Evolution of O Abundance Relative to Fe

We present a three-component mixing model for the evolution of O abundance relative to Fe, taking into account the contributions of the first very massive (> 100 solar masses) stars formed from Big Bang debris. We show that the observations of O and Fe abundances in metal-poor stars in the Galaxy by Israelian et al. and Boesgaard et al. can be well represented both qualitatively and quantitatively by this model. Under the assumption of an initial Fe ([Fe/H] = -3) and O inventory due to the prompt production by the first very massive stars, the data at -3 < [Fe/H] < -1 are interpreted to result from the addition of O and Fe only from type II supernovae (SNII) to the prompt inventory. At [Fe/H] = -1, SNII still contribute O while both SNII and type Ia supernovae contribute Fe. During this later stage, (O/Fe) sharply drops off to an asymptotic value of 0.8(O/Fe)_sun. The value of (O/Fe) for the prompt inventory at [Fe/H] = -3 is found to be (O/Fe) = 20(O/Fe)_sun. This result suggests that protogalaxies with low ``metallicities'' should exhibit high values of (O/Fe). The C/O ratio produced by the first very massive stars is expected to be much less than 1 so that all the C should be tied up as CO and that C dust and hydrocarbon compounds should be quite rare at epochs corresponding to [Fe/H] < -3.Comment: 25 pages, 8 postscript figures, to appear in Ap

A Circumbinary Planet in Orbit Around the Short-Period White-Dwarf Eclipsing Binary RR Cae

By using six new determined mid-eclipse times together with those collected from the literature, we found that the Observed-Calculated (O-C) curve of RR Cae shows a cyclic change with a period of 11.9 years and an amplitude of 14.3s, while it undergoes an upward parabolic variation (revealing a long-term period increase at a rate of dP/dt =+4.18(+-0.20)x10^(-12). The cyclic change was analyzed for the light-travel time effect that arises from the gravitational influence of a third companion. The mass of the third body was determined to be M_3*sin i' = 4.2(+-0.4) M_{Jup} suggesting that it is a circumbinary giant planet when its orbital inclination is larger than 17.6 degree. The orbital separation of the circumbinary planet from the central eclipsing binary is about 5.3(+-0.6)AU. The period increase is opposite to the changes caused by angular momentum loss via magnetic braking or/and gravitational radiation, nor can it be explained by the mass transfer between both components because of its detached configuration. These indicate that the observed upward parabolic change is only a part of a long-period (longer than 26.3 years) cyclic variation, which may reveal the presence of another giant circumbinary planet in a wide orbit.Comment: It will be published in the MNRA

Asymptotic behavior of the least common multiple of consecutive arithmetic progression terms

Let $l$ and $m$ be two integers with $l>m\ge 0$, and let $a$ and $b$ be integers with $a\ge 1$ and $a+b\ge 1$. In this paper, we prove that $\log {\rm lcm}_{mn<i\le ln}\{ai+b\} =An+o(n)$, where $A$ is a constant depending on $l, m$ and $a$.Comment: 8 pages. To appear in Archiv der Mathemati

High Fill-Out, Extreme Mass Ratio Overcontact Binary Systems. X. The new discovered binary XY Leonis Minoris

The new discovered short-period close binary star, XY LMi, was monitored photometrically since 2006. It is shown that the light curves are typical EW-type and show complete eclipses with an eclipse duration of about 80 minutes. By analyzing the complete B, V, R, and I light curves with the 2003 version of the W-D code, photometric solutions were determined. It is discovered that XY LMi is a high fill-out, extreme mass ratio overcontact binary system with a mass ratio of q=0.148 and a fill-out factor of f=74.1%, suggesting that it is on the late evolutionary stage of late-type tidal-locked binary stars. As observed in other overcontact binary stars, evidence for the presence of two dark spots on both components are given. Based on our 19 epoches of eclipse times, it is found that the orbital period of the overcontact binary is decreasing continuously at a rate of dP/dt=-1.67\times10^{-7}\,days/year, which may be caused by the mass transfer from the primary to the secondary or/and angular momentum loss via magnetic stellar wind. The decrease of the orbital period may result in the increase of the fill-out, and finally, it will evolve into a single rapid-rotation star when the fluid surface reaching the outer critical Roche Lobe.Comment: 19 pages, 4 figures, 9 table

Electron Depletion Due to Bias of a T-Shaped Field-Effect Transistor

A T-shaped field-effect transistor, made out of a pair of two-dimensional electron gases, is modeled and studied. A simple numerical model is developed to study the electron distribution vs. applied gate voltage for different gate lengths. The model is then improved to account for depletion and the width of the two-dimensional electron gases. The results are then compared to the experimental ones and to some approximate analytical calculations and are found to be in good agreement with them.Comment: 16 pages, LaTex (RevTex), 8 fig

Galilean invariance of lattice Boltzmann models

It is well-known that the original lattice Boltzmann (LB) equation deviates from the Navier-Stokes equations due to an unphysical velocity dependent viscosity. This unphysical dependency violates the Galilean invariance and limits the validation domain of the LB method to near incompressible flows. As previously shown, recovery of correct transport phenomena in kinetic equations depends on the higher hydrodynamic moments. In this Letter, we give specific criteria for recovery of various transport coefficients. The Galilean invariance of a general class of LB models is demonstrated via numerical experiments