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The so-called curl-curl equation will be treated in the following on a finite domain with adequate boundary conditions (BC) and initial values (IV).
Based on the curved beam theory, the governing equation for the bending deformation of the ring is derived, in combination with adequate boundary conditions.
The model is characterized by a set of PDEs coupled with adequate boundary conditions that are solved by the method of lines.
One of the main properties is their instability, due to their high free energy; stability requires special measures, usually done by making an adequate boundary layer structure at the interfaces.
Usage of continuity conditions between the individual laminate layers and formulation of adequate boundary conditions at the free edges in an integral sense then lead to complete representations for displacements, strains and stresses at every location in the considered laminate.
If adequate boundary demarcation could not be achieved, the segment was not included in the final analysis (5% excluded).
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It solved the problem of finding an adequate geographical boundary to Europe by substituting a political one – all of the Soviet Union would be considered part of Europe.
Biomechanical evaluation methods are carried out based on simulation of the bone-implant fracture fixation with consideration of adequate physiological boundary and loading conditions.
The BMP antagonists may represent an important target to improve bone healing when inter-related to adequate mechanical boundary conditions.
For the 3D case, this complicates the governing equation and creates difficulties in formulating an adequate number of boundary conditions.
It was acknowledged that the SRES Scenarios were an adequate set of boundary conditions for the climate model versions of that time, albeit a first set that requires improvement, e.g., with respect to the assumptions concerning atmospheric sulphur (Johns et al., 2011) or the inclusion of direct political climate change mitigation measures.
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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