Sentence examples for a theorem on the structure of from inspiring English sources

In this section, we give a theorem on the structure of the matrix, and provide an example for illustration.

The second part is a course on the basics of combinatorial number theory (or additive combinatorics): cardinality inequalities (Plünnecke's graph theoretical method), Freiman's theorem on the structure of sets with a small sumset, inequalities for the Schnirelmann and asymptotic density of sumsets, analogous results for the measure of sumsets of reals, the connection with the Bohr topology.

The proof of Theorem 3.3 is based on abstract Theorems 2.1, 2.3, 2.4 and on the following theorem on the structure of the fractional spaces E α ( C [ 0, 1 ], A t, x ).

The following Scorza-Dragoni theorem explains the structure of the Carathéodory functions on a bounded interval.

An important normal form theorem for the structure of cut-free proofs was provided by Andreoli (1992).

We first prove the following theorem on the separator structure of G ′ (M).

Our algorithm is based on some simple theorems that characterize the structure of the k-way cut.

The central point of this theory is a constructive theorem on the existence of the general decomposition structures and conditions under which the corresponding structures exist.

Characterization theorems tell us how the structure of reliable methods corresponds to the structure of the hypotheses under investigation.

Topics include groups, groups acting on sets, Sylow theorems; rings, factorization: Euclidean rings, principal ideal domains, the structure of finitely generated modules over a principal ideal domain, fields, and Galois theory.

This assumption is used to obtain Lemma 5 and Theorem 7. We also place an upper bound on the distance between consecutive points according to the structure of proteins.