Those authors denote $f_{\rm {irr}}$ by x, $f_{\rm {int}}$ by G(x) and $\frac{{\rm d}f_{\rm {int}}}{{\rm d}f_{\rm {irr}}}$ by -g(x).

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"Optically thin'' means optically thin for the outgoing radiation field. The same atmospheric layers can be optically thick for the incoming radiation field.

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...##)

In that paper q is defined as $\frac{M_{1}}{M_{2}}$ , i.e., inverse of the definition here.

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... assuming

This assumption is not necessarily fulfilled, especially for giants, but it simplifies the following equations and does not affect the results significantly.

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... derivative

In that paper K is defined as $\left( \frac{{\rm d}\!\ln R}{{\rm d}t}\right) _{\rm {th}}^{-1}$ .

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... shows

To perform the evolutionary computations shown in Figs. 16 and 22 from the initial turn-on of mass transfer to the minimum period without any discontinuity we used opacity tables for solar composition in the outer layers. Comparisons with computations using correct Helium and CNO abundances for the final mass transfer phase indicate that, though using "incorrect'' opacity tables in that evolutionary stage leads to a different stellar radius, it does not affect the mass transfer cycles significantly.

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