Moduli spaces of coherent systems of small slope on algebraic curves

Let $C$ be an algebraic curve of genus $g\ge2$. A coherent system on $C$ consists of a pair $(E,V)$, where $E$ is an algebraic vector bundle over $C$ of rank $n$ and degree $d$ and $V$ is a subspace of dimension $k$ of the space of sections of $E$. The stability of the coherent system depends on a parameter $\alpha$. We study the geometry of the moduli space of coherent systems for $0<d\le2n$. We show that these spaces are irreducible whenever they are non-empty and obtain necessary and sufficient conditions for non-emptiness.Comment: 27 pages; minor presentational changes and typographical correction

Assessment of the corneal collagen organization after chemical burn using second harmonic generation microscopy

The organization of the corneal stoma is modified due to different factors, including pathology, surgery or external damage. Here the changes in the organization of the corneal collagen fibers during natural healing after chemical burn are investigated using second harmonic generation (SHG) imaging. Moreover, the structure tensor (ST) was used as an objective tool for morphological analyses at different time points after burn (up to 6 months). Unlike control corneas that showed a regular distribution, the collagen pattern at 1 month of burn presented a non-organized arrangement. SHG signal levels noticeably decreased and individual fibers were hardly visible. Over time, the healing process led to a progressive re-organization of the fibers that could be quantified through the ST. At 6 months, the stroma distribution reached values similar to those of control eyes and a dominant direction of the fibers re-appeared. The present results show that SHG microscopy imaging combined with the ST method is able to objectively monitor the temporal regeneration of the corneal organization after chemical burn. Future implementations of this approach into clinically adapted devices would help to diagnose and quantify corneal changes, not only due to chemical damages, but also as a result of disease or surgical procedures

Regulators and environmental groups: better together or apart?

This paper examines green alliances between environmental groups (EGs) and polluting firms, which have become more common in the last decades, and analyzes how they affect policy design. We first show that the activities of regulators and EGs are strategic substitutes, giving rise to free-riding incentives on both agents. Nonetheless, the presence of the EG yields smaller welfare benefits when firms are subject to regulation than when they are not. In addition, the introduction of environmental policy yields large welfare gains when the EG is absent but small benefits when the EG is already present

Ionized and neutral gas in the peculiar star/cluster complex in NGC 6946

The characteristics of ionized and HI gas in the peculiar star/cluster complex in NGC 6946, obtained with the 6-m telescope (BTA) SAO RAS, the Gemini North telescope, and the Westerbork Synthesis Radio Telescope (WSRT), are presented. The complex is unusual as hosting a super star cluster, the most massive known in an apparently non-interacting giant galaxy. It contains a number of smaller clusters and is bordered by a sharp C-shaped rim. We found that the complex is additionally unusual in having peculiar gas kinematics. The velocity field of the ionized gas reveals a deep oval minimum, ~300 pc in size, centered 7" east of the supercluster. The Vr of the ionized gas in the dip center is 100 km/s lower than in its surroundings, and emission lines within the dip appear to be shock excited. This dip is near the center of an HI hole and a semi-ring of HII regions. The HI (and less certainly, HII) velocity fields reveal expansion, with the velocity reaching ~30 km/s at a distance about 300 pc from the center of expansion, which is near the deep minimum position. The super star cluster is at the western rim of the minimum. The sharp western rim of the whole complex is plausibly a manifestation of a regular dust arc along the complex edge. Different hypotheses about the complex and the Vr depression origins are discussed, including a HVC/dark mini-halo impact, a BCD galaxy merging, and a gas outflow due to release of energy from the supercluster stars.Comment: MN RAS, accepte