Hyperbolic-like estimates for higher order equations

The main goal of this paper is to derive long time estimates of the energy for the higher order hyperbolic equations with time-dependent coefficients. in particular, we estimate the energy in the hyperbolic zone of the extended phase space by means of a function f (t) which depends on the principal part and on the coefficients of the terms of order m - 1. Then we look for sufficient conditions that guarantee the same energy estimate from above in all the extended phase space. We call this class of estimates hyperbolic-like since the energy behavior is deeply depending on the hyperbolic structure of the equation. In some cases, these estimates produce a dissipative effect on the energy. (C) 2012 Elsevier Inc. All rights reserved.

Ahamulina n. gen. (Cestoda: Diphyllidea) from the polkadot catshark, Scyliorhinus besnardi (Carcharhiniformes: Scyliorhinidae), off Brazil

A new genus and species of diphyllidean, Ahamulina catarina n. gen. n. sp., is described from the polkadot catshark, Scyliorhinus besnardi, from Santa Catarina, Brazil. The new genus exhibits apical organ armature that is unique among diphyllideans in the arrangement and shape of the apical hooks as well as in the lack of lateral hooklets. The taxon also exhibits a bipartite cirrus sac. This is the seventh diphyllidean reported from a shark, and the third reported from a catshark suggesting that the dearth of cestode data for these particular sharks belies the true extent of diphyllidean diversity they host.