Sentence examples for illustrative proof from inspiring English sources

Choi and Srivastava [2] proved Eq. (2.7) as a special case of (2.1) here and presented another illustrative proof.

Depending on the search terms entered by the user, these filters may serve many purposes, which are best understood in the context of our illustrative proof of concept searches (Table 3).

In addition to detailed derivations of the new controller design and a rigorous sketch of all the associated stability and attitude error convergence proofs, illustrative simulation results of an application to flexible spacecraft show that high precise attitude control and vibration suppression are successfully achieved using various scenarios of controlling effective failures.

Eighty percent of the education process should include aggressively targeting media, buyers and other influential audiences with objective support for your differentiators -- research data, expert opinions, illustrative anecdotes or other proof points.

Correspondence, manuscripts, proofs, and illustrative material.

Illustrative of this is his proof of the cobordism hypothesis, a result that links purely categorical concepts of duality with the topology of manifolds and also supplies a classification of topological quantum field theories.

The above derivation is an illustrative example of Bolzano's importation of proof methods from mathematics — such as the methods of indirect proof and of mathematical induction — into philosophy.

In comparison with [8], it contains full proofs of the results, illustrative examples, and a correction for a normalization rule.

Comparing to [7], in the current paper, we additionally provide the standard model semantics for WORL, a direct method for checking stratifiability of TBoxes, all the proofs and a number of illustrative examples.

In addition to presenting the mathematical theory of EpGPT to eigenvalue problems, illustrative numerical experiments will be conducted serving as proof of principle.

For this reason the proof of concept searches should be viewed as illustrative examples, not as evidence of further filter validation.