Exact(7)
The optimization approach uses a derivative variation method to efficiently identify the optimization range through analyzing the first order derivatives of the optimized quantity and the non-linear deviation profile of the derivative value.
The PID controller calculation involves three separate parameters: the proportional, the integral and derivative values, denoted P, I, and D. The proportional value determines the reaction to the current error, the integral value determines the reaction based on the sum of recent errors, and the derivative value determines the reaction based on the rate at which the error has been changing.
As illustrated in the scheme, the current feed rate at that time point will be 10% reduced when the derivative value is more than or equal to the upper threshold signal (N′ ≥ 1.3 rel. unit/min).
(In the course of his argument, Beardsley rejects the sort of "dialectical demonstration" of intrinsic value that was attempted in the last section, when an explanation of the derivative value of helping others was given in terms of some nonderivative value).
By contrast with that, the condition u ( 1 ) + σ D 0 + γ u ( 1 ) = 0 in BVP (1.5) shows that relation between the derivatives of different order u(1) and D 0 + γ u ( 1 ) is regarded as the derivative value of zero order of u at t = 1), which brings about more difficulties in deducing the property of green's function than the former.
It can also be rearranged to the derivative value of the RPI to the cumulative injection volume: gamma = frac{{text{d} beta }}{{text{d} W}}, (10 where γ is the rate of change of the RPI in MPa d/m6; and W is the cumulative injection volume in m3.
Similar(53)
The heat map used to visualize the derivative values is a mean to display all influences on the current design point in one graph.
The derivative values of α calculated from positive- and negative-offset directions had large values but opposite signs at ~250 m.
Since the derivative values of S j ( x ) defined by (2.4), (2.8), (2.9) and (2.10) are not known at each grid point ( x l, t j ), we use the following approximations for the derivatives of S j ( x ).
Since the derivative values of (S_{j}(x)) defined by (2.7 - 2.10) are not known at each grid point ((x_{l},t_{j})), we use the following approximations for the derivatives of (S_{j}(x)).
Let the derivative values satisfy the necessary conditions for monotonicity, namely { d i = d i + 1 = 0 for △ i = 0, sgn ( d i ) = sgn ( d i + 1 ) = sgn ( △ i ) for △ i ≠ 0. (30..
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