al. (2009) [10]. Using some estimates for the elementary symmetric polynomials, we show that the track (1,…,n) over Fp is practically always k-admissible; i.e., the scheme allows to place the secret as an arbitrary coefficient of its generic polynomial even for relatively small p. Here k is the threshold and n the number of shareholders.     

Solving Multi-dimensional Evolution Problems with Localized Structures using Second Generation Wavelets

A dynamically adaptive numerical method for solving multi-dimensional evolution problems with localized structures is developed. The method is based on the general class of multi-dimensional second-generation wavelets and is an extension of the second-generation wavelet collocation method of Vasilyev and Bowman to two and higher dimensions and irregular sampling intervals. Wavelet decomposition is used for grid adaptation and interpolation, while O ( N ) hierarchical finite difference scheme, which takes advantage of wavelet multilevel decomposition, is used for derivative calculations. The prowess and computational efficiency of the method are demonstrated for the solution of a number of two-dimensional test problems.     

一类时滞SIS传染病模型的讨论

对一类具有生理阶段结构的SIS传染病模型进行了分析，得到了传染病最终消除和成为地方病的阈值．     

树上秘密共享体制的信息率

研究以树G为通道结构的秘密共享体制的最优信息率ρ（G）。得到了ρ（G）＝2／3的要条件。证明了ρ（G）不会介于实数区间（3／5，2／3）中，给出了以树G的阶数表示的ρ（G）的下界，求出两类具有某种结构的树的最优信息率。     

一类非线性时序模型非遍历性的一个充分条件

本文研究了一类由紧算子与加性i.i.d.干扰确定的非线性时间序列的非遍历性,揭示了这类非线性时间序列的非遍历性与其相应确定性部分的Lyapunov函数之间的联系。