Sentence examples for were derived previously from inspiring English sources
The non-linear equations of motion including stretching due to immovable end conditions were derived previously [1] (Özkayaet al. 1997Journal of Sound and Vibration199, 679 696).
While both the two-way wave advection and the associated numerical schemes were derived previously, these approaches have never been combined with level set advection.
Tractable expressions for the first moment statistics of the number of load exceedances and damage duration were derived previously, primarily for a Poisson square wave process and for material with a bilinear force-deformation relationship.
Similar decay rates were derived previously by Munk (1963) and Van Dorn (1984) from much scarcer data sets than those employed in the recent study by Rabinovich et al. (2013).
The tool is based on a supervised PCA analysis using classifiers that were derived previously and were extensively tested and validated.
Tumorigenic BEP2D cells were derived previously from treatment of exponentially growing BEP2D cells with a single 60 cGy dose of alpha-particles (Hei et al, 1996).
A similar transport equation has been derived previously, but a more general expression is obtained through the present derivation.
An exact nonreflecting boundary condition was derived previously for use with the time dependent wave equation in three space dimensions.
In two limiting cases, isolated spherical particles (in a matrix or not) and layer structures, the solution for the stress reduces to results which have been derived previously.
An exact nonreflecting boundary condition was derived previously for timedependent elastic waves in three space dimensions [SIAM J. Appl. Math.60, 803 (2000)].
It has been derived previously for a liquid state of water produced by the fuel cell and given by [29].
