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A bridge's dynamic response in the time domain can be obtained through solution of the FEM for train track bridge coupled vibration; it could then be transferred into the frequency domain via fast Fourier transform.
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The relation between the Reynolds number and differential producer discharge coefficient was obtained through solutions to the steady, Reynolds-averaged Navier Stokes equations.
Accordingly, the schedule of DERs, bidding strategy and MCP can be obtained through the solution procedure above.
The first is Baxter type of solutions if they can be obtained through gauge Baxter solutions together with some solution transformations.
The second is Free-Fermion type of solutions if they can be obtained through gauge Free-Fermion solutions with some solution transformations.
As the critical buckling temperatures cannot be obtained through a closed-form solution, the optimization process takes a lot of time.
The lack of such a two-dimensional theory has made the analysis of surface acoustic wave propagation in various waveguides primitive and difficult because the precise solutions cannot be obtained through any analytical effort and numerical solutions are also difficult to obtain because of the complicated nature of problems.
Thus in the case of ship, all user needs can be captured and translated into the overall ship functions: to float, to navigate, to (be easy to) control and manoeuvre, all of which can be further decomposed and in turn imply and can be obtained through a series of technical solutions for the boat structure.
If the exact, closed form fundamental solutions are not available, then approximate fundamental solutions can be obtained through a simple and efficient numerical method.
(v) The ODEs solution can be obtained through the iterative integration of the right hand side term of each equation.
Its solution can be obtained through the SVD of the matrix obtained by stacking all the local IKs (vectorized) we want to interpolate.
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