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In particular, letting, we get a function given by.
All what is required is to get a function which satisfies the suitable approximation inequality (4).
Assume that we can measure the state of the process at any time to get a function x.
Similar as in Case 1, we can get the expression of cos τ ω denoted as f 1 ∗ and the expression of sin τ ω denoted by f 2 ∗ , and further we get a function with respect to ω that can be established by f 1 ∗ 2 + f 2 ∗ 2 = 1.
In such a case, the function often takes extreme values near the boundary: consequently, by adding a virtual point outside of V that takes a still more extreme value, we can eliminate the domain boundary so that we get a function on a manifold without boundary.
Since (b_{1}), (b_{2}) are not equal to zero simultaneously, thus (3.4) is the RBVP with discontinuous coefficients and nodal point (itau_{1}) on (operatorname{Im}xi=tau_{1}), and it can be described as follows: we want to get a function (Phi z)) such that it is analytic in (operatorname{Im} xi>tau_{1}), (operatorname{Im} xi
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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