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Newton optimization methods use the second order gradient information to calculate the step direction.
Here we use the second order fractional central difference method provided in [27, 34] to discrete the Riesz fractional derivative of equation (1.1).
In the (mathrm {P}^{3}mathrm{T}) scheme, we use the second order approximation; begin{aligned} boldsymbol {w}(t+delta t) = e^{delta t /2 {, H_{mathrm{soft}}}}e^{delta t {, H_{mathrm{hard}}}}e^{delta t /2 {, H_{mathrm{soft}}}} boldsymbol {w}(t) + Obigl(delta t ^{3}bigr).
Here we use the second order derivatives as a smoothing weighting factor.
(b) Boundary optimization : We use the second order differences of control points, i.e., b α − 2 b α + 1 + b α + 2. We choose this method in order to maintain cylinders/cones and to minimize the curvature along the boundary.
But the expressions for the first moments, the population sizes we are interested in, are completely determined by first and second moments, and we could use the second order as a upper cutoff.
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We use the third order explicit TVD Runge-Kutta method in time direction [13].
Instead we decided to use the first order differencing to eliminate the trend component.
Autopilot control law has been designed for Micro Aerial Vehicle MAVV) using the second order sliding mode (SOSM) approach.
The final column of the table shows the calculated turbidity from our meter using the second order regression equation.
The DHSVM model was calibrated and validated using the second order watershed.
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