Sentence examples for using the analytical equations from inspiring English sources

For small-scaled I-beams, the critical loads obtained from the proposed experimental method were in good agreement with those calculated using the analytical equations.

Flux ratios were determined from the mass isotopomer distribution of the protein-bound amino acids with the software FiatFlux [ 38] using the analytical equations developed by Blank and Sauer (2004) [ 21].

As plant fires can impact a wide area, this study further investigated using the analytical equation to model fire on a detailed geometry of a pressurized vessel with associated piping.

The simulated neural network model is trained and validated using the analytical solution of Richards' equation.

The approach is based on the integration of the Navier Stokes equations using the analytical solutions for the two-dimensional local velocity and pressure fields obtained from the asymptotic developments at low filtration Reynolds number proposed by Berman (J. Appl. Phys. 24 (1953 12322) and Yuan and Finkelstein (Trans. ASME 74 (1956) 719).

The focal length, which is the necessary distance to effectively concentrate particles in a microchannel, is calculated using the analytical solution of the particle equation of motion.

Publishing House of the Faculty of Mechanics and Mathematics of the Moscow State University (in Russian), 2007] is that the given observations are approximated using the analytical solution of the fundamental differential equations of the meteor physics.

The predictions of the proposed GEP-based models were compared with the results obtained using the existing analytical equations proposed in the current literature.

A typical example problem is used to compare the analytical equations that are derived with the analytical equations that are presented in the US Army Corps of Engineers USACEE) levee design manual.

The model is validated using the advection diffusion analytical equation.

The analytical equations used to represent the far-field temperatures are presented in continuous form.