Decidability of an Expressive Description Logic with Rational Grading

In this paper syntactic objects---concept constructors called part restrictions which realize rational grading are considered in Description Logics (DLs). Being able to convey statements about a rational part of a set of successors, part restrictions essentially enrich the expressive capabilities of DLs. We examine an extension of well-studied DL ALCQIHR+ with part restrictions, and prove that the reasoning in the extended logic is still decidable. The proof uses tableaux technique augmented with indices technique, designed for dealing with part restrictions.

Geomagnetic Earthquake Precursors Improvement Formulation on the basis of SKO (Skopje) and PAG (Intermagnet) Geomagnetic Data

In this paper we show that the simple analysis of the local geomagnetic field behaviour can serve as reliable imminent precursor for regional seismic activity increasing. As the first step the problem was investigated using one- component Dubna fluxgate magnetometer. The result of 2001-2004 Sofia monitoring confirmed many old papers for connection between Earth tide (Sun- Moon tides as earthquakes trigger) and jump (Geomagnetic quake) of daily averaged one minute standart deviation of the geomagnetic field. The second step (2004-present), which included analisys of three-component Danish fluxgate magnetometer data, worked in Skopje Seismological observatory, confirmed the first step result. The analysis of INTERMAGNET data stations around which was happened stronger earthquakes also confirmed our result. The distribution of time difference between the times of such earthquakes and local daily averaged tide vector movement for impending tide extreme confirms our estimate that the increasing seismicity is realized in time window about +/- 2.7 days. The Complex program for researching the possibility for when, where and how earthquakes prediction is proposed as well as the short description of FORTRAN codes for analysis of earthquakes, geomagnetic and tide data, their correlations and visualization.

Quasar optical variability: searching for interband time delays

Aims. The main purpose of this paper is to study time delays between the light variations in different wavebands for a sample of quasars. Measuring a reliable time delay for a large number of quasars may help constraint the models of their central engines. The standard accretion disk irradiation model predicts a delay of the longer wavelengths behind the shorter ones, a delay that depends on the fundamental quasar parameters. Since the black hole masses and the accretion rates are approximately known for the sample we use, one can compare the observed time delays with the expected ones. Methods. We applied the interpolation cross-correlation function (ICCF) method to the Giveon et al. sample of 42 quasars, monitored in two (B and R) colors, to find the time lags represented by the ICCF peaks. Different tests were performed to assess the influence of photometric errors, sampling, etc., on the final result. Results. We found that most of the objects show a delay in the red light curve behind the blue one (a positive lag), which on average for the sample is about +4 days (+3 for the median), although the scatter is significant. These results are broadly consistent with the reprocessing model, especially for the well-sampled objects. The normalized time-lag deviations do not seem to correlate significantly with other quasar properties, including optical, radio, or X-ray measurables. On the other hand, many objects show a clear negative lag, which, if real, may have important consequences for the variability models.

A thermodynamic approach to quantum measurement and quantum probability

A simple model of quantum particle is proposed in which the particle in a {it macroscopic} rest frame is represented by a {it microscopic d}-dimensional oscillator, {it s=(d-1)/2} being the spin of the particle. The state vectors are defined simply by complex combinations of coordinates and momenta. It is argued that the observables of the system are Hermitian forms (corresponding uniquely to Hermitian matrices). Quantum measurements transforms the equilibrium state obtained after preparation into a family of equilibrium states corresponding to the critical values of the measured observable appearing as values of a random quantity associated with the observable. Our main assumptions state that: i) in the process of measurement the measured observable tends to minimum, and ii) the mean value of every random quantity associated with an observable in some state is proportional to the value of the corresponding observable at the same state. This allows to obtain in a very simple manner the Born rule.

Normal frames and the validity of the equivalence principle. I. Cases in a neighborhood and at a point

A treatment in a neighborhood and at a point of the equivalence principle on the basis of derivations of the tensor algebra over a manifold is given. Necessary and sufficient conditions are given for the existence of local bases, called normal frames, in which the components of derivations vanish in a neighborhood or at a point. These frames (bases), if any, are explicitly described and the problem of their holonomicity is considered. In particular, the obtained results concern symmetric as well as nonsymmetric linear connections.