Sentence examples for provided the assumption from inspiring English sources

Theorem  5 remains true if certain involved terms namely: O̅-complete, O̅-continuous, and the ICC property are, respectively, replaced by O-complete, O-continuous and the MCC property provided the assumption (d) is replaced by the following (besides retaining the rest): ((mathrm{d})^{primeprime}) :  there exists (x_{0}in X) such that (x_{0}precsucc f(x_{0})).

Theorem  5 remains true if certain involved terms namely: O̅-complete, O̅-continuous and the ICC property are, respectively, replaced by (underline{mathrm{O}} -complete, (underline{mathrm{O}} -completeunderline{mathrm{O}} -continuous the assumptiO}} -continuousced by the following (besides retanding the rest): ((mathrm{DCC^{property:  there exists (x_{0}in X) such that (x_{0}succeq f(x_{0})).

However, these data would also be suitable for analysis using two-way ANOVA to examine disgustingness ratings, with synchronism (synchronous vs asynchronous) and stimulus type (disgust stimulus vs clean tissue) as within-participant factors, provided the assumption of normality was met.

Differences between pre and post-intervention measures will be examined using paired t-tests for all interval scaled measures, provided the assumption of normality is met [ 51].

Cox regression will be used to compare survival curves (time to recovery from pain) of manipulation and mobilisation groups, provided the assumption of proportional hazards is met.

As the Apgar categories constitute a multinomial endpoint, we intended to fit a proportional odds logistic model, provided the assumption of a constant odds ratio was met [ 35].

The value of su produced by Eq. 4 is a best linear unbiased estimator of σu – provided the assumptions underlying its derivation hold.

His influence extended far beyond sociology: for example, his work provided the assumptions of much current research in language and social interaction within the discipline of communication.

In contrast, STs maintain validity independent of the test protocol applied provided the assumptions of the statistical test are met.

The main advantage of a ST is that it can be applied without prior knowledge of the performance criteria of the test, provided the assumptions of the ST are valid.

Binding energy positions at 397.2, 398.1, and 399.8 eV provide the assumption about an interstitial nitrogen incorporation with the trace of remained nitrogen-carbon bonds.