Sentence examples for established the completeness from inspiring English sources
Scott established the completeness and decidability of various axiomatic tense logics.
In 2008, Qui and Shu [12] established the completeness of (mathcal{CB}(X)) with respect to the completeness of the metric space X, where (mathcal{CB}(X)) denotes the class of fuzzy sets with nonempty bounded closed α-cut sets equipped with the generalized Hausdorff metric (d_{infty}), which takes the supremum on the Hausdorff distances between the corresponding α-cut sets.
An alternative proof, developed by Skolem in 1922 to avoid appealing to the principles of set theory, has turned out to be useful also for establishing the completeness of the calculus.
Similarly to the previous case, we can show that the operator T ˜ f = ∑ n v n ( f ) ( e i λ n t − e i μ n t ), ∀ f ∈ L p t, is bounded in L p t. Introducing the new system { e i ω n t } n ∈ Z in the same manner we establish the completeness of the system (1) in L p t, if λ i ≠ λ j for i ≠ j.
The database was designed to confirm the validity of the identification codes, establish the completeness of the information keyed in and to perform basic data checks.
This study aims to establish the completeness and accuracy of smoking status recording in patients' primary care medical records and the level of interest in receiving smoking cessation support amongst primary care patients in an inner city UK population.
Having established the record of completeness for each source in the database a procedure analogous to developing earthquake magnitude-frequency distributions for PSHA is adopted here for assessing the annual rate of occurrence for eruptions of different magnitudes at each source (Musson 2000).
These general connectives are shown to be definable in terms of the standard ones, establishing the expressive completeness of the standard intuitionistic connectives.
Under a proximal orbital completeness assumption, we established the existence and uniqueness of best proximity points for such mappings.
We first establish the soundness and the completeness of the labelled tableau calculus based on the soundness and completeness results of its constituent logics.
