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The calculated hole profile using the analytical method was in good agreement with experimental data.
The Monte Carlo calculated NK agreed within 1.77%% of that obtained using the analytical method.
The predicted deflections using the analytical method and FEA method both agree well with the test results.
The strain energy release rates determined using the analytical method correlate well with the results from the finite element analyses.
In the first stage of the work, the composite column was designed as an alternative to the existing steel column using the analytical method.
The inner thermal barrier cylinder is solved by the finite difference method, and the outer cylindrical shell is solved by using the analytical method.
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Exact solution of resulting nonlinear integro-differential equations are obtained by using the analytical methods of homotopy and Adomian.
Final solutions were tested for concentration using the analytical methods described below.
Major physico-chemical parameters were analyzed in quality assured laboratories in Oman using the analytical methods and instrumental techniques shown in Table 1.
Using the analytical methods to estimate SRV parameters, it assumes a homogeneous single-porosity system and a fully stimulated pore volume with 100%% productive shale (optimistic assumption), which may result in under-estimation of hydraulic fracture size.
Of course, more accurate bounds also can be obtained for specific arrays of specified fluorochromes using the analytical methods described in this paper.
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