On Completely Mixed Stochastic Games

In this paper, we consider a zero-sum undiscounted stochastic game which has finite state space and finitely many pure actions. Also, we assume the transition probability of the undiscounted stochastic game is controlled by one player and all the optimal strategies of the game are strictly positive. Under all the above assumptions, we show that the $\beta$-discounted stochastic games with the same payoff matrices and $\beta$ sufficiently close to 1 are also completely mixed. We give a counterexample to show that the converse of the above result in not true. We also show that, if we have non-zero value in some state for the undiscounted stochastic game then for $\beta$ sufficiently close to 1 the $\beta$-discounted stochastic game also possess nonzero value in the same state

Circumstellar dust shells of hot post-AGB stars

Using a radiative transfer code (DUSTY) parameters of the circumstellar dust shells of 15 hot post-AGB stars have been derived. Combining the optical, near and far-infrared (ISO, IRAS) data of the stars, we have reconstructed their spectral energy distributions (SEDs) and estimated the dust temperatures, mass loss rates, angular radii of the inner boundary of the dust envelopes and the distances to these stars. The mass loss rates (10$^{-6}-10^{-5}$M$_{\odot}$yr$^{-1}$) are intermediate between stars at the tip of the AGB and the PN phase. We have also studied the ISO spectra of 7 of these stars. Amorphous and crystalline silicate features were observed in IRAS14331-6435 (Hen3-1013), IRAS18062+2410 (SAO85766) and IRAS22023+5249 (LSIII +5224) indicating oxygen-rich circumstellar dust shells. The presence of unidentified infrared (UIR) band at 7.7$\mu$, SiC emission at 11.5$\mu$ and the "26$\mu$" and "main 30$\mu$" features in the ISO spectrum of IRAS17311-4924 (Hen3-1428) suggest that the central star may be carbon-rich. The ISO spectrum of IRAS17423-1755 (Hen3-1475) shows a broad absorption feature at 3.1$\mu$ due to C$_{2}$H$_{2}$ and/or HCN which is usually detected in the circumstellar shells of carbon-rich stars.Comment: 18 pages, accepted for publication in A&

UV (IUE) spectra of the central stars of high latitude planetary nebulae Hb7 and Sp3

We present an analysis of the UV (IUE) spectra of the central stars of Hb7 and Sp3. Comparison with the IUE spectrum of the standard star HD 93205 leads to a spectral classification of O3V for these stars, with an effective temperature of 50,000 K. From the P-Cygni profiles of CIV (1550 A), we derive stellar wind velocities and mass loss rates of -1317 km/s +/- 300 km/s and 2.9X10^{-8} solar mass yr^{-1} and -1603 km/s +/- 400 km/s and 7X10^{-9} solar mass yr^{-1} for Hb7 and Sp3 respectively. From all the available data, we reconstruct the spectral energy distribution of Hb7 and Sp3.Comment: 4 pages, 3 figures, latex, accepted for publication in Astronomy & Astrophysic

Photometry and low resolution spectroscopy of hot post-AGB candidates

We have obtained Johnson U, B, V and Cousins R, I photometry and low resolution spectra of a small sample of hot post-AGB candidates. Using the present data in combination with JHK data from 2MASS, infrared data from the MSX catalog and the IRAS fluxes, we have studied the spectral energy distribution (SED) of these stars. Using the DUSTY code we have estimated the dust temperatures, the distances to the stars, the mass-loss rates, angular radii of the inner boundary of the dust envelopes and dynamical ages from the tip of the AGB. These candidates have also been imaged through a narrow band H-alpha filter, to search for nebulosity around the central stars. Our H-alpha images revealed the bipolar morphology of the low excitation PN IRAS 17395-0841 with an angular extent of 2.8arcsec. The bipolar lobes of IRAS 17423-1755 in H-alpha were found to have an angular extent of 3.5arcsec (south-east lobe) and 2.2arcsec (north-west lobe). The dust envelope characteristics, low resolution spectrum and IRAS colors suggest that IRAS 18313-1738 is similar to the proto-planetary nebula (PPN) HD 51585. The SED of IRAS 17423-1755, IRAS 18313-1738 and IRAS 19127+1717 show a warm dust component (in addition to the cold dust) which may be due to recent and ongoing mass-loss.Comment: 20 pages, 6 figures, h-alpha figure compressed with XV, paper accepted for publication in Astronomy & Astrophysic

High resolution spectroscopy of the high velocity hot post-AGB star LS III +52 24 (IRAS 22023+5249)

The first high-resolution (R~50,000) optical spectrum of the B-type star, LS III +52 24, identified as the optical counterpart of the hot post-AGB candidate IRAS 22023+5249 (I22023) is presented. We report the detailed identifications of the observed absorption and emission features in the full wavelength range (4290-9015 A) as well as the atmospheric parameters and photospheric abundances (under the Local Thermodinamic Equilibrium approximation) for the first time. The nebular parameters (Te, Ne) are also derived. We estimate Teff=24,000 K, log g=3.0, xi=7 kms-1 and the derived abundances indicate a slightly metal-deficient evolved star with C/O<1. The observed P-Cygni profiles of hydrogen and helium clearly indicate on-going post-AGB mass loss. The presence of [N II] and [S II] lines and the non-detection of [O III] indicate that photoionisation has just started. The observed spectral features, large heliocentric radial velocity, atmospheric parameters, and chemical composition indicate that I22023 is an evolved post-AGB star belonging to the old disk population. The derived nebular parameters (Te=7000 K, Ne=1.2x104 cm-3) also suggest that I22023 may be evolving into a compact, young low-excitation Planetary Nebula. Our optical spectroscopic analysis together with the recent Spitzer detection of double-dust chemistry (the simultaneous presence of carbonaceous molecules and amorphous silicates) in I22023 and other B-type post-AGB candidates may point to a binary system with a dusty disk as the stellar origin common to the hot post-AGB stars with O-rich central stars.Comment: Accepted for publication in MNRAS (22 pages, 4 figures, and 8 tables). arXiv admin note: substantial text overlap with arXiv:0707.059

Comment on ``Intermittent Synchronization in a Pair of Coupled Chaotic Pendula"

The main aim of this comment is to emphasize that the conditional Lyapunov exponents play an important role in distinguishing between intermittent and persistent synchronization, when the analytic criteria for asymptotic stability are not uniformly obeyed.Comment: 2 pages, RevTeX 4, 1 EPS figur