Approach to a rational rotation number in a piecewise isometric system

We study a parametric family of piecewise rotations of the torus, in the limit in which the rotation number approaches the rational value 1/4. There is a region of positive measure where the discontinuity set becomes dense in the limit; we prove that in this region the area occupied by stable periodic orbits remains positive. The main device is the construction of an induced map on a domain with vanishing measure; this map is the product of two involutions, and each involution preserves all its atoms. Dynamically, the composition of these involutions represents linking together two sector maps; this dynamical system features an orderly array of stable periodic orbits having a smooth parameter dependence, plus irregular contributions which become negligible in the limit.Comment: LaTeX, 57 pages with 13 figure

Geometric representation of interval exchange maps over algebraic number fields

We consider the restriction of interval exchange transformations to algebraic number fields, which leads to maps on lattices. We characterize renormalizability arithmetically, and study its relationships with a geometrical quantity that we call the drift vector. We exhibit some examples of renormalizable interval exchange maps with zero and non-zero drift vector, and carry out some investigations of their properties. In particular, we look for evidence of the finite decomposition property: each lattice is the union of finitely many orbits.Comment: 34 pages, 8 postscript figure

DIRAC Experiment and Test of Low-Energy QCD

The low-energy QCD predictions to be tested by the DIRAC experiment are revised. The experimental method, the setup characteristics and capabilities, along with first experimental results are reported. Preliminary analysis shows good detector performance: alignment error via $\Lambda$ mass measurement $m_\Lambda = 1115.6 MeV/c^2$ with $\sigma = 0.92 MeV/c^2$, $p \pi^-$ relative momentum resolution $\sigma_Q \approx 2.7 MeV/c$, and evidence for $\pi^

Detection of Pionium with DIRAC

The aim of the DIRAC experiment at CERN is to provide an accurate determination of S-wave pion-pion scattering lengths from the measurement of the lifetime of the pi+ pi- atom. The measurement will be done with precision comparable to the level of accuracy of theoretical predictions, formulated in the context of Chiral Perturbation Theory. Therefore, the understanding of chiral symmetry breaking of QCD will be submitted to a stringent test

Value proposition-driven reconfiguration of business models in dynamic industries: a design-science approach

PurposeThis paper aims to better understand and structure the process of business model (BM) redesign in dynamic industry contexts by exploring the interactions of BM components through a configuration and design-science lens. While these interactions have been investigated broadly in the BM literature, detailed studies on their properties and structures are limited.Design/methodology/approachA design-science methodology was utilised to conceptualise a BM design artefact based on literature, the components' interactions of which were investigated and iteratively validated through a case study of an organisation going through a BM change. The artefact served as a framework to capture the case firm's BM and value proposition through semi-structured interviews.FindingsThe results suggest that the interaction of BM components is represented by the value proposition as an integrating mechanism, which can be expressed as a combination of tangible, intangible and monetary inter-component flows. The value proposition, rather than being pre-determined and static, is dynamic and evolves as its flows are exchanged across the value creation, delivery, customer and capture components of the BM. These exchanges and interactions are facilitated by the components' input-process-output capabilities and drive BM reconfiguration through five value flow “properties”, expressed in terms of change in quantity, speed/frequency, composition, quality and value.Research limitations/implicationsWhile developed with inputs from a complex business environment that provides a rich research context, this work acknowledges the trade-off between in-depth single case analysis in theory building, and the need for follow-on research to address the limiting contextual variables and extend generalisability.Practical implicationsThe study offers a framework-based sequence of activities that managers can adopt for the BM design process in dynamic industry environments.Originality/valueThis work contributes to BM theory by setting out a mechanism that helps better understand interactions of BM components in dynamic environments, while also challenging the established definition of the value proposition concept – a key BM component – thus presenting significant implications for theory.</jats:sec

Test of chiral perturbation theory with DIRAC at CERN

The DIRAC experiment at CERN aims to form pi /sup +/ pi /sup -/ atomic states and to measure their lifetime with 10% accuracy. This will give a precision of 5% in the determination of pi pi S-wave scattering lengths, of the same level of Chiral Perturbation Theory calculations. In this way a crucial test on the theory validity would be performed. (13 refs)