Sentence examples for a length connection from inspiring English sources

Making use of Weyl (1923a, 124 125) shows that the conformal structure supplemented with the structure of a length connection or gauge field \(A_{j}(x)\) singles out a unique connection from the equivalence class \(K = [\Gamma]\) of conformally equivalent connections.[48] This unique connection, which is called the Weyl connection, is given by which is analogous to (14).

Weyl shows that this hypothesis does in fact single out metrics of the Pythagorean-Riemannian type by proving the following theorem: Theorem 4.2 If a specific length connection is such that it determines a unique symmetric linear connection, then the metric must be of the Pythagorean-Riemannian form (for some signature).

Weyl's Length Connection: A point \(p\) is length connected with its infinitesimal neighborhood, if and only if for every length at \(p\), there is determined at every point \ q\) infinitesimally close to \(p\) a length to which the length at \(p\) gives rise when it is congruently displaced from \(p\) to \ q\).

Thus, a conformal structure plus length connection or gauge field \(A_{j}(x)\) determines a Weyl geometry equipped with a unique Weyl connection.

Next, Weyl points out that what has been provided so far is merely an explication of the concepts metric, length connection and symmetric linear connection.

Weyl called this additional structure the "metric connection" on a manifold; however, we shall use the term "length connection" instead, in order to avoid confusion with the modern usage of the term "metric connection", which today denotes the symmetric linear connection that is uniquely determined by a Riemannian metric tensor according to (9).

Speaking of the SEO and length connection, it has also been discovered that longer posts increase your chances of gaining quality backlinks.

Weyl showed that this additional structure is provided by the length connection or gauge field \(A_{j}\) that governs the congruent displacement of lengths.

The nonlinear semi-rigid behaviour of beam-to-column connections is simulated using a zero-length connection element.

Our data not only reveals intermediate length connections between V1 and V2 or between V2 and V3, but also the well known long range connections such as i) the optic radiation linking the lateral geniculate body to V1, ii) V1 homotopic callosal projections, which are connections that take actually their origin more at the junction between V1 and V2 [56] and iii) V2 V5.

This problem is also called the minimum Steiner tree problem in graphs, which is of practical importance in several areas, e.g. chip design or shortest-length connection of households to a power grid.