Sentence examples for using this analytical method from inspiring English sources

By using this analytical method, exact buckling and vibration solutions are obtained for rectangular plates having one- and two-step thickness variations.

Using this analytical method, for the first time, we were able to image the structural expansion of four members of the RHO family of embedded isoreticular zeolites along [001] orientation and thus to identify the main constituent cages, conforming their structures.

The reasons for using this analytical method were twofold.

Approximated solutions for both the crack propagation path and the stress intensity factor are derived, and the fatigue predictions using this simple analytical method are finally compared with the numerical results.

Transcripts were normalized to RPL32 mRNA control using the analytical method of 2−ΔΔ CT [ 62].

The variance of the difference was computed using the analytical method.

However, to avoid potential error in branch length estimates suggested by results from this study, we used the analytical method suggested to be more accurate -- ML.

In this report, based on this analytical method using the d'Alembert's solution, we design control laws to stabilize steady solutions and synchronize a pair of the distributed parameter systems.

The limitation of this analytical method used here is that we do not know what fraction of total poultry movements could be traced through the Internet.

Of course, more accurate bounds also can be obtained for specific arrays of specified fluorochromes using the analytical methods described in this paper.

Such calculation can be conducted for a specific choice of the operating regime using the analytical methods described in this paper.