Spectral multiplicity for powers of weakly mixing automorphisms

We study the behavior of maximal multiplicities $mm (R^n)$ for the powers of a weakly mixing automorphism $R$. For some special infinite set $A$ we show the existence of a weakly mixing rank-one automorphism $R$ such that $mm (R^n)=n$ and $mm(R^{n+1}) =1$ for all $n\in A$. Moreover, the cardinality $cardm(R^n)$ of the set of spectral multiplicities for $R^n$ is not bounded. We have $cardm(R^{n+1})=1$ and $cardm(R^n)=2^{m(n)}$, $m(n)\to\infty$, $n\in A$. We also construct another weakly mixing automorphism $R$ with the following properties: $mm(R^{n}) =n$ for $n=1,2,3,..., 2009, 2010$ but $mm(T^{2011}) =1$, all powers $(R^{n})$ have homogeneous spectrum, and the set of limit points of the sequence $\{\frac{mm (R^n)}{n} : n\in \N \}$ is infinite

Sub-wavelength imaging: Resolution enhancement using metal wire gratings

An experimental evidence of subwavelength imaging with a "lens", which is a uniaxial negative permittivity wire medium slab, is reported. The slab is formed by gratings of long thin parallel conducting cylinders. Taking into account the anisotropy and spatial dispersion in the wire medium we theoretically show that there are no usual plasmons that could be exited on surfaces of such a slab, and there is no resonant enhancement of evanescent fields in the slab. The experimentally observed clear improvement of the resolution in the presence of the slab is explained as filtering out the harmonics with small wavenumbers. In other words, the wire gratings (the wire medium) suppress strong traveling-mode components increasing the role of evanescent waves in the image formation. This effect can be used in near-field imaging and detection applications.Comment: 12 pages, 6 figure

Detection of organic materials by spectrometric radiography method

In this paper we report a spectrometric approach to dual-energy digital radiography that has been developed and applied to identify specific organic substances and discern small differences in their effective atomic number. An experimental setup has been designed, and a theoretical description proposed based on the experimental results obtained. The proposed method is based on application of special reference samples made of materials with different effective atomic number and thickness, parameters known to affect X-ray attenuation in the low-energy range. The results obtained can be used in the development of a new generation of multi-energy customs or medical X-ray scanners.Comment: 6 pages, 2 tables, 5 figures, will be presented at the Workshop on X-Ray Imaging, 22-24 October, 2008, Dresden, German

Ontology-based data access with a horn fragment of metric temporal logic

We advocate datalogMTL, a datalog extension of a Horn fragment of the metric temporal logic MTL, as a language for ontology-based access to temporal log data. We show that datalogMTL is EXPSPACE-complete even with punctual intervals, in which case MTL is known to be undecidable. Nonrecursive datalogMTL turns out to be PSPACE-complete for combined complexity and in AC0 for data complexity. We demonstrate by two real-world use cases that nonrecursive datalogMTL programs can express complex temporal concepts from typical user queries and thereby facilitate access to log data. Our experiments with Siemens turbine data and MesoWest weather data show that datalogMTL ontology-mediated queries are efficient and scale on large datasets of up to 11GB