Unimodal Levy Processes on Bounded Lipschitz Sets

We give asymptotics near the boundary for the distribution of the first exit time of the isotropic alpha-stable Levy process on bounded Lipschitz sets in real euclidean space. These asymptotics bear some relation to the existence of limits in the Yaglom sense of alpha-stable processes. Our approach relies on the uniform integrability of the ratio of Green functions on bounded Lipschitz sets. We use bounds for the heat remainder to give the first two terms in the small time asymptotic expansion of the trace of the heat kernel of unimodal Levy processes satisfying some weak scaling conditions on bounded Lipschitz domains

Cold and humid Atlantic forest during the late glacial, northern Espírito Santo state, southeastern Brazil

The Atlantic Rainforest, covering the area from the northern Espirito Santo to Southern Bahia states, has been considered as a stable forest during Pleistocene Glacial times. Despite the modelling and phylogenetic studies, this hypothesis has never been tested with empirical paleo-data and vegetation reconstruction. By using palynology, radiocarbon dating, carbon and nitrogen elemental and isotope of organic matter, we reconstructed the vegetation dynamics and inferred climatic changes since Late Pleistocene in the centre of this global biodiversity hotspot. Our results show that the forest biome was resilient to Last Glacial Maximum - LGM conditions, but floristics has changed when compared to nowadays. Since late glacial, the dense forest changed from cold to warm specimens. Major vegetation changes also occurred during early and mid-Holocene less humid conditions, with an opening of the forest, suggesting that future drought may have negative impacts and highlighting the importance of forest conservation to keep the Atlantic Rainforest biodiversity

The polyhedra of equisingularity of pre quasi-homogeneous germs

Não disponívelIn this work we introduce the notion of a pre-weighted homogeneus germ and we show that they are G-finite for G = A and K. We obtain results on the equisingularity of families of hipersurfaces defined by such germs as a consequence of a caracterization of the polihedron of Equisingularity of an analitic germ with isolated singularity. We also show that the gradient polihedron defined by E. Yoshinaga [Y], the filtration conditions defined by J.Damon and T. Gaffney [D G], and the algebraic approach of integral closure of ideais considered by Teissier [T1],[T2] lead to the same convex subset of the polihedron of equisingularity. A partial extension of the above results for complete intersection with isolated singularity is obtained

The polyhedra of equisingularity of pre quasi-homogeneous germs

Não disponívelIn this work we introduce the notion of a pre-weighted homogeneus germ and we show that they are G-finite for G = A and K. We obtain results on the equisingularity of families of hipersurfaces defined by such germs as a consequence of a caracterization of the polihedron of Equisingularity of an analitic germ with isolated singularity. We also show that the gradient polihedron defined by E. Yoshinaga [Y], the filtration conditions defined by J.Damon and T. Gaffney [D G], and the algebraic approach of integral closure of ideais considered by Teissier [T1],[T2] lead to the same convex subset of the polihedron of equisingularity. A partial extension of the above results for complete intersection with isolated singularity is obtained

Not available

Não disponívelIn this work, we want to establish conditions equivalence between a bi-A-orbit and a bi-K-orbit for germs (fo1, fo2): (Rn, 0) &rarr; (Rp x Rq,0). To this end, we make use of the action of bi-isotropie groups end generalize the results of J. Martinet [M1] for germs f : (Rn, 0) &rarr; (Rm</, O)

Not available

Não disponívelIn this work, we want to establish conditions equivalence between a bi-A-orbit and a bi-K-orbit for germs (fo1, fo2): (Rn, 0) &rarr; (Rp x Rq,0). To this end, we make use of the action of bi-isotropie groups end generalize the results of J. Martinet [M1] for germs f : (Rn, 0) &rarr; (Rm</, O)

Pre-weighted homogeneous map germs finite determinacy and topological triviality

In this paper we introduce the notion of G-pre-weighted homogeneous map germ, (G is one of Mather's groups A or K.) and show that any G-pre-weighted homogeneous map germ is G-finitely determined. We also give an explicit order, based on the Newton polyhedron of a pre-weighted homogeneous germ of function, such that the topological structure is preserved after perturbations by terms of higher order