Decay of Nuclear Giant Resonances: Quantum Self-similar Fragmentation

Scaling analysis of nuclear giant resonance transition probabilities with increasing level of complexity in the background states is performed. It is found that the background characteristics, typical for chaotic systems lead to nontrivial multifractal scaling properties.Comment: 4 pages, LaTeX format, pc96.sty + 2 eps figures, accepted as: talk at the 8th Joint EPS-APS International Conference on Physics Computing (PC'96, 17-21. Sept. 1996), to appear in the Proceeding

Different fractal properties of positive and negative returns

We perform an analysis of fractal properties of the positive and the negative changes of the German DAX30 index separately using Multifractal Detrended Fluctuation Analysis (MFDFA). By calculating the singularity spectra $f(\alpha)$ we show that returns of both signs reveal multiscaling. Curiously, these spectra display a significant difference in the scaling properties of returns with opposite sign. The negative price changes are ruled by stronger temporal correlations than the positive ones, what is manifested by larger values of the corresponding H\"{o}lder exponents. As regards the properties of dominant trends, a bear market is more persistent than the bull market irrespective of the sign of fluctuations.Comment: presented at FENS2007 conference, 8 pages, 4 Fig

Cross-correlations in Warsaw Stock Exchange

We study the inter-stock correlations for the largest companies listed on Warsaw Stock Exchange and included in the WIG20 index. Our results from the correlation matrix analysis indicate that the Polish stock market can be well described by a one factor model. We also show that the stock-stock correlations tend to increase with the time scale of returns and they approach a saturation level for the time scales of at least 200 min, i.e. an order of magnitude longer than in the case of some developed markets. We also show that the strength of correlations among the stocks crucially depends on their capitalization. These results combined with our earlier findings together suggest that now the Polish stock market situates itself somewhere between an emerging market phase and a mature market phase.Comment: presented by R.Rak at FENS2007 conference, 9 pages, 4 Fig

Pathological Behavior in the Spectral Statistics of the Asymmetric Rotor Model

The aim of this work is to study the spectral statistics of the asymmetric rotor model (triaxial rigid rotator). The asymmetric top is classically integrable and, according to the Berry-Tabor theory, its spectral statistics should be Poissonian. Surprisingly, our numerical results show that the nearest neighbor spacing distribution $P(s)$ and the spectral rigidity $\Delta_3(L)$ do not follow Poisson statistics. In particular, $P(s)$ shows a sharp peak at $s=1$ while $\Delta_3(L)$ for small values of $L$ follows the Poissonian predictions and asymptotically it shows large fluctuations around its mean value. Finally, we analyze the information entropy, which shows a dissolution of quantum numbers by breaking the axial symmetry of the rigid rotator.Comment: 11 pages, 7 figures, to be published in Phys. Rev.

Invariant Manifolds and Collective Coordinates

We introduce suitable coordinate systems for interacting many-body systems with invariant manifolds. These are Cartesian in coordinate and momentum space and chosen such that several components are identically zero for motion on the invariant manifold. In this sense these coordinates are collective. We make a connection to Zickendraht's collective coordinates and present certain configurations of few-body systems where rotations and vibrations decouple from single-particle motion. These configurations do not depend on details of the interaction.Comment: 15 pages, 2 EPS-figures, uses psfig.st

Measurement of Spinal Sagittal Curvatures using the Laser Triangulation Method

The purpose of the first part of the study was to establish the variability of repeated measurements in different measuring conditions. In the second part, we performed in a large number of patients, a measurement of thoracic kyphosis and lumbar lordosis and compared them to age, gender, and level of nourishment. In the first part, measurements were performed on a plastic model of the back of a patient with a rigid and a normal spine. In the second part, 250 patients participated in the study (126 men and 124 women). For measuring spinal curvatures we used an apparatus for laser triangulation constructed at the Faculty of Mechanical Engineering, University of Ljubljana. A comparison of 30 repeated measurements was shown as the average value±2 SD which included 95% of the results. Thirty repeated readings of one 3D measurement: thoracic kyphosis 41.2°±0.6°, lumbar lordosis 4.4°±1.2°; 30 measurements on a plastic model: thoracic kyphosis 36.8°±1.2°, lumbar lordosis 30.9°±2.0°; 30 measurements on a patient with a rigid spine: thoracic kyphosis 41.5°±2.4°, lumbar lordosis 4.0°±1.8°; 30 measurements on a patient with a normal spine: thoracic kyphosis 48.8°±7.4°, lumbar lordosis 21.1°±4.4°. The average size of thoracic kyphosis in 250 patients was 46.8° (SD 10.1°) and lumbar lordosis 31.7° (SD 12.5°). The angle size was statistically significantly correlated to gender (increased thoracic kyphosis and lumbar lordosis in women) and body mass index (increased thoracic kyphosis and lumbar lordosis in more nourished patients). Age was not significantly correlated to the observed angles. During measurements of the spinal angles it was important to pay attention to relaxation and the patient’s position as well as to perform more measurements providing the average value. The age and the level of nourishment influence the size of the sagittal spinal angles. In the observed sample the effect of age was not confirmed

Many-body Systems Interacting via a Two-body Random Ensemble (I): Angular Momentum distribution in the ground states

In this paper, we discuss the angular momentum distribution in the ground states of many-body systems interacting via a two-body random ensemble. Beginning with a few simple examples, a simple approach to predict P(I)'s, angular momenta I ground state (g.s.) probabilities, of a few solvable cases, such as fermions in a small single-j shell and d boson systems, is given. This method is generalized to predict P(I)'s of more complicated cases, such as even or odd number of fermions in a large single-j shell or a many-j shell, d-boson, sd-boson or sdg-boson systems, etc. By this method we are able to tell which interactions are essential to produce a sizable P(I) in a many-body system. The g.s. probability of maximum angular momentum $I_{max}$ is discussed. An argument on the microscopic foundation of our approach, and certain matrix elements which are useful to understand the observed regularities, are also given or addressed in detail. The low seniority chain of 0 g.s. by using the same set of two-body interactions is confirmed but it is noted that contribution to the total 0 g.s. probability beyond this chain may be more important for even fermions in a single-j shell. Preliminary results by taking a displaced two-body random ensemble are presented for the I g.s. probabilities.Comment: 39 pages and 8 figure

Absolute properties of the binary system BB Pegasi

We present a ground based photometry of the low-temperature contact binary BB Peg. We collected all times of mid-eclipses available in literature and combined them with those obtained in this study. Analyses of the data indicate a period increase of 3.0(1) x 10^{-8} days/yr. This period increase of BB Peg can be interpreted in terms of the mass transfer 2.4 x 10^{-8} Ms yr^{-1} from the less massive to the more massive component. The physical parameters have been determined as Mc = 1.42 Ms, Mh = 0.53 Ms, Rc = 1.29 Rs, Rh = 0.83 Rs, Lc = 1.86 Ls, and Lh = 0.94 Ls through simultaneous solution of light and of the radial velocity curves. The orbital parameters of the third body, that orbits the contact system in an eccentric orbit, were obtained from the period variation analysis. The system is compared to the similar binaries in the Hertzsprung-Russell and Mass-Radius diagram.Comment: 17 pages, 3 figures, accepted for Astronomical Journa