Asymptotic stability for time-variant systems and observability: Uniform and nonuniform criteria

This paper presents some new criteria for uniform and nonuniform asymptotic stability of equilibria for time-variant differential equations and this within a Lyapunov approach. The stability criteria are formulated in terms of certain observability conditions with the output derived from the Lyapunov function. For some classes of systems, this system theoretic interpretation proves to be fruitful since - after establishing the invariance of observability under output injection - this enables us to check the stability criteria on a simpler system. This procedure is illustrated for some classical examples.

A derivation of the asymptotic random-coding prefactor

This paper studies the subexponential prefactor to the random-coding bound for a given rate. Using a refinement of Gallager's bounding techniques, an alternative proof of a recent result by Altuǧ and Wagner is given, and the result is extended to the setting of mismatched decoding. © 2013 IEEE.

Asymptotic periodicity of the Volterra equation with infinite delay

For some species, hereditary factors have great effects on their population evolution, which can be described by the well-known Volterra model. A model developed is investigated in this article, considering the seasonal variation of the environment, where the diffusive effect of the population is also considered. The main approaches employed here are the upper-lower solution method and the monotone iteration technique. The results show that whether the species dies out or not depends on the relations among the birth rate, the death rate, the competition rate, the diffusivity and the hereditary effects. The evolution of the population may show asymptotic periodicity, provided a certain condition is satisfied for the above factors. (c) 2006 Elsevier Ltd. All rights reserved.

Asymptotic weighted-periodicity of the impulsive parabolic equation with time delay

The main aim of this paper is to investigate the effects of the impulse and time delay on a type of parabolic equations. In view of the characteristics of the equation, a particular iteration scheme is adopted. The results show that Under certain conditions on the coefficients of the equation and the impulse, the solution oscillates in a particular manner-called "asymptotic weighted-periodicity".

Asymptotic behaviour of the elastic solution near the tip of a crack situated at a nonideal interface

Mishuris, G; Kuhn, G., (2001) 'Asymptotic behaviour of the elastic solution near the tip of a crack situated at a nonideal interface', Zeitschrift f?r Angewandte Mathematik und Mechanik 81(12) pp.811-826 RAE2008

Analysis of an asymptotic preserving scheme for linear kinetic equations in the diffusion limit

We present a mathematical analysis of the asymptotic preserving scheme proposed in [M. Lemou and L. Mieussens, SIAM J. Sci. Comput., 31 (2008), pp. 334-368] for linear transport equations in kinetic and diffusive regimes. We prove that the scheme is uniformly stable and accurate with respect to the mean free path of the particles. This property is satisfied under an explicitly given CFL condition. This condition tends to a parabolic CFL condition for small mean free paths and is close to a convection CFL condition for large mean free paths. Our analysis is based on very simple energy estimates. © 2010 Society for Industrial and Applied Mathematics.

High-resolution Keck I spectroscopy of Galactic halo post-asymptotic giant branch stars

Absolute and differential abundance analyses have been performed from high-resolution, high signal-to-noise ratio optical (Keck I) spectra for three evolved Galactic halo stars, namely PG 1704 + 222, HD 341617 and LSIV -0401. Their derived atmospheric parameters indicate that all three objects are undergoing a post-asymptotic giant branch (post-AGB) phase of evolution. A differential abundance analysis reveals HD 341617 as having a mild carbon deficiency of 0.74 dex, possibly due to the star having evolved off the AGB before the onset of the third dredge-up. Although such carbon underabundances are typical of hot post-AGB objects, the same trend is not observed in PG 1704 + 222, where the carbon abundance is found to be consistent with those derived for nitrogen and oxygen. Hence, a dredge-up scenario need not be invoked to explain the chemical composition of PG 1704 + 222. For LSIV -0401 no iron deficiency is apparent relative to magnesium and silicon, and hence a gas- dust separation event in the AGB progenitor need not be invoked for this star.

