Minimal generating subspaces of “weak PBW-type” for vertex operator algebras are studied and a procedure is developed for finding such subspaces. As applications, some results on generalized modules are obtained for vertex operator algebras that satisfy a certain condition, and a minimal generating space of weak PBW-type is produced for VL with L any positive-definite even lattice.

Given a projective scheme X over a field k, an automorphism σ : X → X, and a σ-ample invertible sheaf L, one may form the twisted homogeneous coordinate ring B = B(X,L, σ), one of the most fundamental constructions in noncommutative projective algebraic geometry. We study the primitive spectrum of B, as well as that of other closely related algebras such as skew and skew-Laurent extensions of c...

BACKGROUND The lung-protective ventilation bundle has been shown to reduce mortality in adult acute respiratory distress syndrome (ARDS). This concept has expanded to other areas of acute adult ventilation and is recommended for pediatric ventilation. A component of lung-protective ventilation relies on a prediction of lean body weight from height. The predicted body weight (PBW) relationship e...

INTRODUCTION Little is known about the mechanisms through which intensivist physician staffing influences patient outcomes. We aimed to assess the effect of closed-model intensive care on evidence-based ventilatory practice in patients with acute lung injury (ALI). METHODS We conducted a secondary analysis of a prospective population-based cohort of 759 patients with ALI who were alive and ve...

Non-normal mixture distributions have received increasing attention in recent years. Finite mixtures of multivariate skew-symmetric distributions, in particular, the skew normal and skew t-mixture models, are emerging as promising extensions to the traditional normal and t-mixture models. Most of these parametric families of skew distributions are closely related, and can be classified into fou...

We define a set of PBW-semistandard tableaux that is in weight preserving bijection with the monomials corresponding to integral points Feigin-Fourier-Littelmann-Vinberg polytope for highest modules symplectic Lie algebra. then show these parametrize bases homogeneous coordinate rings complete original and PBW degenerate flag varieties. From this construction, we provide explicit relations gene...

The sensitivity of a multiple eigenvalue of a matrix under perturbations can be measured by its Hölder condition number. Various extensions of this concept are considered. A meaningful notion of structured Hölder condition numbers is introduced and it is shown that many existing results on structured condition numbers for simple eigenvalues carry over to multiple eigenvalues. The structures inv...

Abstract We consider extensions of non-singular maps which are exact, respectively K-mixing, or at least have a decomposition into positive-measure components. The fibers the extension spaces countable (finite infinite) cardinality and action on them is assumed surjective bijective. call these systems, respectively, fiber-surjective fiber-bijective extensions. Technically, they skew products, t...