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For the simplicity, we shall not change the notations when choosing the local coordinates such that the equation of (U_0cap S_0) is (x_n=0).
Thus, (W, dw) is a G-observer compatible with the helicoidal coordinates such that dw is defined by the uv-plane which is the symmetry cell.
A theorem is provided showing that for any choice of local representation for the rotations, there is a change of coordinates such that the transformed system has a well known structure.
In order to avoid numerical problems of convergence of the proposed state estimation approach, the set of current phasor measurements is represented in rectangular coordinates, such that their corresponding variances are also recalculated according to the uncertainty propagation theory.
The essence of the method is to introduce the modulated coordinates such that the periodically time-varying linear differential equations can be effectively transformed to the equivalent time-invariant linear differential equations.
As was pointed out in [11], we can always find a non-autonomous change of coordinates such that the linear parts of the maps f n all become lower triangular.
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In space-time diagrams it is customary to adopt a scaling of the time coordinate such that the light cones have a half angle of 45°.
The designs at all nodes are harmonized and coordinated such that no additional signaling overhead is needed.
Here, we use a moving coordinate such that the zero height coincides with the surface average and the term is dropped.
(a) Dynamic FFR in this case, to mitigate the interference from a dominant neighboring cell at a particular cell-edge user, the two BSs (serving BS as well as the dominant interfering BS) are coordinated such that the dominant neighboring BS will not use a certain quantity of resources that is allocated to the cell-edge user.
The approach was to divide entire tail modeling region between x=−10 R E and x=−30 R E into a sequence of eight overlapping 5 R E-wide bins of the x-coordinate, such that each bin spanned the interval x i −2.5≤x≤x i +2.5 R E, where x i =−10−2.5·i with i=1,2,…,8.
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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