Geometrical classification of Killing tensors on bidimensional flat manifolds

Valence two Killing tensors in the Euclidean and Minkowski planes are classified under the action of the group which preserves the type of the corresponding Killing web. The classification is based on an analysis of the system of determining partial differential equations for the group invariants and is entirely algebraic. The approach allows to classify both characteristic and non characteristic Killing tensors.Comment: 27 pages, 20 figures, pictures format changed to .eps, typos correcte

Eigenvalues of Killing Tensors and Separable Webs on Riemannian and Pseudo-Riemannian Manifolds

Given a n-dimensional Riemannian manifold of arbitrary signature, we illustrate an algebraic method for constructing the coordinate webs separating the geodesic Hamilton-Jacobi equation by means of the eigenvalues of m ≤ n Killing two-tensors. Moreover, from the analysis of the eigenvalues, information about the possible symmetries of the web foliations arises. Three cases are examined: the orthogonal separation, the general separation, including non-orthogonal and isotropic coordinates, and the conformal separation, where Killing tensors are replaced by conformal Killing tensors. The method is illustrated by several examples and an application to the L-systems is provided

Invariant classification of the rotationally symmetric R-separable webs for the Laplace equation in Euclidean space

An invariant characterization of the rotationally symmetric R-separable webs for the Laplace equation in Euclidean space is given in terms of invariants and covariants of a real binary quartic canonically associated to the characteristic conformal Killing tensor which defines the webs.Comment: 25 pages, recently submitted to the Journal of Mathematical Physic

Frequency and Types of Healthcare Encounters in the Week Preceding a Sepsis Hospitalization: A Systematic Review

OBJECTIVES: Early recognition and treatment are critical to improving sepsis outcomes. We sought to identify the frequency and types of encounters that patients have with the healthcare system in the week prior to a sepsis hospitalization. DATA SOURCES: PubMed, Cumulative Index to Nursing and Allied Health Literature, Scopus, and the Cochrane Library. STUDY SELECTION: Observational cohort studies of patients hospitalized with sepsis or septic shock that were assessed for an outpatient or emergency department encounter with the healthcare system in the week prior to hospital admission. DATA EXTRACTION: The primary outcome was the proportion of patients with a healthcare encounter in the time period assessed (up to 1 week) prior to a hospitalization with sepsis. DATA SYNTHESIS: Six retrospective observational studies encompassing 6,785,728 sepsis admissions were included for evaluation, ranging from a 263-patient single-center cohort to a large database evaluating 6,731,827 sepsis admissions. The average (unweighted) proportion of patients having an encounter with the healthcare system in the week prior to a sepsis hospitalization was 32.7% and ranged from 10.3% to 52.9%. These encounters commonly involved presentation or potential symptoms of infectious diseases, antibiotic prescriptions, and appeared to increase in frequency closer to a sepsis hospitalization admission. No consistent factors were identified that distinguished a healthcare encounter as more or less likely to precede a sepsis hospitalization in the subsequent week. CONCLUSIONS: Patients that present to the hospital with sepsis are frequently evaluated in the healthcare system in the week prior to admission. Further research is necessary to understand if these encounters offer earlier opportunities for intervention to prevent the transition from infection to sepsis, whether they merely reflect the comorbidities of sepsis patients with a high baseline rate of healthcare encounters, or the declining trajectory of a patient\u27s overall health in response to infection