Sentence examples for by using this expansion from inspiring English sources

By using this expansion and the extrapolation framework, they were able to derive a second-order approximation to E (f (x (t ) ) ).

We formulate a new model for the fractional Boussinesq equation by using this new Taylor series expansion.

The eigenvalue equation was first derived analytically by using the expansion theorem and then the eigenvalues and eigenvectors were calculated numerically.

Finally, the sound power and radiation efficiency spectra, under the application of two simultaneously applied harmonic forces, are calculated by using the expansion procedure.

For promoting working efficiency by using the expansion energy of the compressed air, we proposed a new type of expansion energy used air-powered vehicle using pneumatic-hydraulic transmission.

By using these expansions in the three-dimensional equations of motions, a set of recursion relations is identified expressing higher displacement coefficients in terms of lower order ones.

For this purpose, by using approximate expansion of 1/r 2 different than that used by Pahlavani et al., Schrodinger equation has been transformed to the analytically solvable differential equation of NU method.

In this paper, we present a new version of the iQIST software package, which is capable of solving various quantum impurity models by using the hybridization expansion (or strong coupling expansion) continuous-time quantum Monte Carlo algorithm.

The beam is analyzed by using modal expansion theorem.

Estimation of LPV models is efficiently solvable by using series expansion type of model structures, like orthonormal basis function models.

This paper examines features and driving forces of urban sprawl in Hangzhou from 1995 to 2005 by using urban expansion classification, density analysis, spatial metrics, and geospatial analysis.