Sentence examples for by using the lower from inspiring English sources

Although early workers attempted to address this problem by using the lower dimensional dihedral angle space as opposed to Cartesian space, more useful methodologies such as diagonalization in mixed basis (DIMB) were later proposed by Perahia and colleagues.

According to Judge Moskowitz's decision, assets are to be returned to each investor within 30 days by using the lower number from two accounting treatments that remain in dispute.

with some quite general nonlinear boundary conditions by using the lower and upper solution method.

Finally, error concealment for the EL slices is done by concealing the missing slice by using the lower quality slice.

By using the lower and upper solution method and fixed point theorem, they obtained some new existence results.

We then identify the transition point with the largest gradient of P by using the lower plot in Figure 5.

The largest Lyapunov exponent is obtained explicitly by using the lower-dimensional approximate Itô equations.

By using the lower-order model correction, a novel nonlinear multi-level moment solver is developed.

However, the results can be improved by using the lower-order CCs in the estimate, whose variance is shown to be less than that of corresponding higher orders.

Red Line users are supposed to access the opposite platform by either using the upper-level faregate mezzanines at 13th or 11th streets NW or by using the lower-level Orange and Blue line platform.

Moreover, by using the weakly lower semicontinuity of the norm on and (3.9), we obtain (3.10).