Unilateral progressive osseous heteroplasia

A 50-year-old male patient presented with firm subcutaneous nodules and plaques with a gritty texture, unilaterally affecting the left side of the trunk and the left limbs. These lesions had had a progressive course since early childhood and caused functional impairment. There was no family history of similar disorders. No phospho-calcium metabolism abnormalities were observed. Biopsies of the affected areas demonstrated osteoma cutis. Analysis of DNA showed no mutation of the GNAS gene. The clinical features were consistent with progressive osseous heteroplasia, atypically presented in a unilateral form, probably revealing a mosaic distribution

Manejo de plantas daninhas na cultura da mandioca no Agreste Alagoano.

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Auslander-Buchweitz approximation theory for triangulated categories

We introduce and develop an analogous of the Auslander-Buchweitz approximation theory (see \cite{AB}) in the context of triangulated categories, by using a version of relative homology in this setting. We also prove several results concerning relative homological algebra in a triangulated category \T, which are based on the behavior of certain subcategories under finiteness of resolutions and vanishing of Hom-spaces. For example: we establish the existence of preenvelopes (and precovers) in certain triangulated subcategories of \T. The results resemble various constructions and results of Auslander and Buchweitz, and are concentrated in exploring the structure of a triangulated category \T equipped with a pair (\X,\omega), where \X is closed under extensions and $\omega$ is a weak-cogenerator in \X, usually under additional conditions. This reduces, among other things, to the existence of distinguished triangles enjoying special properties, and the behavior of (suitably defined) (co)resolutions, projective or injective dimension of objects of \T and the formation of orthogonal subcategories. Finally, some relationships with the Rouquier's dimension in triangulated categories is discussed.Comment: To appear at: Appl. Categor. Struct. (2011); 22 page