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Due to the ability of Butterfly-Net to approximate Fourier and local Fourier transforms, the result can be used for approximation upper bound for CNNs in a large class of problems.
It is used for approximation and data reduction, and for data reduction in cases the curve or surface does not change neither geometrically nor parametrically.
It will be shown that the backflow cell model may be used for approximation of the dispersion model.
Wavelet networks, which are having superior learning capability in comparison to conventional neural network, are used for approximation of unknown system dynamics.
In proposed control scheme wavelet networks are used for approximation of unknown system dynamics as well as a wavelet based compensator is designed to deal with actuator saturation.
The finite element method is used for spatial approximation of the field, and the implicit finite-difference scheme is used for approximation of the field in time.
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The evolution of seismicity can be written as a Ricatti Equation (Ince 1956, pp. 23 35), which is used for approximations as well as for numerical implementation.
An interesting and open question for the author is how the solution Eq. (48) could be efficiently used for approximations and solving differential equations.
When continuous values were described by median and IQR or range instead of mean and SD, the following formula was used for approximations: Mean = Median; SD = IQR/1.35; if 15 < n <70, SD = (b a)/4, (Minimum (a), Maximum (b)); if n >70, SD = (b a)/6 [ 27, 28].
For this approximation, the order used for the approximation of each delay is chosen to be roughly proportional to the duration of the delay.
The approximation of the critical crack length is performed using the same calibration samples as those used for the approximation of the crack length.
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