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The numerical value of these expressions is given in Table 6.
Then the type system T (_{mathbf{E}}) induced by T (_{reg}) (or T (_{mathbf{E}}) ifT (_{mathrm{reg}}) is understood) containing the regular element expressions is given by the following grammar: Elementary element types and regular element expressions TAG:((E_{1},ldots,E_{mathrm{n}})) are called element types.
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The solution of the problem under discussion is expressed in terms of the Lamé scalar and vector potentials and analytical expressions are given for the wave motion characteristics.
These expressions are given below.
Explicit expressions are given for special cases for further use.
The interference power expressions are given by (21) and (22): (22).
The mathematical expressions are given in formula (26) and (27).
Three simplified power expressions are given corresponding to frequencies below coincidence, above coincidence and near coincidence.
In addition, expressions are given for the maximum available power from a source.
Expressions are given for transfer functions for downhole movements and pressures (surge and swab).
The exact expressions are given in the following lemma whose proof is reported in the Appendix.
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CEO of Professional Science Editing for Scientists @ prosciediting.com