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The simulated results suggest that the platform plays a major role and the vegetation plays a supporting role in reducing wave transmission except for some special cases.
While for the linear model analytical solutions and stability conditions are available, it is not generally the case for non-linear system except for some special cases.
Each generator can be used to produce infinite number of isotropic manipulators, and no constraint equation is needed except for some special cases such as the design of symmetric isotropic manipulators.
The general problem of accurately predicting the motions of more than two bodies under their mutual attractions is quite complicated; analytical solutions of the three-body problem are unobtainable except for some special cases.
In general, except for some special cases of G(r), (23) should be numerically calculated.
To the best of our knowledge, there is little literature about nodal periodic solutions (that is, periodic solutions may change sign) except for some special cases.
Similar(43)
These reduce to known results for some special cases.
For some special cases, surface wave velocities are derived explicitly.
For validation, the direct problem solver is verified by the existing solutions for some special cases.
The numerical results for some special cases agree with those of previous workers where available.
Analytical expressions are validated with existing results in the literature for some special cases.
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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