Sentence examples for expanding the solutions from inspiring English sources
By expanding the solutions of the displacements in terms of the two-dimensional Fourier series, the final governing equations are reduced to an eigenvalue and eigenvector problem.
By expanding the solutions of the extended displacements in terms of two-dimensional Fourier series, the final governing equations of motion with modified couple-stress effect are reduced to an eigenvalue system of ordinary differential equations.
The solutions under time-dependent or static surface loadings and due to initial displacements and velocities are then obtained by expanding the solutions in terms of the modes of free vibration of the shell for each Fourier component.
The method is based on expanding the solution by Chebyshev wavelets with unknown coefficients.
The method is based on reducing the equation to a system of algebraic equations by expanding the solution as Euler wavelet with unknown coefficients.
Sentinel Labs has several beta testers, but is still working on expanding the solution to almost all desktop, server and mobile platforms.
We consider elliptic stochastic partial differential equations (SPDEs) with random coefficients and solve them by expanding the solution using generalized polynomial chaos (gPC).
By expanding the solution of the the two-body, bound-state Bethe Salpeter equation in terms of basis functions that obey the boundary conditions, solutions can be obtained to some, if not many, equations that have heretofore proved intractable.
We first expand the solutions in terms of the two-dimensional Fourier series in the horizontal plane to reduce the governing equations to a system of ordinary differential equations, from which we drive analytically the general solution in each layer.
Future work should expand the solutions to higher degree to obtain improved resolution or should assess the utility of local solutions over bounded regions to fully extract the signal inherent in the KBRR tracking data.
Jeanne Medina, a spokeswoman for United, said that her airline had already cut 7.5percentt and that until O'Hare could be expanded, the solution was for others to cut their schedules, too.
