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with α i, i = 0, 1, 2, …, m, λ and μ being constants to be determined.
For simplicity of presentation, we consider only the polytropic gas, i.e. P = Aρ γ with A > 0 being constants.
Lately, Li and Zhang [17] discussed (1.1) with V ( x ) and K ( x ) being constants and obtained the existence of a positive radially symmetric solution without compactness conditions.
Next the optimized results are presented by taking the heat transfer rate and fin volume as functions of Biot number and only one of the three geometric parameters, the other two being constants.
Then (1) conditions (ii) are satisfied; (2) condition (i) is satisfied for w ≡ const or for p and p ¯ being constants outside some large interval [ − m 0, m 0 ], m 0 ∈ Z. .
conditions (ii) are satisfied; condition (i) is satisfied for w ≡ const or for p and p ¯ being constants outside some large interval [ − m 0, m 0 ], m 0 ∈ Z. Proof.
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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