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Our use of penalized regression techniques to model the functional data and construct the function signatures allows us to consider a relatively large number of individual annotation variables while controlling for over fitting.
We construct the function f ( z ) θ 3 ( z | τ ).
Inverse Problem 3 Given the Weyl function M , construct the function q ( x ).
Using the solution of the main equation, one can construct the function q ( x ).
To construct the function f 1, it is sufficient to consider the sequences b = { 1 ( | m | + 1 ) ? 1 } m ?
Now, let us construct the function S ( x, λ ) by (3) and the function Ω ( x ) by (4).
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We follow the guidelines in [20] in order to construct the functions.
Given the scattering data, we can use formulas (3.15) to construct the functions and write out the fundamental equation (3.14) for the unknown function.
Furthermore, we construct the functions S ( x, λ ) and Φ ( x, λ ) via (46) and (47) and the function q ( x ) by formulae (56), (57) and (60).
We note that, due to the representation (47), we shall construct the functions (theta ^{varepsilon }_{n}) in Lemma 5.4 directly, without referring to Assumption 5.3.
These data were used in this study to construct the functions of M (T β ) and F g (T β ).
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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