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We use this generic 3D continuum formulation as a starting point to derive the governing equations for slender bodies, which can be solved in a weak sense to find an approximate analytical formulation for large deflections and non-linear ferromagnetic materials.
(Yack (2012, 203ff) starts from the same point to derive much more pessimistic conclusions).
These expressions are the starting point to derive the exact results proposed in this work.
The key point to derive the optimal solution to the differential game model Γ HHCC is also illustrated with a block diagram depicted in Fig. 4b.
The key point to derive the optimal solution to the differential game model Γ PLPC is illustrated with a block diagram shown in Fig. 4a.
The set of weight matrices selected by co-occurrence analysis was subsequently used as starting point to derive more complex promoter models.
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Nevertheless, Kohlschütter's analyses were hypothesis driven, as he discarded almost 50% of the data points to derive what he called an "idealized curve of sleep".
There are three primary points to derive from extant research.
Battiato [10] proposed a method based on the position of the lines and the vanishing points to derive a suitable assignment of depth.
These relative heights are then calibrated against one or more points to derive absolute divergence time estimates.
Next, we will apply the Krasnoselskii-Zabreiko fixed point theorem to derive an existence result.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com