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Disturbances are modeled as Gaussian allowing for an explicit transformation of the probabilistic constraints into simple algebraic constraints.
By constructing an explicit transformation, which maps VCNLS to the classical coupled nonlinear Schrödinger equations (CNLS), we obtain Bright Dark and Bright Bright solitons for VCNLS.
Although it is difficult to obtain an explicit transformation between them, simple but tedious calculations show that they are equivalent.
This is achieved by specifying three separate yet inter-connected modules: a comprehensive biological description of the problem, a computational definition of the problem and an explicit transformation from one to the other.
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For star-shaped geometry, we propose an explicit global transformation map which can be easily differentiated and inverted.
Clearly the Milesians were interested in the original stuff from which the world was formed (Anaximander and Anaximenes are explicit about transformations of such an eternal original stuff), but the view that this endured as a single substratum may not have been theirs.
Standard time integration schemes make it possible to eliminate explicit use of transformation operators, thus significantly reducing the number of calculations.
Given a data set, the approach begins by building a low-complexity, linear model composed of explicit non-linear transformations of the independent variables.
We consider several aspects of the underlying speech representations, such as signal scales, input domain representations, network structures (shallow vs. multilayer/hierarchical), and ways of sampling for templates and transformations (explicit or learned discriminatively/unsupervised).
The Oulipo made this transformation visible, explicit, putting the scaffolding on the outside, "almost exactly like lobsters," he told his girlfriend who at that point began asking around discreetly for therapist recommendations but what fiction was innocent of it?
In this paper, we newly derive the explicit form of the transformation matrix relating six field variables of two box beams at a joint axial displacement, transverse displacement, in-plane bending/shear rotation, bending warping, and two bending distortions.
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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