Sentence examples for defined in example from inspiring English sources

Let T be a mapping as defined in Example 1.6.

where the associated parameters are defined in Example 1.

Let p be the τ-distance defined in Example 2.10.

We take the functions φ, F, and ψ defined in Example 2.4.

Consider the sequence ((E_{k})) of subsets of M as defined in Example 2.6.

Consider the (C^ -algebra (mathbb{A}=mathbb{R}^{2}) as defined in Example 2.2.

For example, from the uniqueness of strict vector ordering (Theorem 5.1), it follows that ≺ defined by (5.3) is not a strict vector ordering in the ordered vector spaces defined in Examples 5.1-5.3 5.1-5.3

Remark 12.4 Observe that ( X, p ) and ( X, T ) defined in Examples 12.3 and 12.4 are identical, note that we may apply Theorem 10.1 with defined by (12.3) and (12.4) and satisfying J ≠ P = { p } and note, however, that we do not apply Theorem 10.1 with J = P = { p }. Thus the existence of a -family such that J ≠ P is essential.

We generate 40 data sets for each model defined in Examples 1 and 2. Our simulated data sets are sparse with two amplifications and one deletion, and only 5 true breakpoints for each data set.

Validation XML rules have to have a specific format as defined in the example below.

The way the early surrogate is defined in our example, without separate standardization by geographic region, the only connection to an individual is through age.