Convergence and multiplicities for the Lempert function

Given a domain $\Omega \subset \mathbb C$, the Lempert function is a functional on the space Hol (\D,\Omega) of analytic disks with values in $\Omega$, depending on a set of poles in $\Omega$. We generalize its definition to the case where poles have multiplicities given by local indicators (in the sense of Rashkovskii's work) to obtain a function which still dominates the corresponding Green function, behaves relatively well under limits, and is monotonic with respect to the indicators. In particular, this is an improvement over the previous generalization used by the same authors to find an example of a set of poles in the bidisk so that the (usual) Green and Lempert functions differ.Comment: 24 pages; many typos corrected thanks to the referee of Arkiv for Matemati

Jacobi Identity for Vertex Algebras in Higher Dimensions

Vertex algebras in higher dimensions provide an algebraic framework for investigating axiomatic quantum field theory with global conformal invariance. We develop further the theory of such vertex algebras by introducing formal calculus techniques and investigating the notion of polylocal fields. We derive a Jacobi identity which together with the vacuum axiom can be taken as an equivalent definition of vertex algebra.Comment: 35 pages, references adde

Bird community patterns in sub–Mediterranean pastures: the effects of shrub cover and grazing intensity

Shrubs are widely considered a threat to grassland biodiversity. We investigated the effects of shrub cover and grazing intensity on bird communities in sub–Mediterranean pastures in Bulgaria. The point–count method was used on 80 plots in open (&lt; 10% shrub cover) and shrubby (approx. 20% cover) pastures under either intensive or extensive management (grazing intensity) from 2008 to 2009. We recorded a total of 1,956 observations of birds from 53 species. Main environmental gradients accounting for the bird community pattern were related to vegetation succession and land productivity. Bird species richness was higher in shrubby pastures than in open sites, while no effect was found in respect to total bird abundance. Bird species diversity (i.e. H’ index) was highest in extensive shrubby pastures. Shrubland specialists were positively affected by shrub cover and extensive management of pastures while grassland and woodland specialists showed no significant response to these factors. We conclude that a small proportion of shrubs within pastures may be beneficial for farmland birds and sustainable management of pastures could be achieved by greater flexibility of national agri–environmental schemes. Key words: Agri–environmental scheme, Farmland birds, Grassland management, Semi–natural habitats, Shrubby vegetation.Se suele considerar a los arbustos como una amenaza a la biodiversidad de los pastos. Investigamos los efectos de la cubierta arbustiva y la intensidad del pastoreo sobre las comunidades de aves en los pastos submediterráneos de Bulgaria. Se utilizó el método de estaciones de escucha en 80 puntos de registro en pastos abiertos (cubierta arbustiva < 10%) y arbustivos (aproximadamente un 20% de la superficie cubierta), con una gestión de pastoreo tanto intensiva como extensiva desde 2008 a 2009. Registramos un total de 1.956 observaciones de aves pertenecientes a 53 especies distintas. Los gradientes ambientales principales responsables de los patrones de las comunidades de aves se relacionaron con la sucesión de la vegetación y la productividad de la tierra. La riqueza de especies de aves era mayor en los pastos arbustivos que en los lugares abiertos, aunque no se observó efecto alguno con respecto a la abundancia total de aves. La mayor diversidad de especies de aves (índice H’) se daba en los pastos arbustivos con gestión extensiva. Los especialistas en zonas arbustivas se veían afectados positivamente por la cubierta arbustiva y la gestión extensiva de los pastos, mientras que los especialistas de praderas y bosques no presentaron ninguna respuesta positiva a dichos factores. Nuestra conclusión es que una pequeña proporción de arbustos dentro de los pastos puede ser beneficiosa para las aves de tierras de labrantío, y la gestión sostenible de los pastos podría alcanzarse mediante una mayor flexibilidad de los esquemas agroambientales nacionales. Palabras clave: Esquema agroambiental, Aves de labrantío, Gestión de prados, Hábitats seminaturales, Vegetación arbustiva.Shrubs are widely considered a threat to grassland biodiversity. We investigated the effects of shrub cover and grazing intensity on bird communities in sub–Mediterranean pastures in Bulgaria. The point–count method was used on 80 plots in open (&lt; 10% shrub cover) and shrubby (approx. 20% cover) pastures under either intensive or extensive management (grazing intensity) from 2008 to 2009. We recorded a total of 1,956 observations of birds from 53 species. Main environmental gradients accounting for the bird community pattern were related to vegetation succession and land productivity. Bird species richness was higher in shrubby pastures than in open sites, while no effect was found in respect to total bird abundance. Bird species diversity (i.e. H’ index) was highest in extensive shrubby pastures. Shrubland specialists were positively affected by shrub cover and extensive management of pastures while grassland and woodland specialists showed no significant response to these factors. We conclude that a small proportion of shrubs within pastures may be beneficial for farmland birds and sustainable management of pastures could be achieved by greater flexibility of national agri–environmental schemes. Key words: Agri–environmental scheme, Farmland birds, Grassland management, Semi–natural habitats, Shrubby vegetation

CELL DEATH DIFFERENTIATION IN BLACK HEADED RAMS SPERMATOZOA, USING FLUORESCENT LABELED ANNEXIN V

Double staining kit of Annexin V Cy3.18/6-CFDA was used to investigate the changes in phospholipide asymmetry after treating sperm cells with dexamethasone. The % of spermatozoa with registered translocation of PS in treated with dexamethazone groups at the 10-th min and in control no treated varied from 2.74%±0.65 to 2.30%±0.89. After the 5 hour of incubation these % increased to 39.83±3.33 for the treated group and 23.44±1.12 for the control. It was concluded that Annexin V binding assay is more sensitive in the detection of deterioration in membrane function than other conventional methods such as motility analysis and supravital techniques