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Numerical analysis is performed via Finite Element Method (FEM) with a damage model written as a UMAT (User Material Subroutine) and linked to commercial software.
The first scheme (method A) is based on the use of a primal-mixed formulation of the DD model written as a function of the quasi-Fermi potential gradient (see [12] and [13]).
The selection equation is a binominal probit model written as follows (McKelvey, and Zavoina [19]): d n * = a ' X n + b * 1 − exp β n + c * δ n + d * 1 − γ n + u n, d n = 1 if d n * > 0 and 0 otherwise.
The average particle size of the nanocores was estimated by applying the Debye-Scherrer model, written as d = 0.9λ/ß d cosθ, where d is the crystallite diameter, λ = 1.540562 Å for Cu Kα line, ß d is the full width at half maximum of the strongest reflection peak, and θ is the corresponding Bragg angle [58].
Unexplained residual variability for PSA kinetics was modeled using an exponential residual error model, written as an additive model for the log-transformed PSA observations and predictions (log-transformation both sides).
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In other words, for a given gene, the output of the model writes as follows: (5) Equation (5) shows that the expression level of gene i at time t + 1 is modeled by a linear combination of nonlinear terms that share parameter C. The function f ij itself is a nonparametric function built from training data.
For the independence model, which assumes that ratings are statistically independent, the model is written as: (1) where μ is the overall effect and and are A and B effects on category i and j, respectively.
The model is written as an algebraic structure with unknown parameters and/or functions.
The syntax of this generalized linear model is written as following.
The frame is treated as a single-degree-of-freedom system, and the hysteretic model is written as a small system of ordinary differential equations.
The corresponding dynamic model is written as (19).
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com