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These problems, which one comes face to face with in life, cannot be solved using classical mathematic methods.
Such a design can be formulated as a non-linear max min optimization problem, hard to be solved using classical numerical techniques.
Most random noise and vibration problems cannot be solved using classical methods; SEA thus provides a basis for prediction of the average noise emitted by a structure, especially at high frequencies, where the associated modal density is high.
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The existence of a minimizer for a special version of the Monge Kantorovich problem is solved using classical tools of functional analysis, and it is shown that the minimizer is not unique.
Hence, a 3D wedge problem can be solved using those classical solutions for half-spaces once the equivalent loads are obtained.
A hitherto unavailable HSDT (higher-order shear deformation theory -based boundary-discontheory -baseder solution to the class of problems of general cross-ply plates that cannot be solved using the classical Navier or Levy type approach is presented.
Let us mention that most valuation problems examined in the existing literature are local and thus they can be solved using existing results for classical BSDEs.
The problem in (20) belongs to the classical setting of CS and, thus, can be solved using convex relaxation, greedy pursuit, or combinatorial algorithms [39 43].
Equation 8 is solved using a classical Block Lanczos algorithm implemented in the commercial FE code ANSYS (Rel. 12).
While the second-stage FIM stage is solved using a classical iterative solver, the multiscale stage is investigated in full detail.
The solution in the classical regions is solved using a particle method and interface condition combined with the Hamiltonian-preserving scheme.
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