Sentence examples for the corresponding statements from inspiring English sources

The corresponding statements are left to the reader.

This barely scratches the surface and yet already the corresponding statements of wellfoundedness have become less evident.

Remark 3.2 If we consider linear case p = 2 in Theorems 3.1, 3.2 and the scalar case with zero boundary condition at the left endpoint in [4], Theorems 5.3, 5.4], then the corresponding statements, i.e. the equivalence between the nonnegativity of the functional and nonexistence of the coupled point, coincide.

Finally, we define recurrent domains for semigroups in Sect. 5 and provide a classification of such domains under some conditions which are generalizations of the corresponding statements of Fornaess Sibony [5] for the iterates of a single holomorphic endomorphism of (mathbb C^k,; kge 2).

and the second and third isomorphism theorem can be formulated and proven in a way very similar to the corresponding statements for groups.

The standards of quality for different study designs were derived from the corresponding statements, such as CONSORT, STROBE, STARD and TREND statement [7] [10].

Standard logic includes the "distributive" law, by which a statement of the form "X and either Y or Z" is equivalent to the corresponding statement of the form "Either X and Y or X and Z".

We also show that the corresponding statement holds true for the commutant of ˜π(C X)) under the assumption that a certain family of pure states of ˜π(C∗ is total.

The corresponding statement for triangulated categories is not true.

The problem covers the corresponding statement with p-Laplacian in the principal part, for which it is sufficient to take (mu=0).

The core of the procedure just described is the following: Something is true for the natural numbers exactly when the corresponding statement holds for all simple infinities (i.e., is a semantic consequence of the Dedekind-Peano axioms).