Search results
Results from the WOW.Com Content Network
The action of GL(n) extends naturally to a free transitive action of the affine group Aff(n) on FA, so that FA is an Aff(n)-torsor, and the choice of a reference frame identifies FA → A with the principal bundle Aff(n) → Aff(n)/GL(n). On FA there is a collection of n + 1 functions defined by
The Levi-Civita connection is named after Tullio Levi-Civita, although originally "discovered" by Elwin Bruno Christoffel.Levi-Civita, [1] along with Gregorio Ricci-Curbastro, used Christoffel's symbols [2] to define the notion of parallel transport and explore the relationship of parallel transport with the curvature, thus developing the modern notion of holonomy.
Efficient and economical water splitting would be a technological breakthrough that could underpin a hydrogen economy. A version of water splitting occurs in photosynthesis, but hydrogen is not produced. The reverse of water splitting is the basis of the hydrogen fuel cell. Water splitting using solar radiation has not been commercialized.
The fundamental theorem of Riemannian geometry states that on any Riemannian manifold (or pseudo-Riemannian manifold) there is a unique affine connection that is torsion-free and metric-compatible, called the Levi-Civita connection or (pseudo-) Riemannian connection of the given metric.
This definition should be taken as defining the torsion-free spin connection, since, by convention, the Christoffel symbols are derived from the Levi-Civita connection, which is the unique metric compatible, torsion-free connection on a Riemannian Manifold. In general, there is no restriction: the spin connection may also contain torsion.
In small capillary hemodynamics, the cell-free layer is a near-wall layer of plasma absent of red blood cells since they are subject to migration to the capillary center in Poiseuille flow. [1] Cell-free marginal layer model is a mathematical model which tries to explain Fåhræus–Lindqvist effect mathematically.
If the principal bundle P is the frame bundle, or (more generally) if it has a solder form, then the connection is an example of an affine connection, and the curvature is not the only invariant, since the additional structure of the solder form θ, which is an equivariant R n-valued 1-form on P, should be taken into account.
The Correlation Spectroscopy experiment operates by correlating nuclei coupled to each other through scalar coupling, also known as J-coupling. [8] This coupling is the interaction between nuclear spins connected by bonds, typically observed between nuclei that are 2-3 bonds apart (e.g., vicinal protons).