Tensor, Clifford and Grassmann algebras belong to a wide class of non-commutative algebras that have a Poincaré-Birkhoff-Witt (PBW) “monomial” basis. The necessary and sufficient condition for an algebra to have the PBW basis has been established by T. Mora and then V. Levandovskyy as the so called “non-degeneracy condition”. This has led V. Levandovskyy to a re-discovery of the so called G-alg...

BACKGROUND Ventilator practices in patients at risk for acute lung injury (ALI) and ARDS are unclear. We examined factors associated with choice of set tidal volumes (VT), and whether VT < 8 mL/kg predicted body weight (PBW) relates to the development of ALI/ARDS. METHODS We performed a secondary analysis of a multicenter cohort of adult subjects at risk of lung injury with and without ALI/AR...

We study skew inverse power series extensions R[[y−1; τ, δ]], where R is a noetherian ring equipped with an automorphism τ and a τ -derivation δ. We find that these extensions share many of the well known features of commutative power series rings. As an application of our analysis, we see that the iterated skew inverse power series rings corresponding to nth Weyl algebras are complete, local, ...

We introduce a class of posets, which includes both ribbon posets (skew shapes) and $d$-complete such that their number linear extensions is given by determinant matrix whose entr...

This article summarizes the various ways one may use to construct the Skew Brownian motion, and shows their connections. Recent applications of this process in modelling and numerical simulation motivates this survey. This article ends with a brief account of related results, extensions and applications of the Skew Brownian motion. AMS 2000 subject classifications: Primary 60J60; secondary 60H1...

BACKGROUND There is a growing concern of the potential injurious role of ventilatory over-distention in patients without lung injury. No formal guidelines exist for intraoperative ventilation settings, but the use of tidal volumes (VT) under 10 mL/kg predicted body weight (PBW) has been recommended in healthy patients. We explored the incidence and risk factors for receiving large tidal volumes...