Stability of gradient semigroups under perturbations

In this paper we prove that gradient-like semigroups (in the sense of Carvalho and Langa (2009 J. Diff. Eqns 246 2646-68)) are gradient semigroups (possess a Lyapunov function). This is primarily done to provide conditions under which gradient semigroups, in a general metric space, are stable under perturbation exploiting the known fact (see Carvalho and Langa (2009 J. Diff. Eqns 246 2646-68)) that gradient-like semigroups are stable under perturbation. The results presented here were motivated by the work carried out in Conley (1978 Isolated Invariant Sets and the Morse Index (CBMS Regional Conference Series in Mathematics vol 38) (RI: American Mathematical Society Providence)) for groups in compact metric spaces (see also Rybakowski (1987 The Homotopy Index and Partial Differential Equations (Universitext) (Berlin: Springer)) for the Morse decomposition of an invariant set for a semigroup on a compact metric space).

Structural studies on zinc(II) complexes with 2-benzoylpyridine-derived hydrazones

2-Benzoylpyridine-phenylhydrazone (H2BzPh), 2-benzoylpyridine-para-chloro-phenylhydrazone (H2BzpClPh), and 2-benzoylpyridine-para-nitro-phenyl (H2BzpNO(2)Ph) hydrazone were obtained and fully characterized, as well as their zinc(II) complexes [Zn(H2BzPh)Cl(2)] (1), [Zn(H2BzClPh)Cl(2)] (2) and [Zn(H2BzpNO(2)Ph)Cl(2)] (3). During the syntheses of complex 1 a second product crystallized, which was characterized as [Zn(2BzPh)(2)] (1a). Upon re-crystallization in 1: 9 DMSO: acetone conversion of 2 into [Zn(H2BzpClPh)Cl2] center dot H(2)O (2a) and of 3 into [Zn(2BzpNO(2)Ph)Cl(DMSO)] (3a) occurred. The crystal structures of 1a, 2a and 3a were determined. In 1a the two nearly perpendicular H2BzPh ligands give rise to a distorted octahedral environment around the metal. The 5-fold coordination around the metal is completed with two chloride ions in 2a and with one chloride and one oxygen atom from DMSO in 3a. (c) 2008 Elsevier B.V. All rights reserved.

U-Pb zircon and (40)Ar-(39)Ar K-feldspar dating of syn-sedimentary volcanism of the Neoproterozoic Marica Formation: constraining the age of foreland basin inception and inversion in the Camaqua Basin of southern Brazil

New U-Pb zircon and (40)Ar-(39)Ar K-feldspar data are presented for syn-sedimentary volcanogenic rocks from the Neoproterozoic Marica Formation, located in the southern Brazilian shield. Seven (of nine) U-Pb sensitive high-resolution ion microprobe analyses of zircons from pyroclastic cobbles yield an age of 630.2 +/- 3.4 Ma (2 sigma), interpreted as the age of syn-sedimentary volcanism, and thus of the deposition itself. This result indicates that the Marica Formation was deposited during the main collisional phase (640-620 Ma) of the Brasiliano II orogenic system, probably as a forebulge or back-bulge, craton-derived foreland succession. Thus, this unit is possibly correlative of younger portions of the Porongos, Brusque, Passo Feio, Abapa (Itaiacoca) and Lavalleja (Fuente del Puma) metamorphic complexes. Well-defined, step-heating (40)Ar-(39)Ar K-feldspar plateau ages obtained from volcanogenic beds and pyroclastic cobbles of the lower and upper successions of the Marica Formation yielded 507.3 +/- 1.8 Ma and 506.7 +/- 1.4 Ma (2 sigma), respectively. These data are interpreted to reflect total isotopic resetting during deep burial and thermal effects related to magmatic events. Late Middle Cambrian cooling below ca. 200 degrees C, probably related to uplift, is tentatively associated with intraplate effects of the Rio Doce and/or Pampean orogenies (Brasiliano III system). In the southern Brazilian shield, these intraplate stresses are possibly related to the dominantly extensional opening of a rift or a pull-apart basin, where sedimentary rocks of the Camaqua Group (Santa Barbara and Guaritas Formations) accumulated.