Economy Phase Portraits

Topological terms like attractors and basins are expected to play an ever increasing role in the qualitative description of systems described by differential equations. This paper illustrates those concepts through a detailed study of the phase portraits of various "economic models" treated in the Energy Program of IIASA

Magnetic fields in noncommutative quantum mechanics

We discuss various descriptions of a quantum particle on noncommutative space in a (possibly non-constant) magnetic field. We have tried to present the basic facts in a unified and synthetic manner, and to clarify the relationship between various approaches and results that are scattered in the literature.Comment: Dedicated to the memory of Julius Wess. Work presented by F. Gieres at the conference `Non-commutative Geometry and Physics' (Orsay, April 2007

Assessment of Darkling Beetle Fauna after Implementation of an Environmental Restoration Program in the Southern Iberian Peninsula Affected by the Aznalcóllar Toxic Spill

This study is part of the Follow up Restoration Program of animal communities that colonize the Guadiamar River Basin. In 1998, the area was affected by a release of toxic sludge after the retention walls of the Aznalcóllar Mines (southern Iberian Peninsula) broke. The main objective of this study was to assess the current state of the population of Tenebrionidae, one of the most representative groups of edaphic Coleoptera inhabiting the Guadiamar River Basin. This paper analyses the progress made by the darkling beetle community six years after the disaster occurred and the Restoration Program was implemented. The study is based on faunistic data from systematic sampling carried out for six years to monitor plots distributed across the damaged area. To make an overall assessment of the tenebrionid fauna in relation to adjacent areas qualitative and quantitative ecological indices were applied, and temporal follow up and biogeographical comparisons were also made. The results indicate that, on the whole, tenebrionid fauna was somewhat affected by the Aznalcóllar Mine spill, and that a greater loss of fauna was detected closer to the accident site. The analysis of the temporal population dynamic suggests that the most affected zones are undergoing a process of re-colonization. However, this process varies widely by species and has not yet reached the expected levels of a non-affected river basin in the southern Iberian Peninsula

Mathematical surprises and Dirac's formalism in quantum mechanics

By a series of simple examples, we illustrate how the lack of mathematical concern can readily lead to surprising mathematical contradictions in wave mechanics. The basic mathematical notions allowing for a precise formulation of the theory are then summarized and it is shown how they lead to an elucidation and deeper understanding of the aforementioned problems. After stressing the equivalence between wave mechanics and the other formulations of quantum mechanics, i.e. matrix mechanics and Dirac's abstract Hilbert space formulation, we devote the second part of our paper to the latter approach: we discuss the problems and shortcomings of this formalism as well as those of the bra and ket notation introduced by Dirac in this context. In conclusion, we indicate how all of these problems can be solved or at least avoided.Comment: Largely extended and reorganized version, with new title and abstract and with 2 figures added (published version), 54 page

Game Theoretical Models for Arms Control and Disarmament Verification

In the context of arms control and disarmament, inspections are procedures designed to provide data with which a State’s compliance or non-compliance to a treaty, an agreement or other set of rules can be assessed. There is always, potentially at least, a conflict between the inspection authority (in the following Inspectorate) and the State (in the following Inspectee) who is required to comply,but who may have an interest not to do so. Non-cooperative game theory provides the appropriate tools to analyse these kind of conflicts. The solution concept is hereby the so-called Nash equilibrium. Since inspections, beyond their assessment of compliance or non-compliance, should induce the State to legal behaviour, one may say that effective inspections should be designed such that the Inspectee’s equilibrium strategy of the game theoretical model describing these inspections is legal behaviour of the Inspectee. Game theoretical analyses of arms control and disarmament verification have been performed since the early sixties of the last century. It was, however, the Treaty on the Non-Proliferation of Nuclear Weapons which stimulated more detailed analytical work. During the last 10 years two kinds of topics have been addressed in greater detail, unannounced interim inspections and acquisition path analysis. In this paper, assumptions necessary for a quantitative modelling of unannounced interim inspections are discussed, and one example is presented in major detail. Some thoughts on the art of modelling conflicts of both technical and political nature complement the previous thoughts