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To enhance the quality of approximation, the Rayleigh quotient is approximated in terms of some intermediate variables, using the two-point approximation.
The displacement field is approximated in terms of a set of mesh-free kernel particle functions.
The power spectrum of the finite fractal roughness is approximated in terms of a power-law function for the intermediate wave numbers (spatial frequency components in roughness).
The nonlinear function is approximated in terms of the piecewise linear interpolation model with the look-up table parameters, which can be rewritten as a dot product between the regression vector and unknown parameter vector using membership function.
Lastly, the method is restricted by per-pixel housing supply, which is approximated in terms of inhabitant capacity in the model and is instrumental in imposing a larger degree of inertia on the model results.
Therefore, a difference between the 10th and 12th reaction terms is approximated in terms of (37) ∫ 0 t κ 7 Z 3 N, 2 s ds, which converges to ∫ 0 t κ 7 Z ¯ 3 2 (s ) ds from (34).
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Then lim N → ∞ u N ( x ) = u ( x ) under the condition A + | β | T + T B ≪ 1. Proof Since the known functions a ( x ), g ( x ), and b ˆ 0 ( x ) are approximated in terms of shifted Legendre polynomials, then the obtained solution is an approximated polynomial in the form of u N ( x ).
(16) A function square integrable in ([0, 1]) may be approximated in terms of the normalized Bernstein basis (14).
To close the theory, the tensor ρ k+1) needs to be approximated in terms of lower order tensors.
The nonlinearities in the system dynamics are taken to be unknown, and are approximated in terms of radial basis functions (using a particular neural-net architecture).
This paper presents a nonlinear controller, which can be used to control single-input single-output nonlinear systems that can be approximated in terms of Hammerstein models.
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