High-resolution spectroscopic observations of post-asymptotic giant branch candidates from the Edinburgh-Cape Survey

High spectral resolution ( R similar to 40 000) and signal-to-noise optical spectra, obtained at the Very Large Telescope ( VLT), are presented for three post-asymptotic giant branch ( AGB) candidates selected from the Edinburgh-Cape ( EC) Faint Blue Object Survey. The stellar atmospheric parameters and chemical compositions, derived using sophisticated non-local thermodynamic equilibrium calculations, reveal that EC 14102-1337 and EC 20068-7324 are both in an evolved post-horizontal branch ( HB) evolutionary state. However, EC 11507-2253 is most likely a post-AGB star.

High-resolution spectroscopy of globular cluster post-Asymptotic Giant Branch stars

We present model atmosphere analyses of high resolution Keck and VLT optical spectra for three evolved stars in globular clusters, viz. ZNG-1 in M 10, ZNG-1 in M 15 and ZNG-1 in NGC 6712. The derived atmospheric parameters and chemical compositions confirm the programme stars to be in the post- Asymptotic Giant Branch (post-AGB) evolutionary phase. Differential abundance analyses reveal CNO abundance patterns in M 10 ZNG-1, and possibly M 15 ZNG-1, which Suggest that both objects may have evolved off the AGB before the third dredge-up occurred. The abundance pattern of these stars is similar to the third class of optically, bright post-AGB objects discussed by van Winckel (1997). Furthermore, M 10 ZNG-1 exhibits a large C underabundance (with Delta[C/O] similar to -1.6 dex), typical of other hot post-AGB objects. Differential Delta[alpha/Fe] abundance ratios in both M 10 ZNG-1 and NGC 6712 ZNG-1 are found to be approximately 0.0 dex, with the Fe abundance of the former being in disagreement with the cluster metallicity of M 10. Given that the Fe absorption features in both M 10 ZNG-1 and NGC6712 ZNG-1 are well observed and reliably modelled, we believe that these differential Fe abundance estimates to be secure. However, our Fe abundance is difficult to explain in terms of previous evolutionary processes that Occur oil both the Horizontal Branch and the AGB.

Iron abundances of B-type post-asymptotic giant branch stars in globular clusters: Barnard29 in M13 and ROA5701 in ωCen

High-resolution optical and ultraviolet (UV) spectra of two B-type post-asymptotic giant branch (post-AGB) stars in globular clusters, Barnard29 in M13 and ROA5701 in ?Cen, have been analysed using model atmosphere techniques. The optical spectra have been obtained with FEROS on the ESO 2.2-m telescope and the 2d-Coudé spectrograph on the 2.7-m McDonald telescope, while the UV observations are from the Goddard high-resolution spectrograph on the Hubble Space Telescope (HST). Abundances of light elements (C, N, O, Mg, Al and S) plus Fe have been determined from the optical spectra, while the UV data provide additional Fe abundance estimates from FeIII absorption lines in the 1875-1900 Å wavelength region. A general metal underabundance relative to young B-type stars is found for both Barnard29 and ROA5701. These results are consistent with the metallicities of the respective clusters, as well as with previous studies of the objects. The derived abundance patterns suggest that the stars have not undergone a gas-dust separation, contrary to previous suggestions, although they may have evolved from the AGB before the onset of the third dredge-up. However, the Fe abundances derived from the HST spectra are lower than those expected from the metallicities of the respective clusters, by 0.5 dex for Barnard29 and 0.8 dex for ROA5701. A similar systematic underabundance is also found for other B-type stars in environments of known metallicity, such as the Magellanic Clouds. These results indicate that the FeIII UV lines may yield abundance values which are systematically too low by typically 0.6 dex and hence such estimates should be treated with caution.

Chemistry in anisotropic asymptotic giant branch winds

We have constructed a model for chemistry in the outflow of an asymptotic giant branch (AGB) star, using a spheroidal anisotropy in density, after that used by Jura. The predicted distributions of a selection of representative species are shown, and it is suggested that the abundance distributions observed by interferometry in IRC + 10216 may be the result of directional variation in outflow velocity.