997 resultados para algebra di Lie gruppi risolubili nilpotenti


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Collection : Italian books before 1601 ; 103.1

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Age related macular degeneration (AMD) is a pathological aging of the macula, brought about by the interaction of genetic and environmental factors. It induces geographic atrophy of the retina and/or choroidal neovascularization. In the latter, abnormal vessels develop from the choriocapillaris, with the involvement of VEGF (vascular endothelial growth factor). The VEGF family includes several factors, including VEGF-A, B, C, D, F and PlGF (placental growth factor). Their biological properties and their affinities to the VEGFR1, VEGFR2 and VEGFR3 receptors found on endothelial cells differ. Exudative AMD involves mainly VEGF-A and VEGF-R2. Anti-VEGF agents used in ophthalmology (ranibizumab, bevacizumab and aflibercept) are designed to primarily target this pathway. In vitro, all have sufficient affinity to their ligands. Their therapeutic efficacy must therefore be judged based on clinical criteria. In clinical practice, the minimum number of injections required for a satisfactory result appears to be comparable with all the three. The few available studies on therapeutic substitutions of anti-VEGF compounds suggest that some patients may benefit from substituting the anti-VEGF in cases of an unsatisfactory response to an initial molecule. Although local side effects, including increased risk of geographic atrophy, and systemic effects, including vascular accidents, have been suggested, these risks remain low, specially compared to the benefits of the treatment. Differences in safety between anti-VEGF are theoretically possible but unproven.

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This paper provides an explicit cofibrant resolution of the operad encoding Batalin-Vilkovisky algebras. Thus it defines the notion of homotopy Batalin-Vilkovisky algebras with the required homotopy properties. To define this resolution we extend the theory of Koszul duality to operads and properads that are defind by quadratic and linear relations. The operad encoding Batalin-Vilkovisky algebras is shown to be Koszul in this sense. This allows us to prove a Poincare-Birkhoff-Witt Theorem for such an operad and to give an explicit small quasi-free resolution for it. This particular resolution enables us to describe the deformation theory and homotopy theory of BV-algebras and of homotopy BV-algebras. We show that any topological conformal field theory carries a homotopy BV-algebra structure which lifts the BV-algebra structure on homology. The same result is proved for the singular chain complex of the double loop space of a topological space endowed with an action of the circle. We also prove the cyclic Deligne conjecture with this cofibrant resolution of the operad BV. We develop the general obstruction theory for algebras over the Koszul resolution of a properad and apply it to extend a conjecture of Lian-Zuckerman, showing that certain vertex algebras have an explicit homotopy BV-algebra structure.