A simple, accurate depth check guage

Easily made, pen-light battery operated production check gauge has probe-activated switch with fail-safe features to insure proper operation. Parts can be reliably and quickly checked. Gauge is equipped with tolerance band adjustment and can use interchangeable probes for different applications. Accompanying tester permits frequent check of calibration

Stationary problems for equation of the KdV type and dynamical rr-matrices.

We study a quite general family of dynamical $r$-matrices for an auxiliary loop algebra ${\cal L}({su(2)})$ related to restricted flows for equations of the KdV type. This underlying $r$-matrix structure allows to reconstruct Lax representations and to find variables of separation for a wide set of the integrable natural Hamiltonian systems. As an example, we discuss the Henon-Heiles system and a quartic system of two degrees of freedom in detail.Comment: 25pp, LaTe

Stellar laboratories: new Ge V and Ge VI oscillator strengths and their validation in the hot white dwarf RE 0503-289

State-of-the-art spectral analysis of hot stars by means of non-LTE model-atmosphere techniques has arrived at a high level of sophistication. The analysis of high-resolution and high-S/N spectra, however, is strongly restricted by the lack of reliable atomic data for highly ionized species from intermediate-mass metals to trans-iron elements. Especially data for the latter has only been sparsely calculated. Many of their lines are identified in spectra of extremely hot, hydrogen-deficient post-AGB stars. A reliable determination of their abundances establishes crucial constraints for AGB nucleosynthesis simulations and, thus, for stellar evolutionary theory. In a previous analysis of the UV spectrum of RE 0503-289, spectral lines of highly ionized Ga, Ge, As, Se, Kr, Mo, Sn, Te, I, and Xe were identified. Individual abundance determinations are hampered by the lack of reliable oscillator strengths. Most of these identified lines stem from Ge V. In addition, we identified Ge VI lines for the first time. We calculated Ge V and Ge VI oscillator strengths to consider their radiative and collisional bound-bound transitions in detail in our non-LTE stellar-atmosphere models for the analysis of the Ge IV - VI spectrum exhibited in high-resolution and high-S/N UV spectra of RE 0503-289. We identify four Ge IV, 37 Ge V, and seven Ge VI lines. Most of these are identified for the first time in any star. We reproduce almost all Ge IV, Ge VI, and Ge VI lines in the observed spectrum of RE 0503-289 (Teff = 70 kK, log g = 7.5) at log Ge = -3.8 +/- 0.3 (mass fraction, about 650 times solar). Reliable measurements and calculations of atomic data are a prerequisite for stellar-atmosphere modeling. Our oscillator-strength calculations have allowed, for the first time, Ge V and Ge VI lines to be successfully reproduced in a white dwarf's spectrum and to determine its photospheric Ge abundance.Comment: 54 pages, 8 figure

Fractal geometry of critical Potts clusters

Numerical simulations on the total mass, the numbers of bonds on the hull, external perimeter, singly connected bonds and gates into large fjords of the Fortuin-Kasteleyn clusters for two-dimensional q-state Potts models at criticality are presented. The data are found consistent with the recently derived corrections-to-scaling theory. However, the approach to the asymptotic region is slow, and the present range of the data does not allow a unique identification of the exact correction exponentsComment: 7 pages, 8 figures, Late

EC 11481-2303 - A Peculiar Subdwarf OB Star Revisited

EC 11481-2303 is a peculiar, hot, high-gravity pre-white dwarf. Previous optical spectroscopy revealed that it is a sdOB star with an effective temperature (Teff) of 41790 K, a surface gravity log(g)= 5.84, and He/H = 0.014 by number. We present an on-going spectral analysis by means of non-LTE model-atmosphere techniques based on high-resolution, high-S/N optical (VLT-UVES) and ultraviolet (FUSE, IUE) observations. We are able to reproduce the optical and UV observations simultaneously with a chemically homogeneous NLTE model atmosphere with a significantly higher effective temperature and lower He abundance (Teff = 55000 K, log (g) = 5.8, and He / H = 0.0025 by number). While C, N, and O appear less than 0.15 times solar, the iron-group abundance is strongly enhanced by at least a factor of ten.Comment: 8 pages, 11 figure

Quantum Mechanics in Non-Inertial Frames with a Multi-Temporal Quantization Scheme: II) Non-Relativistic Particles

The non-relativistic version of the multi-temporal quantization scheme of relativistic particles in a family of non-inertial frames (see hep-th/0502194) is defined. At the classical level the description of a family of non-rigid non-inertial frames, containing the standard rigidly linear accelereted and rotating ones, is given in the framework of parametrized Galilei theories. Then the multi-temporal quantization, in which the gauge variables, describing the non-inertial effects, are not quantized but considered as c-number generalized times, is applied to non relativistic particles. It is shown that with a suitable ordering there is unitary evolution in all times and that, after the separation of center of mass, it is still possible to identify the inertial bound states. The few existing results of quantization in rigid non-inertial frames are recovered as special cases

Spacetime perspective of Schwarzschild lensing

We propose a definition of an exact lens equation without reference to a background spacetime, and construct the exact lens equation explicitly in the case of Schwarzschild spacetime. For the Schwarzschild case, we give exact expressions for the angular-diameter distance to the sources as well as for the magnification factor and time of arrival of the images. We compare the exact lens equation with the standard lens equation, derived under the thin-lens-weak-field assumption (where the light rays are geodesics of the background with sharp bending in the lens plane, and the gravitational field is weak), and verify the fact that the standard weak-field thin-lens equation is inadequate at small impact parameter. We show that the second-order correction to the weak-field thin-lens equation is inaccurate as well. Finally, we compare the exact lens equation with the recently proposed strong-field thin-lens equation, obtained under the assumption of straight paths but without the small angle approximation, i.e., with allowed large bending angles. We show that the strong-field thin-lens equation is remarkably accurate, even for lightrays that take several turns around the lens before reaching the observer.Comment: 22 pages, 6 figures, to appear in Phys. Rev.

Light Curves of Rapidly Rotating Neutron Stars

We consider the effect of rapid rotation on the light curves of neutron stars with hot polar caps. For $P \approx 3$ms spin periods, the pulse fractions can be as much as an order of magnitude larger than with simple slowly-rotating (Schwarzschild) estimates. Doppler boosting, in particular, leads to characteristic distortion and ``soft lags'' in the pulse profiles, which are easily measurable in light curves with moderate energy resolution. With $\sim 10^5$ photons it should also be possible to isolate the more subtle distortions of light travel time variations and frame dragging. Detailed analysis of high quality millisecond pulsar data from upcoming X-ray missions must include these effects

The blue-edge problem of the V1093 Her instability strip revisited using evolutionary models with atomic diffusion

We have computed a new grid of evolutionary subdwarf B star (sdB) models from the start of central He burning, taking into account atomic diffusion due to radiative levitation, gravitational settling, concentration diffusion, and thermal diffusion. We have computed the non-adiabatic pulsation properties of the models and present the predicted p-mode and g-mode instability strips. In previous studies of the sdB instability strips, artificial abundance enhancements of Fe and Ni were introduced in the pulsation driving layers. In our models, the abundance enhancements of Fe and Ni occur naturally, eradicating the need to use artificial enhancements. We find that the abundance increases of Fe and Ni were previously underestimated and show that the instability strip predicted by our simulations solves the so-called blue edge problem of the subdwarf B star g-mode instability strip. The hottest known g-mode pulsator, KIC 10139564, now resides well within the instability strip {even when only modes with low spherical degrees (l<=2) are considered.Comment: 7 pages, 7 figures. Accepted for publication in Astronomy & Astrophysic