On p-adic lattices and Grassmannians

It is well-known that the coset spaces G(k((z)))/G(k[[z]]), for a reductive group G over a field k, carry the geometric structure of an inductive limit of projective k-schemes. This k-ind-scheme is known as the affine Grassmannian for G. From the point of view of number theory it would be interesting to obtain an analogous geometric interpretation of quotients of the form G(W(k)[1/p])/G(W(k)), where p is a rational prime, W denotes the ring scheme of p-typical Witt vectors, k is a perfect field of characteristic p and G is a reductive group scheme over W(k). The present paper is an attempt to describe which constructions carry over from the function field case to the p-adic case, more precisely to the situation of the p-adic affine Grassmannian for the special linear group G=SL_n. We start with a description of the R-valued points of the p-adic affine Grassmannian for SL_n in terms of lattices over W(R), where R is a perfect k-algebra. In order to obtain a link with geometry we further construct projective k-subvarieties of the multigraded Hilbert scheme which map equivariantly to the p-adic affine Grassmannian. The images of these morphisms play the role of Schubert varieties in the p-adic setting. Further, for any reduced k-algebra R these morphisms induce bijective maps between the sets of R-valued points of the respective open orbits in the multigraded Hilbert scheme and the corresponding Schubert cells of the p-adic affine Grassmannian for SL_n.Comment: 36 pages. This is a thorough revision, in the form accepted by Math. Zeitschrift, of the previously published preprint "On p-adic loop groups and Grassmannians

Times of arrival: Bohm beats Kijowski

We prove that the Bohmian arrival time of the 1D Schroedinger evolution violates the quadratic form structure on which Kijowski's axiomatic treatment of arrival times is based. Within Kijowski's framework, for a free right moving wave packet, the various notions of arrival time (at a fixed point x on the real line) all yield the same average arrival time. We derive an inequality relating the average Bohmian arrival time to the one of Kijowksi. We prove that the average Bohmian arrival time is less than Kijowski's one if and only if the wave packet leads to position probability backflow through x. Otherwise the two average arrival times coincide.Comment: 9 page

A new approach to quantum backflow

We derive some rigorous results concerning the backflow operator introduced by Bracken and Melloy. We show that it is linear bounded, self adjoint, and not compact. Thus the question is underlined whether the backflow constant is an eigenvalue of the backflow operator. From the position representation of the backflow operator we obtain a more efficient method to determine the backflow constant. Finally, detailed position probability flow properties of a numerical approximation to the (perhaps improper) wave function of maximal backflow are displayed.Comment: 12 pages, 8 figure

System for 3D Visualization of Flaws for Eddy Current Inspection

This paper presents a novel method for 3D visualization of flaws detected during Eddy Current (EC) inspection. The EC data was acquired using an automated scanning system equipped with precise eddy current probe positioning. The method was tested on a single frequency instrument with an absolute probe. The EC inspection procedure is implemented statically by registering the operating point of the instrument at each equidistant point on a tested object.The paper describes a data processing method based on the Fourier transform enabling 3D visualization of flaws. This three-dimensional image of the result of a scan enables the position of flaws to be determined, and the size and bevel (angle to the surface) of each detected flaw to be estimated. This research investigated flaws rising from the surface of the tested object, and flaw depth was not evaluated in this work. This method of visualization is simple to implement and is currently targeted for application in EC scanning devices.

Bohmian transmission and reflection dwell times without trajectory sampling

Within the framework of Bohmian mechanics dwell times find a straightforward formulation. The computation of associated probabilities and distributions however needs the explicit knowledge of a relevant sample of trajectories and therefore implies formidable numerical effort. Here a trajectory free formulation for the average transmission and reflection dwell times within static spatial intervals [a,b] is given for one-dimensional scattering problems. This formulation reduces the computation time to less than 5% of the computation time by means of trajectory sampling.Comment: 14 pages, 7 figures; v2: published version, significantly revised and shortened (former sections 2 and 3 omitted, appendix A added, simplified mathematics

Assessment of public health issues of migrants at the Greek-Turkish border, April 2011

A joint mission to assess the public health situation of migrants in Greek detention centres was undertaken in April 2011 by the European Centre for Disease Prevention and Control (ECDC) and the World Health Organization (WHO) Regional Office for Europe. The assessment visit follows the increased migration to the Evros prefecture, Eastern Macedonia and Thrace region, at the Greek-Turkish border where large numbers of migrants are entering Greece via the Evros River, a natural border. Migrants are housed in local detention centres. The main problem in detention centres are the substandard hygiene conditions, especially overcrowding and lack of personal hygiene facilities, lack of basic supplies and lack of access to fresh air and physical exercise. As the migration route via the Evros region is increasingly used since 2009, and due to the unstable political situation in North Africa and the Middle East, an increased influx of migrants was to be expected with the falling water levels of the Evros River in summer, resulting in further deterioration of the already critical situation in the Thrace region’s detention centres

Radial Velocity Variations in Pulsating Ap Stars III. The Discovery of 16.21 min Oscillations in Beta CrB

We present the analysis of 3 hrs of a rapid time series of precise stellar radial velocity (RV) measurements (sigma = 4.5 m/s) of the cool Ap star Beta CrB. The integrated RV measurements spanning the wavelength interval 5000-6000 Ang. show significant variations (false alarm probability = 10^-5) with a period of 16.21 min (nu = 1028.17 micro Hz) and an amplitude of 3.54 +/- 0.56 m/s. The RV measured over a much narrower wavelength interval reveals one spectral feature at 6272 Ang. pulsating with the same 16.21 min period and an amplitude of 138 +/- 23 m/s. These observations establish Beta CrB to be a low-amplitude rapidly oscillating Ap star.Comment: 5 Pages, 5 figure

Diffraction in time of a confined particle and its Bohmian paths

Diffraction in time of a particle confined in a box which its walls are removed suddenly at $t=0$ is studied. The solution of the time-dependent Schr\"{o}dinger equation is discussed analytically and numerically for various initial wavefunctions. In each case Bohmian trajectories of the particles are computed and also the mean arrival time at a given location is studied as a function of the initial state.Comment: 8 pages, 6 figure

Ethanol Vapours to Complement or Replace Sulfur Dioxide Fumigation of Table Grapes

Recent studies have shown that dipping table grapes in ethanol solutions at harvest improved storage of the fruit. We report here the first results obtained by treating "Chasselas" table grapes (Vitis vinifera) with ethanol vapours over the storage period. We tested the effect of ethanol at 0, 4 and 8 g/kg fruit during cold storage for 2, 4 and 6 weeks. We measured berry shatter, stem browning, Botrytis rot incidence and sensory appreciation by tasting panels. Ethanol vapours reduced Botrytis rot incidence and berry shatter, but hastened stem browning. Sensory analyses did not detect any differences between treatments

Melamine contamination of dairy products in China – public health impact on citizens of the European Union

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