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The optimality conditions in (3.20 - 3.22) are the semi-discrete approximation to the problem (3.3 - 3.5 3.3 - 3.5
Let us consider the question about validity of applicability of the WKB approximation to the problem under consideration.
Equations 7 and 8 represent mean-field approximation to the problem and are valid not too very close to the value of J = Jc 1, where thermal fluctuations are important [13, 21].
We apply the modern technique of approximation of multivariate functions – tensor train cross approximation – to the problem of the description of physical interactions between complex-shaped bodies in a context of computational nanomechanics.
The big approximation is your approximation to the problem you want to solve.
More generally, the model described here uses a simple linear response model and thus clearly only implements a rough approximation to the problem solved by the nervous system.
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Lemaréchal's problem was additively separable, and each summand function was non-convex; nonetheless, a solution to the dual problem provided a close approximation to the primal problem's optimal value.
We apply the same three node subgraph approximation to the routing problem in mesh networks.
This paper derives a mixed frequency-transient model as approximation to the original problem.
In this section we investigate a space-time spectral approximation to the optimization problem (2.12).
The second is derived by a block Toeplitz approximation to the descretized problem.
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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