Higher Haantjes Brackets and Integrability

We propose a new, infinite class of brackets generalizing the Frölicher–Nijenhuis bracket. This class can be reduced to a family of generalized Nijenhuis torsions recently introduced. In particular, the Haantjes bracket, the first example of our construction, is relevant in the characterization of Haantjes moduli of operators. We also prove that the vanishing of a higher-level Nijenhuis torsion of an operator field is a sufficient condition for the integrability of its eigen-distributions. This result (which does not require any knowledge of the spectral properties of the operator) generalizes the celebrated Haantjes theorem. The same vanishing condition also guarantees that the operator can be written, in a local chart, in a block-diagonal form.

Underreported Risk of Lisinopril-Induced Angioedema in a Veteran Population

Background: Lisinopril-induced angioedema (LIA) is a rare but serious adverse drug event (ADE) with a published incidence of 0.1% to 0.7%. It is well known that ADEs are widely underreported; however, LIA is one of the most reported ADEs within the Veterans Health Administration (VHA). Objective: To estimate the effect of underreporting on the risk of LIA within VHA. Methods: The reported risk of LIA was calculated from reports submitted to the Veterans Affairs (VA) Adverse Drug Event Reporting System (VA ADERS) and the number of veterans prescribed lisinopril. To estimate underreporting, local chart review identified cases of LIA that were compared to reports submitted. The underreporting rate was then applied to the national reported risk. Results: Locally, 68 reports of LIA were submitted of the 21 262 patients prescribed lisinopril, for a reported risk of 0.32%. Nationwide, 14 289 reports of LIA were submitted of the 3 109 661 patients prescribed lisinopril, for a crude reported risk of 0.46%. Of the 324 patients identified for chart review, 240 patients were diagnosed with LIA, suggesting that at least 71.7% of cases were unreported. When this underreporting rate is extrapolated to the national reported risk, a better estimate of the risk of LIA within VHA could increase to 1.6%. Conclusion and Relevance: When estimating the effect of underreporting, the risk of LIA increases to approximately 1.6% or 1 in 63 patients. Because this ADE may affect more patients than previously understood, providers may wish to take LIA into consideration when prescribing lisinopril.

ON THE QUADRATIC HEISENBERG GROUP

In this paper we introduce the quadratic Weyl operators canonically associated to the one mode renormalized square of white noise (RSWN) algebra as unitary operator acting on the one mode interacting Fock space {Γ, {ωn, n ∈ ℕ}, Φ} where {ωn, n ∈ ℕ} is the principal Jacobi sequence of the nonstandard (i.e. neither Gaussian nor Poisson) Meixner classes. We deduce the quadratic Weyl relations and construct the quadratic analogue of the Heisenberg Lie group with one degree of freedom. In particular, we determine the manifold structure of the group and introduce a local chart containing the identity on which the group law has a simple rational expression in the chart coordinates (see Theorem 6.3).

MULTIVECTOR AND EXTENSOR FIELDS ON SMOOTH MANIFOLDS

The main objective of this paper (second in a series of four) is to show how the Clifford and extensor algebras methods introduced in a previous paper of the series are indeed powerful tools for performing sophisticated calculations appearing in the study of the differential geometry of a n-dimensional manifold M of arbitrary topology, supporting a metric field g (of given signature (p,q)) and an arbitrary connection ∇. Specifically, we deal here with the theory of multivector and extensor fields on M. Our approach does not suffer the problems of earlier attempts which are restricted to vector manifolds. It is based on the existence of canonical algebraic structures over the canonical (vector) space associated to a local chart (Uo, ϕo) of a given atlas of M. The key concepts of a-directional ordinary derivatives of multivector and extensor fields are defined and their properties studied. Also, we recall the Lie algebra of smooth vector fields in our formalism, the concept of Hestenes derivatives and present some illustrative applications.

‘Martelli's Tables’

As the hitherto anonymous reviser who prepared the current G.H.A. edition of Martelli's Tables, was interested, instructed and surprised by Captain Cotter's article in the Forum on this subject. I was surprised that he should write of them as if they were things of the past. In fact they are available off the shelf at my local chart agents, and no doubt elsewhere, so a demand presumably exists today, and they are in current use. From some of the comments which he makes, and the extract from Table 5 which he reproduces, it appears that he has not seen the current edition.