Sentence examples for using the bernoulli basis from inspiring English sources

In this article, using the Bernoulli basis {B0 x),..., B n (x)} for ℙ n consisting of Bernoulli polynomials, we investigate some new and interesting identities and formulae for the product of two Bernoulli and Euler polynomials like Carlitz did.

Here, in Theorems 2-9, we use the Bernoulli basis in order to express certain polynomials as linear combinations of that basis and hence to get some new and interesting polynomial identities.

Specifically, the existence of stochastic actuator faults are described by using the Bernoulli distribution.

For (q=1) we can prove it directly and for (qge 2) using the Bernoulli inequality.

Data were analysed for spatial clustering using the Bernoulli model and the significance of clusters were tested using the Kulldorff scan statistic.

All of these were identified using the Bernoulli model.

Results were consistent with SaTScan cluster detection using the Bernoulli probability model.

Using the Bernoulli model, clusters with increased relative risk were identified.

Pulmonary artery systolic pressure was calculated according to velocity of tricuspid regurgitation using the Bernoulli equation.

Due to the high prevalences, some of the adjusted GLM analyses could not converge using the Bernoulli family.

In addition, we explored spatial clusters of Ciudad Real municipalities at high risk by using the Bernoulli model [ 29].