Let In be the class of all signed involutions in the hyperoctahedral group Bn and let In(T ) be the set of involutions in In which avoid a set T of signed patterns. In this paper, we complete a further case of the program initiated by Simion and Schmidt [6] by enumerating In(T ) for all signed permutations T ⊆ B2.

The title compound, C(10)H(7)Cl(3)O, obtained as a major byproduct from a classical Schmidt reaction. The cyclohexyl ring is distorted from a classical chair conformation, as observed for monocyclic analogues, presumably due to conjugation of the planar annulated benzo ring and the ketone group (r.m.s. deviation 0.024 Å). There are no significant intermolecular interactions.

Abstract We prove that if the Auslander–Reiten triangles generate relations for Grothendieck group of a Hom-finite Krull–Schmidt triangulated category with (co)generator, then has only finitely many isomorphism classes indecomposable objects up to translation. This gives converse theorem Butler and on groups. Our approach applications in context Frobenius categories.

In this short note we show that for a Markovian open quantum system it is always possible to construct a unique set of perfectly consistent Schmidt paths, supporting quasi-classicality. Our Schmidt process, elaborated several years ago, is the ∆t → 0 limit of the Schmidt chain constructed very recently by Paz and Zurek.