Manifold actions for other growth factors and their receptors systems have been described in cancer, e.g. IGF (insulin-like growth factor)/IGFR system and HGF (hepatocyte growth factor)/HGFR systems [ 11- 13].
Such observations illustrate the complex manifold actions of 4-HPR, which may cause cell death by mixed apoptosis/necrosis by both caspase-dependent and -independent pathways (DiPietrantonio et al, 1998; Maurer et al, 1999).
The attractions of the Titanic story, with its manifold ingredients — action, romance, tragedy, salvation, history, culture, huge metal machines — are obvious.
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).
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.
The stress trajectory is a coadjoint orbit on the Poisson manifold under a coadjoint action by the Lie-group SO(n).
With a group action on manifold M, we can geometrically characterize invariant fields: The symmetry transformations g of M define correspondences between the points of M, and the pushforwards of g define correspondences between the tangent vectors at corresponding points.
Thus, a G-invariant form ω equals to its pullback under the symmetry transformations, i.e., g*ω = ω holds for all g ∈ G. On the other hand, the group action on manifold M induces a group action on the set of differential forms Ω M) such that the pullbacks g* are the symmetry transformations of Ω M).
This might be due to its manifold putative sites of action when interfering with the pain system, that is, locally at the nerve endings [ 17], at the dorsal root ganglia [ 28], or on the spinal level [ 29].
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.
