On quasi quantum Poisson algebras : Lie-algebraic characterization

We prove a Lie-algebraic characterization of vector bundle for the Lie algebra $\mathcal{D}(E,M)$ of all linear operators acting on sections of a vector bundle $E$. We obtain similar result for its Lie subalgebra $\mathcal{D}^1(E,M)$ of all linear first-order differential operators. Thanks to a well-chosen filtration, $\mathcal{D}(E,M)$ becomes $\mathcal{P}(E,M)$ and we prove that $\mathcal{P}^1(E,M)$ characterizes the vector bundle without the hypothesis of being seen as module on the space of smooth functions of $M$.Comment: 17 page

Classical Poisson algebra of a vector bundle : Lie-algebraic characterization

We prove that the Lie algebra $\mathcal{S}(\mathcal{P}(E,M))$ of symbols of linear operators acting on smooth sections of a vector bundle $E\to M,$ characterizes it. To obtain this, we assume that $\mathcal{S}(\mathcal{P}(E,M))$ is seen as ${\rm C}^\infty(M)-$module and that the vector bundle is of rank $n>1.$ We improve this result for the Lie algebra $\mathcal{S}^1(\mathcal{P}(E,M))$ of symbols of first-order linear operators. We obtain a Lie algebraic characterization of vector bundles with $\mathcal{S}^1(\mathcal{P}(E,M))$ without the hypothesis of being seen as a ${\rm C}^\infty(M)-$module.Comment: 16 page

On a Lie Algebraic Characterization of Vector Bundles

We prove that a vector bundle $\pi : E \to M$ is characterized by the Lie algebra generated by all differential operators on $E$ which are eigenvectors of the Lie derivative in the direction of the Euler vector field. Our result is of Pursell-Shanks type but it is remarkable in the sense that it is the whole fibration that is characterized here. The proof relies on a theorem of [Lecomte P., J. Math. Pures Appl. (9) 60 (1981), 229-239] and inherits the same hypotheses. In particular, our characterization holds only for vector bundles of rank greater than 1

Implementing Acute Stroke Services in sub-Saharan Africa: Steps, Progress and Perspectives from the Tanzania Stroke Project

Stroke is a leading cause of morbidity and mortality globally, with Africa bearing a disproportionately high burden of poor outcomes. In sub-Saharan Africa, acute stroke care remains inconsistent, with organized stroke units being either absent or rarely available, contributing to the high stroke mortality rates in the region. To address this issue, the Tanzania Stroke Project (TSP) was launched, aimed at establishing acute stroke services at two of the largest tertiary care centers in collaboration with the Tanzanian Ministry of Health, the World Stroke Organization and Hospital Directorates