Sentence examples for primary theorem from inspiring English sources

We start by stating our primary theorem: Theorem 12 Let ( X, d, ⪯ ) be a partially ordered complete metric space.

Our results not only extend some primary theorems to ordered dislocated metric spaces, but also restrict the contractive conditions on a closed ball only.

We now present the primary estimates which have been used for the proof of the main theorem.

□ Theorem 2 together with Theorem 6 gives the main theorem of this paper.

Our primary result (Theorem 3.1) is about spacelike surfaces in (mathbb {R}^{2,1}), with singularities at which the tangent planes become lightlike.

Based on the control theorem, a primary resonant optimal control technique (PROCT for short) is applied to a general single-dof nonlinear oscillator.

\(\qed\) Theorem (Gärdenfors' Triviality Theorem).

We calculated PPVs for the risk of oesophago-gastric cancer in patients consulting in primary care using Bayes' theorem (Knottnerus 2002).

It was possible to calculate PPVs for the risk of pancreatic cancer in patients consulting in primary care using Bayes' theorem (Knottnerus, 2002).

Although this may impose a constraint on the range of achievable sum rates by the primary network, we showed in Theorem 5 and Corollary 5 that there exists a condition for which this constraint only enhances the achievable rates for the secondary link without degrading the range of achievable rates by the primary network.

It is worth emphasizing that many results in normative economics are mathematical theorems with a primary analytical function.