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The full solution of the Riemann problem (Riemann solver) is also given by elementary functions.
The full solution of the time dependent Navier-Stokes equations was used to model inertial deposition on cylindrical collector at 30 ≲Rec ≲ 40,000.
Aforementioned 1D procedures were then compared to a procedure wherein the full solution of Maxwell's equations, which describe the electromagnetic signal response into the soil, is applied.
Although the passage is not easy to interpret, his main point seems to be to emphasize that analysis must be supplemented by synthesis to yield a full solution of anything.
A rigorous approach to obtain μ n (T n ) in the case of strong inhomogeneous instantaneous fields would require a full solution of the microscopic Boltzmann equation, which is practically an impossible task for realistic devices.
This is related to the problem of removing the so called buffer assumption of Hytönen Nazarov, which is the final barrier for the full solution of S. Hofmann's problem.
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Apparent diffuse layer potentials resulting from the fits to the full solutions of the Poisson Boltzmann equation show that the fiber surfaces bear a negative surface charge.
Numerical examples are given comparing the predictions of the surface mode dispersion relation to full solutions of the Pridmore-Brown equation, and the accuracy with which surface modes are predicted is shown to be significantly increased compared with the uniform slipping flow assumption.
A full solution to the problem of young investigators, however, is beyond the reach of NIH.
Traditional gradient-based optimization schemes, employing deterministic design specifications for the objective function, are inefficient and severely limited in their ability to search the full solution space of member cross-sections.
Instead, by utilizing the finite strip method for stability analysis and the Direct Strength Method for the strength calculation, the full solution space of cold-formed steel shapes may be explored.
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