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.     

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Terror and Counterterror Operations: Differential Game with Cyclical Nash Solution

The purpose of this paper is to study efficient measures to combat terror. To choose efficient actions against terror organizations, the response of terrorists has to be taken into consideration. Thus, an appropriate framework to study the intertemporal strategic interactions of Western governments and terror organizations is dynamic game theory. Using the open-loop Nash solution concept, it turns out that the system may exhibit long-run persistent oscillations. However, transitory behavior is nonunique.     

Gabor analysis over finite Abelian groups

Gabor frames for signals over finite Abelian groups, generated by an arbitrary lattice within the finite time–frequency plane, are the central topic of this paper. Our generic approach covers both multi-dimensional signals as well as non-separable lattices, and in fact the multi-window case as well. Our generic approach includes most of the fundamental facts about Gabor expansions of finite signals for the case of product lattices, as they have been given by Qiu, Wexler–Raz or Tolimieri–Orr, Bastiaans and Van-Leest and others. In our presentation the spreading representation of linear operators between finite-dimensional Hilbert space as well as a symplectic version of Poisson's summation formula over the finite time–frequency plane are essential ingredients. They bring us to the so-called Fundamental Identity of Gabor Analysis. In addition, we highlight projective representations of the time–frequency plane and its subgroups and explain the natural connection to twisted group algebras. In the finite-dimensional setting discussed in this paper these twisted group algebras are just matrix algebras and their structure provides the algebraic framework for the study of the deeper properties of finite-dimensional Gabor frames, independent of the structure theory theorem for finite Abelian groups.