Sentence examples for derive a generalization from inspiring English sources

Gödel uses compactness to derive a generalization of the completeness theorem.

Next, we derive a generalization of a fixed point theorem due to F. E. Browder and B. R. Halpern.

After recalling some preliminary facts on matrices in the next section, we state our main results on the asymptotic constancy of the solutions of (1.13), and derive a generalization of the limit formula (1.12) to the time-dependent case (Section 3).

We previously derived a generalization of CA (GCA) to describe the combination effects of full agonists, partial agonists, and competitive antagonists (Howard and Webster 2009).

Finally, the current approach is applied to derive a non-isothermal generalization of a phase-field crystal model for binary alloys in the "Non-isothermal generalization of a phase-field crystal model for binary alloys" section.

We develop explanation structures from these truth criteria, and use them as a common basis to derive a variety of generalization algorithms.

The participants were instructed to type in "None" if they could not derive a comparison or generalization across the pair.

Finally, the current approach is applied to derive a non-isothermal generalization of a phase-field crystal model for binary alloys (see, e.g., Elder et al., Phys. Rev. B 75 6), 064107 (2007)).

After deriving a suitable generalization of the Cahn Hilliard equation, we addressed phase separation for both an idealized regular solution and ternary feldspar.

Using this generalization, we derive a Gaussian isoperimetric inequality for an absolutely continuous probability measure on Euclidean spaces with respect to the Lebesgue measure, whose density is a radial function.

To this end, Dirichlet-, Neumann-type and periodic boundary constraints are derived from a generalization of the Hill-Mandel macro-homogeneity condition towards the coupled electro-mechanical problem.