Use bar for steady states and asterisk for maxima in MSY lecture#765
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Separate the two roles the asterisk was previously overloaded with:
* steady states now use a bar --- the steady-state stock and sustainable
yield become \bar{x}(e) and \bar{y}(e)
* the asterisk is reserved for the maximizer --- the MSY effort becomes e^*
The stock at MSY (= K/2) is the steady state at the optimal effort and is
written \bar{x}(e^*) throughout. Code variables are renamed to match
(x_star -> x_bar, e_msy -> e_star, x_msy -> x_bar_star). The RAM-database
reference points B_{MSY} and F_{MSY} in the lingcod section are left as is.
Co-Authored-By: Claude Opus 4.8 (1M context) <noreply@anthropic.com>
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The ylabel string was a non-raw literal, so the \b in \bar was interpreted as a backspace before matplotlib parsed the mathtext, breaking notebook execution. Make it a raw string. Co-Authored-By: Claude Opus 4.8 (1M context) <noreply@anthropic.com>
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Splits the two roles the asterisk was previously overloaded with in
lectures/msy_fishery.md:The stock at MSY ($=K/2$ ) is the steady state at the optimal effort, so it is written $\bar{x}(e^)$ throughout (rather than the old $x^$).
Code variables are renamed to match the new math:
x_star(e)x_bar(e)e_msye_starx_msyx_bar_starThe RAM Legacy Database reference points$B_{MSY}$ and $F_{MSY}$ in the lingcod section keep the
MSYsubscript, since that is standard fisheries notation and not our steady-state symbol.This is a notation-only change; no model, figure, or numerical result is affected.
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