Almost Global Existence for Some Hamiltonian PDEs with Small Cauchy Data on General Tori.

In this paper we prove a result of almost global existence for some abstract nonlinear PDEs on flat tori and apply it to some concrete equations, namely a nonlinear Schrödinger equation with a convolution potential, a beam equation and a quantum hydrodinamical equation. We also apply it to the stability of plane waves in NLS. The main point is that the abstract result is based on a nonresonance condition much weaker than the usual ones, which rely on the celebrated Bourgain's Lemma which provides a partition of the "resonant sites" of the Laplace operator on irrational tori.

Giant diverticulum of the sigmoid colon with perforation. Report of a case.

We present a case of perforated giant diverticulum of the sigmoid colon. This condition is extremely rare and only a few cases have so far been reported in the literature. Our case involved a 55-year old woman. Diagnosis was easy with barium enema and CT scan examination. Laparotomy revealed a giant diverticulum of the sigmoid colon compressing adjacent structures with signs of inflammation. An en bloc resection of the sigmoid colon, ovary and fallopian tube was performed with primary colon-rectal anastomosis. The post-operative course was uneventful.