[Math/Phys.] Equilibrium & Optimality

[Minh Vu Huynh <huynm000@goofy.zdv.Uni-Mainz.de>]

Cha`o ca? nha`,

cha('c nhie^`u ba'c o+? dda^y bie^'t ba`i toa'n hi`nh ho.c sau tu+` ho^`i 
ho.c pho^? tho^ng:

Cho tru+o+'c tam gia'c ABC . Ti`m ddie^?m M sao cho MA+MB+MC nho? nha^'t ?

Ho^`i ho.c pho^? tho^ng to^i ti`nh co+` tha^'y lo+`i
gia?i va^.t ly' cho ba`i toa'n tre^n trong ta.p chi' Kvant .
Lo+`i gia?i ddo' tu+.a nhu+ sau:

La^'y ba so+.i da^y da`i nhu+ nhau nu't va`o ta.i mo^.t ddie^?m, buo^.c va`o
mo^~i dda^`u da^y 1 tro.ng lu+o+ng gio^'ng nhau ro^`i ke'o
ca'c so+.i da^y na`y qua ca'c ddi?nh cu?a tam gia'c ABC.

Na(ng lu+o+.ng cu?a he^. tho^'ng na`y ti? le^. thua^.n vo+'i to^?ng
MA+MB+MC. Vi` va^.y ddie^?m M pha?i ti`m la` ddie^?m ma` na(ng lu+o+.ng
dda.t cu+.c tie^?u. Mo^.t he^. tho^'ng trong ca^n ba(`ng (Equilibrium)
co' na(ng lu+o+.ng i't nha^'t. Bo+?i va^.y ddie^?m M la` ddie^?m ta.i ddo'
ca'c lu+.c ke'o ca^n ba(`ng nhau. Tu+` ddo' suy ra M la` ddie^?m tho?a ma~n
	<AMB = <BMC = <CMA =120 ddo^.

Ho^`i ddo' to^i ra^'t me^ lo+`i gia?i na`y bo+?i no' cho phe'p to^?ng qua't
ho'a cho dda gia'c, hoa(.c min cu?a to^?ng a_1*MA_1+...+a_n*MA_n

Trong Kinh te^' mo^n to^i ho.c ba^y gio+` kha'i nie^.m Equilibrium va` ly'
thuye^'t ve^` no' tu+o+ng ddo^'i quan tro.ng . Thu+o+`ng ga('n lie^`n vo+'i
Equilibrium la` 1 tra.ng tha'i cu+.c tri. (vi' du. optimale allocation,
optimale Welfare - Pareto efficient).

Ca'c ba'c ngihie^n cu+'u toa'n va` ly' co' the^? cho to^i lessons ve^`
Equilibrium trong Math va Phys. (for dummies only!) ddu+o+.c kho^ng.
What is equilibrium in math/phys sense? Which energie is in equilibrium
minimal (What's the intuition for that) ? What is energie? 

Ca'm o+n ca'c ba'c tru+o+'c,

Vu~