Sentence examples for by the classification theorem from inspiring English sources

By the classification theorem of one-dimensional smooth manifolds, Γ w ( 0 ) is diffeomorphic either to a unit circle or to a unit interval.

By Elliott′s classification theorem, the resulting monoid uniquely characterizes A. We give a simple equational characterization of the monoids arising as classifiers.

We give a Kolmogorov-type theorem and a classification theorem, connecting the stochastic multiplicative measures with vector-valued Lévy-Khinchine fields.

We overcome this difficulty by combining two different classification theorems of Chen and Li [6], [7] to get the desired bubble.

— will be confused by the classification.

We close this section by the following theorem which is a classification of rings whose annihilating graphs are complete.

The close connection between fdr and the empirical Bayes methodology follows directly from Bayes theorem and this has been established by the "Equivalence theorem"[ 28].

The answer is given by the dominance theorem, introduced in the next section.

The following corollary provides an alternative formulation of the optimality result given by the above theorem.

The convergence of Algorithm 2 to ‖ Υ ‖ is guaranteed by the next theorem.

The relationship between neighbor pairs and patterns are characterized by the following theorem.