Sentence examples for equivalence class of from inspiring English sources

Since the conformal structure determines only an equivalence class of conformally equivalent symmetric linear connections \(K = [\Gamma]\), the affine connection in this type of geometry is not uniquely determined, and the parallel transport of vectors is not generally well defined.

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.

The idea is that the equivalence class of (m,n) is to be viewed as m − n.

For example, the equivalence class of a line for the relation "is parallel to" consists of the set of all lines parallel to it.

Fuzzy numbers are used to define an equivalence class of probability distributions compatible with available data and corresponding upper and lower cumulative density functions.

We complete the characterization of the algebraic equivalence classes by proving that any dimension function corresponds to an equivalence class of idempotents.

It is also shown that the flag structure is rigid, that is, the unitary equivalence class of the operator and the flag structure determine each other.

Our criterion yields examples illustrating pathology and also shows that to each equivalence class of idempotents there corresponds a "dimension function" from β × β into N ∪.

In an equivalence relation, all elements related to a particular element, say a, are also related to each other, and they form what is called the equivalence class of a.

An equivalence class of it is called a cycle.

We denote the equivalence class of P as [P].