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Computing the derivative of high-order determinant is difficult.
Computing the derivative of Green's matrix, we get d G ( t, s ) d t = Q ( t ) G ( t, s ).
In this section, we propose an operational way of computing the derivative of the global utility in a distributive fashion.
We define (F=T+L+T^), and computing the derivative of F along the trajectories yields begin{aligned} dot{F} =& lambda-d_{T} T+rT biggl 1-frac{T}{T_{max}} biggl 1-frac{ T}{d_{L}L leq& -d_{T_{max}{L}L-delta T^+lambiggrT leq& -hF+M_{0}, endeltagned} where (M_{0}=lambda+rT_{0}), (h=min{d_{T}, d_{L}L deleq&).
Computing the derivative of the objective function with respect to changes in the macrostate configuration is not feasible due to the high dimensionality of configuration space.
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The solution of this integrated optimization problem requires sensitivity analysis implying computing the derivatives of the constraints imposed on the optimization problem with respect to the design variables.
One of its main advantages is that it does not require computing the derivatives of the objective function to guarantee convergence.
We highlight that computing the derivatives of the SE based on Parzen windows produces numerically unstable results because d dθ log ( f ( x, θ ) ) = 1 f ( x, θ ) df ( x, θ ) dθ, thus, the errors in the estimation of the pdf are amplified in the derivative.
We relax this limitation by considering current estimates of G when computing the derivatives of Ψ.
In the previous section we computed the derivative of (13) with respect to x to derive a derivative formula for the Bernstein basis functions.
We also computed the derivative of (3) with respect to t to derive the following higher-order partial differential equation: ∂ v f B, k ( x, t ) ∂ t v = ∑ j = 0 v ( v j ) B v − j v ( x ) f B, k − v + j ( x, t ).
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