We describe a ring whose category of Cohen-Macaulay modules provides an additive categorification of the cluster algebra structure on the homogeneous coordinate ring of the Grassmannian of k-planes in n-space. More precisely, there is a cluster character defined on the category which maps the rigid indecomposable objects to the cluster variables and the maximal rigid objects to clusters. This is proved by showing that the quotient of this category by a single projectiveinjective object is Geiss-Leclerc-Schröer's category Sub Q k , which categorifies the coordinate ring of the big cell in this Grassmannian.

A facile and green method was presented to prepare flexible, ultralight, and hydrophobic CA on the chemical cross-linking of cellulose solution, lyophilization and subsequent hydrophobic modification with methyltrichlorosilane by a CVD process.

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We propose a theory of degenerations for derived module categories, analogous to degenerations in module varieties for module categories. In particular we define two types of degenerations, one algebraic and the other geometric. We show that these are equivalent, analogously to the Riedtmann-Zwara theorem for module varieties. Applications to tilting complexes are given, in particular that any twoterm tilting complex is determined by its graded module structure.