Sentence examples for derived the gradient from inspiring English sources
Li [1] derived the gradient estimates and Harnack inequalities for positive solutions of nonlinear equations ( △ − ∂ ∂ t ) u ( x, t ) + h ( x, t ) u α ( x, t ) = 0 and A u + b ∇ u + h u α = 0 on Riemannian manifolds.
We can easily derive the gradient and the Hessian results in a diagonal matrix whose inversion using Newton's method then becomes a point-wise division.
We derive the gradient estimates and Harnack inequalities for positive solutions of nonlinear parabolic and nonlinear elliptic equations (Δ − ∂∂t) u x, t) + h x, t)uα x, t) = 0 and Δu + b · ▽u + huα = 0 on Riemannian manifolds.
We derive the gradient estimate.
Here, we derive the gradient ∂ Y e ( k ) ∂B which is required in calculation of (11).
Moreover, any figure of merit is suitable for optimization with the simplex method, as there is no need to derive the gradient for the optimization functional.
The PAPR reduction problem was formulated as a minimax problem that was solved by deriving the gradient analytically and modifying the SQP algorithm to solve the optimization.
In the following, we first derive the gradient descent flow equation of (13) and then find a simplified flow which has the coincident steady state solution with the original gradient descent flow equation and finally define a new and convex energy in view of the simplified flow.
We derive the gradient descent flow equation of (13) with respect to ϕ. Making the interchange of variables x and y (i.e., x = y, y = x) for (13), we have E ϕ, h 1, h 2 = ∫ y ∈ Ω ∑ i = 1 2 ∫ x ∈ Ω K σ y − x h i y − I x log h i y M i ϵ ϕ x dx dy.
Assuming all the reaction follows mass-action law, we can derive the gradient of the likelihood function using TOPE formula.
The procedure to derive the gradient function was identical to the one described for the in silico case, with the theoretical peptides being replaced by the abundant MS1-features, and the predicted retention times with the observed retention time apexes of these features.
