Sentence examples for using the new equations from inspiring English sources

A spectral solution is used to solve for highly nonlinear steady waves using the new equations, showing that the fully dispersive behavior carries over to nonlinear waves.

The closed-form equations for the torsional compliance of elliptical and circular flexure hinges are derived by using the new equations.

The results prove that the voids in mineral aggregate (VMA) and the initial asphalt content calculated using the new equations proposed by this study based on theoretical analysis are more accurate than those of the traditional Superpave's empirical equations.

Using the new equations, the dynamic response of a cracked rotor near its critical speed has been computed via a numerical method to investigate the influence of nonlinear breathing of the crack and that of the imbalance orientation angle β on the stability, critical speed and peak response of the rotor.

Based on data from the American National Standards Institute (ANSI), error of hydrogen consumption calculated using the new equation is less than 0.5% when hydrogen storage pressure ranges from 0.5 to 70 MPa at 298 K.

Solutions using the new equation set are shown to be grid-independent for the conditions considered and to have an intuitively correct sensitivity to friction, however small instabilities and increased errors on predicted depth were noted when Manning's n = 0.01.

Using the new equation and a list of potential suspects who work in the new hot zone, Don, Terry, and David confront the suspect and find his latest victim.

Laboratory evaluations were performed, and estimated glomerular filtration rate was assessed by using the new equation proposed by investigators in the Chronic Kidney Disease Epidemiology Collaboration.

Values of estimated glomerular filtration rate (e-GFR; mL/min/1.73 m) were calculated by using the new equation proposed by investigators in the Chronic Kidney Disease Epidemiology (CKD-EPI) Collaboration [ 30].

GFR was estimated using the new equation proposed by the Japanese Society of Nephrology as follows: eGFR (mL/min/1.73 m) = 194 × Cr−1.094 × Age−0.287 × 0.739 (if female) (5).

Equations in Word must be created using Equation Editor 3.0 Equations created using the new equation editor in Word 2007 and saved as a "Word 97-2003 Document" (.doc) are converted to graphics and can no longer be edited.