Diophantine approximation on Veech surfaces

We show that Y. Cheung's general $Z$-continued fractions can be adapted to give approximation by saddle connection vectors for any compact translation surface. That is, we show the finiteness of his Minkowski constant for any compact translation surface. Furthermore, we show that for a Veech surface in standard form, each component of any saddle connection vector dominates its conjugates. The saddle connection continued fractions then allow one to recognize certain transcendental directions by their developments

Spectral stability of the Coulomb-Dirac Hamiltonian with anomalous magnetic moment

We show that the point spectrum of the standard Coulomb-Dirac operator H_0 is the limit of the point spectrum of the Dirac operator with anomalous magnetic moment H_a as the anomaly parameter tends to 0. For negative angular momentum quantum number kappa, this holds for all Coulomb coupling constants c for which H_0 has a distinguished self-adjoint realisation. For positive kappa, however, there are some exceptional values for c, and in general an index shift between the eigenvalues of H_0 and the limits of eigenvalues of H_a appears, accompanied with additional oscillations of the eigenfunctions of H_a very close to the origin

Construction and Test of New Precision Drift-Tube Chambers for the ATLAS Muon Spectrometer

ATLAS muon detector upgrades aim for increased acceptance for muon triggering and precision tracking and for improved rate capability of the muon chambers in the high-background regions of the detector with increasing LHC luminosity. The small-diameter Muon Drift Tube (sMDT) chambers have been developed for these purposes. With half of the drift-tube diameter of the MDT chambers and otherwise unchanged operating parameters, sMDT chambers share the advantages of the MDTs, but have an order of magnitude higher rate capability and can be installed in detector regions where MDT chambers do not fit in. The chamber assembly methods have been optimized for mass production, minimizing construction time and personnel. Sense wire positioning accuracies of 5 ?micons have been achieved in serial production for large-size chambers comprising several hundred drift tubes. The construction of new sMDT chambers for installation in the 2016/17 winter shutdown of the LHC and the design of sMDT chambers in combination with new RPC trigger chambers for replacement of the inner layer of the barrel muon spectrometer are in progress

Ergodicity for Infinite Periodic Translation Surfaces

For a Z-cover of a translation surface, which is a lattice surface, and which admits infinite strips, we prove that almost every direction for the straightline flow is ergodic

Recurrence in generic staircases

The straight-line flow on almost every staircase and on almost every square tiled staircase is recurrent. For almost every square tiled staircase the set of periodic orbits is dense in the phase space

A Functional Reference Model for Manufacturing Execution Systems in the Automotive Industry

Being confronted with IT strategic questions of how to constantlyreduce IT operating costs and at the same time live up to everincreasing manufacturing demands, automobile manufacturers areencountering problems to find appropriate IT support forproduction planning and execution. Moreover, they are facing thechallenge to clearly define and demarcate Enterprise ResourcePlanning (ERP) and Manufacturing Execution Systems (MES)functionality. Despite the existence of a number of standardizationefforts addressing MES functionality, automobile manufacturersare still struggling to reach a common understanding for the termMES and a clear functional design. The paper addresses this needby developing a functional reference model for MES in theautomotive industry based on a multiple case study approach. Thecase studies examine the design and implementation ofmanufacturing-related functionality in four leading automotivemanufacturing companies

Probing fractal magnetic domains on multiple length scales in Nd2Fe14B

Using small-angle neutron scattering, we demonstrate that the complex magnetic domain patterns at the surface of Nd2Fe14B, revealed by quantitative Kerr and Faraday microscopy, propagate into the bulk and exhibit structural features with dimensions down to 6 nm, the domain wall thickness. The observed fractal nature of the domain structures provides an explanation for the anomalous increase in the bulk magnetization of Nd2Fe14B below the spin-reorientation transition. These measurements open up a rich playground for studies of fractal structures in highly anisotropic magnetic systems.Comment: Accepted for publication in Phys. Rev. Lett. (4 pages, 4 figures