Contact Lie algebras of vector fields on the plane

The paper is devoted to the complete classification of all real Lie algebras of contact vector fields on the first jet space of one-dimensional submanifolds in the plane. This completes Sophus Lie's classification of all possible Lie algebras of contact symmetries for ordinary differential equations. As a main tool we use the abstract theory of filtered and graded Lie algebras. We also describe all differential and integral invariants of new Lie algebras found in the paper and discuss the infinite-dimensional case.Comment: 20 pages. Published copy, also available at http://www.maths.warwick.ac.uk/gt/GTVol3/paper1.abs.htm

Enterprise Modelling using Algebraic Graph Transformation - Extended Version

An analysis of today's situation at Credit Suisse has shown severe problems, because it is based on current best practices and ad-hoc modelling techniques to handle important aspects of security, risk and compliance. Based on this analysis we propose in this paper a new enterprise model which allows the construction, integration, transformation and evaluation of different organizational models in a big decentralized organization like Credit Suisse. The main idea of the new model framework is to provide small decentralized models and intra-model evaluation techniques to handle services, processes and rules separately for the business and IT universe on one hand and for human-centric and machine-centric concepts on the other hand. Furthermore, the new framework provides inter-modelling techniques based on algebraic graph transformation to establish the connection between different kinds of models and to allow integration of the decentralized models. In order to check for security, risk and compliance in a suitable way, our models and techniques are based on different kinds of formal methods. In this paper, we show that algebraic graph transformation techniques are useful not only for intra-modelling - using graph grammars for visual languages and graph constraints for requirements - but also for inter-modelling - using triple graph grammars for model transformation and integration. Altogether, we present the overall idea of our new model framework and show how to solve specific problems concerning intra- and inter-modelling as first steps. This should give evidence that our framework can also handle important other requirements for enterprise modelling in a big decentralized organization like Credit Suisse

Search for dark matter in the hidden-photon sector with a large spherical mirror

If dark matter consists of hidden-sector photons which kinetically mix with regular photons, a tiny oscillating electric-field component is present wherever we have dark matter. In the surface of conducting materials this induces a small probability to emit single photons almost perpendicular to the surface, with the corresponding photon frequency matching the mass of the hidden photons. We report on a construction of an experimental setup with a large ~14 m2 spherical metallic mirror that will allow for searches of hidden-photon dark matter in the eV and sub-eV range by application of different electromagnetic radiation detectors. We discuss sensitivity and accessible regions in the dark matter parameter space.Comment: 9 pages, proceeding of the 34th International Cosmic Ray Conference (ICRC), July 30 - August 6, 2015, The Hague, The Netherland

Correctness of Generalisation and Customisation of Concurrent Model Synchronisation Based on Triple Graph Grammars

Triple graph grammars (TGGs) have been successfully applied to specify and analyse bidirectional model transformations. Recently, a formal approach to concurrent model synchronisation has been presented, where a source and a target modification have to be synchronised simultaneously. In this approach, conflicts between the given and propagated source or target model modifications are taken into account. A semi-automatic conflict resolution strategy is proposed, where a formal resolution strategy can be combined with a user-specific strategy. Up to now, our approach requires deterministic propagation operations. In this paper, we want to relax this condition and also consider non-deterministic (conflicting) operations which might require backtracking. For optimisation, we propose to eliminate conflicts between the operational rules of a TGG using the concept of filter NACs. Nevertheless, concurrent synchronisation is non-deterministic from a user perspective: The user may choose between forward synchronisation and backward synchronisation. Moreover, the conflict resolution strategy may result in several solutions from which the user has to select the most adequate one. Hence, we discuss different kinds of customisation of the synchronisation process and explain the impacts of the different strategies

Ultracold chemical reactions of a single Rydberg atom in a dense gas

Within a dense environment ($\rho \approx 10^{14}\,$atoms/cm$^3$) at ultracold temperatures ($T < 1\,\mu{}\text{K}$), a single atom excited to a Rydberg state acts as a reaction center for surrounding neutral atoms. At these temperatures almost all neutral atoms within the Rydberg orbit are bound to the Rydberg core and interact with the Rydberg atom. We have studied the reaction rate and products for $nS$ $^{87}$Rb Rydberg states and we mainly observe a state change of the Rydberg electron to a high orbital angular momentum $l$, with the released energy being converted into kinetic energy of the Rydberg atom. Unexpectedly, the measurements show a threshold behavior at $n\approx 100$ for the inelastic collision time leading to increased lifetimes of the Rydberg state independent of the densities investigated. Even at very high densities ($\rho\approx4.8\times 10^{14}\,\text{cm}^{-3}$), the lifetime of a Rydberg atom exceeds $10\,\mu\text{s}$ at $n > 140$ compared to $1\,\mu\text{s}$ at $n=90$. In addition, a second observed reaction mechanism, namely Rb$_2^+$ molecule formation, was studied. Both reaction products are equally probable for $n=40$ but the fraction of Rb$_2^+$ created drops to below 10$\,$% for $n\ge90$.Comment: 13 pages, 13 figure

Safety evaluation of a β-amylase food enzyme obtained from wheat (Triticum spp.)

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Safety evaluation of the food enzyme β-amylase obtained from barley (Hordeum vulgare)

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Safety evaluation of the food enzyme β-amylase obtained from soybean (Glycine max) whey

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