Formal Laurent Series in Several Variables

We explain the construction of fields of formal infinite series in several variables, generalizing the classical notion of formal Laurent series in one variable. Our discussion addresses the field operations for these series (addition, multiplication, and division), the composition, and includes an implicit function theorem

Liouville integrability: An effective Morales–Ramis–Simó theorem

International audienceConsider a complex Hamiltonian system and an integral curve. In this paper, we give an effective and efficient procedure to put the variational equation of any order along the integral curve in reduced form provided that the previous one is in reduced form with an abelian Lie algebra. Thus, we obtain an effective way to check the Morales-Ramis-Simó criterion for testing meromorphic Liouville integrability of Hamiltonian systems

Temporal Trends in the Use of Computed Tomographic Pulmonary Angiography for Suspected Pulmonary Embolism in the Emergency Department : A Retrospective Analysis.

Recently, validated clinical decision rules have been developed that avoid unnecessary use of computed tomographic pulmonary angiography (CTPA) in patients with suspected pulmonary embolism (PE) in the emergency department (ED). To measure any resulting change in CTPA use for suspected PE. Retrospective analysis. 26 European EDs in 6 countries. Patients with CTPA performed for suspected PE in the ED during the first 7 days of each odd month between January 2015 and December 2019. The primary end points were the CTPAs done for suspected PE in the ED and the number of PEs diagnosed in the ED each year adjusted to an annual census of 100 000 ED visits. Temporal trends were estimated using generalized linear mixed regression models. 8970 CTPAs were included (median age, 63 years; 56% female). Statistically significant temporal trends for more frequent use of CTPA (836 per 100 000 ED visits in 2015 vs. 1112 in 2019; P < 0.001), more diagnosed PEs (138 per 100 000 in 2015 vs. 164 in 2019; P = 0.028), a higher proportion of low-risk PEs (annual percent change [APC], 13.8% [95% CI, 2.6% to 30.1%]) with more ambulatory management (APC, 19.3% [CI, 4.1% to 45.1%]), and a lower proportion of intensive care unit admissions (APC, -8.9% [CI, -17.1% to -0.3%]) were observed. Data were limited to 7 days every 2 months. Despite the recent validation of clinical decision rules to limit the use of CTPA, an increase in the CTPA rate along with more diagnosed PEs and especially low-risk PEs were instead observed. None specific for this study