Various preclinical investigations have demonstrated the manifold beneficial actions of arundic acid against neurological diseases, including ischemic stroke, Parkinson's disease, amyotrophic lateral sclerosis and Alzheimer's disease.
Some process philosophers have taken the experience of dynamic sameness in self-experience as the basis for constructing a process-metaphysical account of personhood that defines the core self as a unified manifold of actions and capacities, tendencies, and dispositions to (physical or psychical) actions (see e.g. Rescher 1996 ch.6).
Tubing string may yield, break and buckle perpetually under actions of manifold loads in well testing operation, resulting in severe economic loss.
While the above result includes only three domains, a complete description of general complex manifolds that admit transitive proper actions of groups of dimension (N^2) is probably much larger.
In this survey, we discuss proper actions of Lie groups on smooth manifolds.
In Sect. 2 we review fundamental facts on proper actions starting with the topological setup and gradually progressing to actions of Lie groups on smooth manifolds by diffeomorphisms.
We show that this relation persists for actions of Rl, under mild restrictions on the geometry of the manifold which guarantee the Dixmier traceability of those operators.
We extend the isospectral deformations of Connes, Landi and Dubois-Violette to the case of Riemannian spin manifolds carrying a proper action of the noncompact abelian group Rl.
Therefore a pattern is not an isolated solution but rather generates a manifold of solutions under the action of translations, which is called an orbit under the action of the group of translations.
The attractions of the Titanic story, with its manifold ingredients — action, romance, tragedy, salvation, history, culture, huge metal machines — are obvious.
