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Knowing (R_{text{De}}), Eq. 30 can be solved to get the values of (lambda_{n}).
Knowing (R_{text{De}}), Eq. 109 can be solved to get the value of λ.
The difference is that my advisor had a better sense of which direction the field was headed and what problems needed to be solved to get it there.
And the convex SDP problem in the form of (P3) with the pre-determined binary variables can be solved to get the optimal covariance matrix K x.
Equation (12) is an equation set with 'm' variables and 'm' unknowns and hence can be solved to get the required parameters.
We know that L is an isomorphic mapping from X 2 to Y, then, by applying the implicit theorem tothe second equation of (3.7), it can be solved to get a unique solution ( y, z ) = ( y ( μ, τ, s ), z ( μ, τ, s ) ) near ( 0, 0,).
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Using the accuracy and unconditional stability of the hybrid FE IDQ method, the direct problem is solved to get the dynamic transverse displacements.
Using Fourier transform technique the boundary value problem has been converted to standard Wiener Hopf equation which has been solved to get the analytical expressions for the stress intensity factor and crack opening displacements.
The bridge is modelled as a Bernoulli Euler beam and the boundary value problem of the beam is solved to get the exact mode shape functions of the vibrating beam with intermediate supports.
Then, for a fixed λ, Eq. (12) is solved to get (hat {boldsymbol{beta }}_{lambda }).
Then, another three MMV problems are solved to get the estimates in the β domain.
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