Sentence examples for equivalent connections from inspiring English sources

However, a conformal structure by itself does not determine a unique symmetric linear connection; it only determines an equivalence class of conformally equivalent connections \(K = [\Gamma]\), namely, connections which preserve the conformal structure \(C\) during parallel transport.

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).

The rotation capacity of connections containing radial welds was nearly 30% lower (on average) than equivalent connections without radial welds.

If one would now straightforwardly solve the binary linear program for the unit cell, as we did in Section 3.1, then one would encounter the problem of equivalent connections, i.e., connections that are doubled due to the shifting of the unit cell.

This paper evaluates the hypothesis that welded hollow section connections, which have circular hollow section (CHS) branch (or bracing or web) members welded to a rectangular hollow section (RHS) chord member, may be converted into "equivalent" connections whereby the circular branch member is replaced by a square branch member.

We proceed by comparing the fiber density of every connection with a set of equivalent connections generated in systems where diffusion coherence contrast is removed by randomly reshuffling the orientation distribution functions (ODFs).

The following is the equivalent connection between convexity and Theorem B.

An equivalent connection pattern is presented to facilitate the modeling of switching and routing operations.

Evidently this fundamental principle of infinitesimal geometry is not satisfied for a structure which is merely a conformal structure, since the conformal structure only determines an equivalence class of conformally equivalent symmetric connections.

In the continuous approach the connecting beams are replaced by equivalent continuous connections.

Displacement control quasi-static and also dynamic time-history analyses showed that the performance of the systems with friction devices is significantly improved under seismic loading compared to similar systems with equivalent nailplate connections.