We present the first comprehensive study of the narrow emission lines of T Tauri stars (TTS). These narrow lines have been reported in the literature as originating in the stellar atmosphere and having Gaussian-type profiles centered at the stellar rest velocity, with a base width not larger than 50 km s-1. Here, we concentrate on the Ca n lines XX8498, 8542, and 8662 and the helium line X5876. After applying veiling corrections, the average narrow component line emission is found to be larger than that found in active main-sequence stars: up to several times larger for classical T Tauri stars with strong rates of disk accretion. More striking is the finding that the resulting line emission strengths of these lines correlate with veiling. The correlation is confirmed on individual stars for which observations at several epochs exist and for which veiling varies widely on relatively short timescales. We also find a correlation between the narrow emission fluxes and the near-infrared excesses for stars with low levels of veiling, which includes the few weak-lined TTS of the sample. We discuss possible formation sites for the narrow emission lines in the classical TTS, and we present simple models to explain the observations. In these models, the excess line emission found for the stars with higher accretion rates is assumed to originate in localized regions near the magnetic footpoints of the accretion column. We refer to these hypothetical regions in the atmosphere collectively as the "hot chromosphere" since we assume they are additionally heated by the reprocessed energy of the colliding gas in the accretion process. Computing two chromospheric models, one representing the typical weak TTS chromosphere and the other representing the best guess at the "hot chromosphere," we find the following. The "hot chromosphere" is characterized by a steep temperature gradient beginning at low continuum optical depths in order to give simultaneously the large observed central flux and the relatively narrow baselines (50-60 km s ~1). The chromosphere temperature rise is not similar to the earlier deep chromosphere models in which a sudden chromospheric temperature rise is appended to the photosphere at relatively large mass column. For the most extreme cases (i.e., largest line fluxes), 20%, at most, of the star's surface must be covered by "hot chromospheric" regions.

␤-Defensins are small (3 to 5 kDa in size) secreted antimicrobial and antiviral proteins that are components of innate immunity. ␤-Defensins are secreted by epithelial cells, and they are expressed at high levels in several mucosae, including the mouth, where the concentration of these proteins can reach 100 g/ml. Because of these properties, we wondered whether they could be part of the defenses that lower oral transmission of human immunodeficiency virus (HIV) compared to other mucosal sites. Our data show that select ␤-defensins, especially human ␤-defensin 2 (hBD2) and hBD3, inhibit R5 and X4 HIV infection in a dose-dependent manner at doses that are compatible with or below those measured in the oral cavity. We observed that ␤-defensin treatment inhibited accumulation of early products of reverse transcription, as detected by PCR. We could not, however, detect any reproducible inhibition of env-mediated fusion, and we did not observe any modulation of HIV coreceptors following treatment with hBD1 and hBD2, in both resting and phytohemagglutinin-activated cells. Our data instead suggest that, besides a direct inactivation of HIV virions, hBD2 inhibits HIV replication in the intracellular environment. Therefore, we speculate that ␤-defensins mediate a novel antiretroviral mechanism that contributes to prevention of oral HIV transmission in the oral cavity. Immunohistochemical data on hBD2 expression in oral mucosal tissue shows that hBD2 is constitutively expressed, forming a barrier layer across the epithelium in healthy subjects, while in HIV-positive subjects levels of hBD2 expression are dramatically diminished. This may predispose HIV-positive subjects to increased incidence of oral complications associated with HIV infection.

In this paper we revisit the Lyapunov theory for singular systems. There are basically two well known generalized Lyapunov equations used to characterize stability for singular systems. We start with the Lyapunov theorem of [6], [7]. We show that the Lyapunov equation of that theorem can lead to incorrect conclusion about stability. Some cases where that equation can be used are clari£ed. We also show that an attempt to correct that theorem with a generalized Lyapunov equation similar to the original one leads naturally to the generalized equation of [14].

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