The proton and the photon, who is probing whom in electroproduction?

The latest results on the structure of the proton and the photon as seen at HERA are reviewed while discussing the question posed in the title of the talk.Comment: 18 pages, including 28 figures. To be published in the proceedings of the 2nd KEK-Tanashi International Symposium on Hadron and Nuclear Physics with Electromagnetic Probes, KEK-Tanashi, Tokyo, Japan, October 25-27, 1999. Typos in eqs (8) and (9) corrected and reference 5 update

The statistics of Sco X-1 kHZ QPOs

Recently an additional technique was applied to investigate the properties of kHz QPOS, i.e. the analysis of the distribution of frequency ratios or frequencies themselves. I review the results of such work on the data from ScoX-1: Abramowicz et al. (2003), which was later criticized by Belloni et al.(2005). I conclude that the findings of the latter paper are consistent with results presented earlier: kHz QPOs cluster around the value corresponding to the frequency ratio of 2/3. I also discuss the random walk model of kHz QPOs and possible future observations needed to verify it.Comment: Astronomische Nachrichten, in pres

On the Polish doughnut accretion disk via the effective potential approach

We revisit the Polish doughnut model of accretion disks providing a comprehensive analytical description of the Polish doughnut structure. We describe a perfect fluid circularly orbiting around a Schwarzschild black hole, source of the gravitational field, by the effective potential approach for the exact gravitational and centrifugal effects. This analysis leads to a detailed, analytical description of the accretion disk, its toroidal surface, the thickness, the distance from the source. We determine the variation of these features with the effective potential and the fluid angular momentum. Many analytical formulas are given. In particular it turns out that the distance from the source of the inner surface of the torus increases with increasing fluid angular momentum but decreases with increasing energy function defined as the value of the effective potential for that momentum. The location of torus maximum thickness moves towards the external regions of the surface with increasing angular momentum, until it reaches a maximum an then decreases. Assuming a polytropic equation of state we investigate some specific cases.Comment: 33 pages, 28 figures, 1 table. This is a revised version to meet the published articl

Cumulative Dragging - An Intrinsic Characteristic of Stationary Axisymmetric Spacetime

The Cumulative Drag Index defined recently by Prasanna has been generalised to include the centrifugal acceleration. We have studied the behaviour of the drag index for the Kerr metric and the Neugebauer-Meinel metric representing a self-gravitating rotating disk and their Newtonian approximations. The similarity of the behaviour of the index for a given set of parameters both in the full and approximated forms, suggests that the index characterises an intrinsic property of spacetime with rotation. Analysing the index for a given set of parameters shows possible constraints on them.Comment: Discussion of Neugebauer-Meinel rotating disk and clarifications adde

Spline approximation of a random process with singularity

Let a continuous random process $X$ defined on $[0,1]$ be $(m+\beta)$-smooth, $0\le m, 00$ and have an isolated singularity point at $t=0$. In addition, let $X$ be locally like a $m$-fold integrated $\beta$-fractional Brownian motion for all non-singular points. We consider approximation of $X$ by piecewise Hermite interpolation splines with $n$ free knots (i.e., a sampling design, a mesh). The approximation performance is measured by mean errors (e.g., integrated or maximal quadratic mean errors). We construct a sequence of sampling designs with asymptotic approximation rate $n^{-(m+\beta)}$ for the whole interval.Comment: 16 pages, 2 figure typos and references corrected, revised classes definition, results unchange

Epicyclic orbital oscillations in Newton's and Einstein's dynamics

We apply Feynman's principle, ``The same equations have the same solutions'', to Kepler's problem and show that Newton's dynamics in a properly curved 3-D space is identical with that described by Einstein's theory in the 3-D optical geometry of Schwarzschild's spacetime. For this reason, rather unexpectedly, Newton's formulae for Kepler's problem, in the case of nearly circular motion in a static, spherically spherical gravitational potential accurately describe strong field general relativistic effects, in particular vanishing of the radial epicyclic frequency at the marginally stable orbit.Comment: 8 page