Bulletin of the Brazilian Mathematical Society, New Series

Frid, Hermano

doi: 10.1007/BF01238955pmid: N/A

In this paper we survey recent results on the decay of periodic and almost periodic solutions of conservation laws. We also recall some recent results on the global existence of periodic solutions of conservation laws systems which lie inBV loc and are constructed through Glimm scheme. The latter motivates a discussion on a possible strategy for solving the open problem of the global existence of periodic solutions of the Euler equations for nonisentropic gas dynamics. We base our decay analysis on a general result about space-time functions which are almost periodic in the space variable, established here for the first time. This result is an abstract version of Theorem 2.1 in [31], which in turn is an extention of the combined result given by Theorems 3.1–3.2 in [9].

Vainsencher, Israel

doi: 10.1007/BF01238956pmid: N/A

We consider the smooth compactification constructed in [12] for a space of varieties like twisted cubics. We show this compactification embeds naturally in a product of flag varieties.

Bertola, Marco; Gouthier, Daniele

doi: 10.1007/BF01238957pmid: N/A

We study the geometry of particular classes of Riemannian manifolds obtained as warped products. We focus on the case of constant curvature which is completely classified and on the Einstein case. This study provides nontrivial instances of Einstein manifolds which are warped product of Einstein factors.

Bayer, Valmecir; Hefez, Abramo

doi: 10.1007/BF01238958pmid: N/A

In this paper we describe all irreducible plane algebroid curves, defined over an algebraically closed field of characteristic zero, modulo analytic equivalence, having the property that the difference between their Milnor and Tjurina numbers is 1 or 2. Our work extends a previous result of O. Zariski who described such curves when this difference is zero.

Martins, J.

doi: 10.1007/BF01238959pmid: N/A

The invariants needed to decide when a pair of hypersurfaces ofS 6 orCP n are respectivelyG 2-congruent or holomorpic congruent are determined and this result is used to characterize the hypersurfaces of these spaces whose Hopf vector fields are also Killing fields.