Mathematics of the Quantum Zeno Effect

We present an overview of the mathematics underlying the quantum Zeno effect. Classical, functional analytic results are put into perspective and compared with more recent ones. This yields some new insights into mathematical preconditions entailing the Zeno paradox, in particular a simplified proof of Misra's and Sudarshan's theorem. We empahsise the complex-analytic structures associated to the issue of existence of the Zeno dynamics. On grounds of the assembled material, we reason about possible future mathematical developments pertaining to the Zeno paradox and its counterpart, the anti-Zeno paradox, both of which seem to be close to complete characterisations.Comment: 32 pages, 1 figure, AMSLaTeX. In: Mathematical Physics Research at the Leading Edge, Charles V. Benton ed. Nova Science Publishers, Hauppauge NY, pp. 111-141, ISBN 1-59033-905-3, 2003; revision contains corrections from the published corrigenda to Reference [64

Incentive Systems in Multi-Level Markets for Virtual Goods

As an alternative to rigid DRM measures, ways of marketing virtual goods through multi-level or networked marketing have raised some interest. This report is a first approach to multi-level markets for virtual goods from the viewpoint of theoretical economy. A generic, kinematic model for the monetary flow in multi-level markets, which quantitatively describes the incentives that buyers receive through resales revenues, is devised. Building on it, the competition of goods is examined in a dynamical, utility-theoretic model enabling, in particular, a treatment of the free-rider problem. The most important implications for the design of multi-level market mechanisms for virtual goods, or multi-level incentive management systems, are outlined.Comment: 18 pages, 5 figures; graphics with reduced resolution. Full resolution available on author's homepage. Accepted contribution to the Workshop 'Virtual Goods' at the Conference AXMEDIS 2005, 30. November - 2. December, Florence, Ital

Asymptotic Hyperfunctions, Tempered Hyperfunctions, and Asymptotic Expansions

We introduce new subclasses of Fourier hyperfunctions of mixed type, satisfying polynomial growth conditions at infinity, and develop their sheaf and duality theory. We use Fourier transformation and duality to examine relations of these 'asymptotic' and 'tempered' hyperfunctions to known classes of test functions and distributions, especially the Gelfand-Shilov-Spaces. Further it is shown that the asymptotic hyperfunctions, which decay faster than any negative power, are precisely the class that allow asymptotic expansions at infinity. These asymptotic expansions are carried over to the higher-dimensional case by applying the Radon transformation for hyperfunctions.Comment: 31 pages, 1 figure, typos corrected, references adde

Authorised Translations of Electronic Documents

A concept is proposed to extend authorised translations of documents to electronically signed, digital documents. Central element of the solution is an electronic seal, embodied as an XML data structure, which attests to the correctness of the translation and the authorisation of the translator. The seal contains a digital signature binding together original and translated document, thus enabling forensic inspection and therefore legal security in the appropriation of the translation. Organisational aspects of possible implementation variants of electronic authorised translations are discussed and a realisation as a stand-alone web-service is presented.Comment: In: Peer-reviewed Proceedings of the Information Security South Africa (ISSA) 2006 From Insight to Foresight Conference, 5 to 7 July 2006, Sandton, South Afric