Sentence examples for by taking the quadratic from inspiring English sources

By taking the quadratic polynomial output without cross term as an illustration, the solution of the contribution decomposition is derived analytically using the statistical inference theory.

In order to explore the contributions by correlated input variables to the variance of the polynomial output in general engineering problems, the correlated and uncorrelated contributions by correlated inputs to the variance of model output are derived analytically by taking the quadratic polynomial output without cross term as an illustration.

Cepstral and residual conversion accuracy is measured by taking the Euclidean quadratic distances and determining how close the reconstructed cepstral/residual vectors to the corresponding target cepstral/residual vectors are.

The functionals are constructed by taking the sum of a quadratic form of the current coordinates, integrals over the delay of quadratic forms of the state and its derivative, and the integral of the nonlinear components of the considered system [5, 6, 9 11].

We take the quadratic loss function just for simplicity of exposition.

Again, our N is too small to take the quadratic coefficient within this equation as definitive.

The approach allows to capture the nonlinear dynamic effects without the use of any ad-hoc improvisions, by taking into account both quadratic rotations of the beam cross sections and linear shear deformations.

Fig. 12(b) shows the search of the optimum done by the sequential quadratic programming algorithm, while taking the nominal cylinder as initial design.

By taking full exploitation of the special structure, the method enjoys the advantage of being easily implementable by linearizing the quadratic term of subproblems in the SISR problem.

The 'U'-shaped shape of the age curve for earache is confirmed using multiple regression by a highly significant quadratic effect of age after taking the linear effect into account (p <.001).

Taking the limit as (n rightarrowinfty), one sees that B is quadratic.