Delay-dependent robust stability of stochastic delay systems with Markovian switching

In recent years, stability of hybrid stochastic delay systems, one of the important issues in the study of stochastic systems, has received considerable attention. However, the existing results do not deal with the structure of the diffusion but estimate its upper bound, which induces conservatism. This paper studies delay-dependent robust stability of hybrid stochastic delay systems. A delay-dependent criterion for robust exponential stability of hybrid stochastic delay systems is presented in terms of linear matrix inequalities (LMIs), which exploits the structure of the diffusion. Numerical examples are given to verify the effectiveness and less conservativeness of the proposed method

The monodromy groups of Dolgachev's CY moduli spaces are Zariski dense

Let $\mathcal{M}_{n,2n+2}$ be the coarse moduli space of CY manifolds arising from a crepant resolution of double covers of $\mathbb{P}^n$ branched along $2n+2$ hyperplanes in general position. We show that the monodromy group of a good family for $\mathcal{M}_{n,2n+2}$ is Zariski dense in the corresponding symplectic or orthogonal group if $n\geq 3$. In particular, the period map does not give a uniformization of any partial compactification of the coarse moduli space as a Shimura variety whenever $n\geq 3$. This disproves a conjecture of Dolgachev. As a consequence, the fundamental group of the coarse moduli space of $m$ ordered points in $\mathbb{P}^n$ is shown to be large once it is not a point. Similar Zariski-density result is obtained for moduli spaces of CY manifolds arising from cyclic covers of $\mathbb{P}^n$ branched along $m$ hyperplanes in general position. A classification towards the geometric realization problem of B. Gross for type $A$ bounded symmetric domains is given.Comment: 48 page

Internal Variations in Empirical Oxygen Abundances for Giant HII Regions in the Galaxy NGC 2403

This paper presents a spectroscopic investigation of 11 HII regions in the nearby galaxy NGC 2403. The HII regions are observed with a long-slit spectrograph mounted on the 2.16 m telescope at XingLong station of National Astronomical Observatories of China. For each of the HII regions, spectra are extracted at different nebular radii along the slit-coverage. Oxygen abundances are empirically estimated from the strong-line indices R23, N2O2, O3N2, and N2 for each spectrophotometric unit, with both observation- and model-based calibrations adopted into the derivation. Radial profiles of these diversely estimated abundances are drawn for each nebula. In the results, the oxygen abundances separately estimated with the prescriptions on the basis of observations and models, albeit from the same spectral index, systematically deviate from each other; at the same time, the spectral indices R23 and N2O2 are distributed with flat profiles, whereas N2 and O3N2 exhibit apparent gradients with the nebular radius. Because our study naturally samples various ionization levels which inherently decline at larger radii within individual HII regions, the radial distributions indicate not only the robustness of R23 and N2O2 against ionization variations but also the sensitivity of N2 and O3N2 to the ionization parameter. The results in this paper provide observational corroboration of the theoretical prediction about the deviation in the empirical abundance diagnostics. Our future work is planned to investigate metal-poor HII regions with measurable T_e, in an attempt to recalibrate the strong-line indices and consequently disclose the cause of the discrepancies between the empirical oxygen abundances.Comment: 16 pages, 10 figures, 5 tables; accepted for publication in The Astrophysical Journal; with a minor correction in the tex

Characterizing Ultraviolet and Infrared Observational Properties for Galaxies. II. Features of Attenuation Law

Variations in the attenuation law have a significant impact on observed spectral energy distributions for galaxies. As one important observational property for galaxies at ultraviolet and infrared wavelength bands, the correlation between infrared-to-ultraviolet luminosity ratio and ultraviolet color index (or ultraviolet spectral slope), i.e., the IRX-UV relation (or IRX-beta relation), offered a widely used recipe for correcting dust attenuation in galaxies, but the usability appears to be in doubt now because of considerable dispersion in this relation found by many studies. In this paper, on the basis of spectral synthesis modeling and spatially resolved measurements of four nearby spiral galaxies, we provide an interpretation of the deviation in the IRX-UV relation with variations in the attenuation law. From both theoretical and observational viewpoints, two components in the attenuation curve, the linear background and the 2175 Angstrom bump, are suggested to be the parameters in addition to the stellar population age (addressed in the first paper of this series) in the IRX-UV function; different features in the attenuation curve are diagnosed for the galaxies in our sample. Nevertheless, it is often difficult to ascertain the attenuation law for galaxies in actual observations. Possible reasons for preventing the successful detection of the parameters in the attenuation curve are also discussed in this paper, including the degeneracy of the linear background and the 2175 Angstrom bump in observational channels, the requirement for young and dust-rich systems to study, and the difficulty in accurate estimates of dust attenuations at different wavelength bands.Comment: 25 pages, 23 figures, 5 tables; accepted for publication in The Astrophysical Journa