Manuscript Oai119-A@1 · Oai119-A.tex · section · fdff7292

The mean-dependent production profile

Stage 1: the five proof interfaces › The mean-dependent production profile · lines 419–440

Oai119-A@1#eq:Bprofile

To state the production claim precisely, let

S (s) = F (s) - 2 s (0 \leq s < ℓ), S (s) = 0 (s < 0) .

For $∣ m ∣ < 1$ and $0 \leq I < h (m)$ , define

B_{m} (I) = 2 I + (1 - m^{2}) S (ℓ - \frac{h ( m ) - I}{1 - m ^{2}}), B_{m} (I) = max {B_{m} (I), F (I)} .

These are the source's profiles, expressed using our entropy notation OpenAI119I,OpenAI119Reserve.

Displayed formulas in this passage

Oai119-A@1#eq:Bprofile · line 427
$B_{m} (I) = 2 I + (1 - m^{2}) S (ℓ - \frac{h ( m ) - I}{1 - m ^{2}}), B_{m} (I) = max {B_{m} (I), F (I)} .$
unlabeled · line 422
$S (s) = F (s) - 2 s (0 \leq s < ℓ), S (s) = 0 (s < 0) .$