Re: models ... fuzzy logic

[Nguyen Tien Zung <tienzung@darboux.math.univ-montp2.fr>]

Message-ID: <3320C317.2ED4@math.univ-montp2.fr>
Date: Fri, 07 Mar 1997 17:38:31 -0800
From: Nguyen Tien Zung <tienzung@math.univ-montp2.fr>
Organization: CNRS & Universite Montpellier II
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Subject: Re: models ... fuzzy logic
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Hi ba'c AiViet

Phu.c ba'c AiViet sa't dda^'t. 
Vu+`a ngo ngoe vie^'t ma^'y chu+~ ddu+o+.c ba'c
tra? lo+`i ngay (tui ti'nh ra thi` lu'c ba'c tra? loi+`, be^n Me~o co`n
la` sa'ng so+'m tinh mo+, tui gio+` ddo' o+? dda^y thi` co`n dang ngu?
khi`). Ba'c co' kinh nghie^.m gi` vie^'t ddu+o+.c nhanh + nhie^`u da.y
cho tui va`i chie^u vo+'i. To^'c ddo^. ba'c go~ ma'y pha?i nhanh ga^'p
5-10 la^`n tui (chu+a ke^? lo+`i hay y' dde.p thi` ga^'p nhie^`u ho+n
nu+~a), vi` ne^'u kho^ng thi` ca? nga`y chi? ngo^`i go~ chu+a xong.

Ba`n tie^'p chuye^.n model: tui ddo^`ng y' vo+'i ba'c AiViet la` o+? low
level kho' nha?y le^n high level la('m 
(thu+.c ra ca'i na`y du`ng eletron model 
ddu+o+.c ro^`i ca^`n qua'i gi` o^ng Zeeman). Tui khi no'i ve~ 1
ddu+o+`ng o+? du+o+'i kho^ng co' y' ba?o co' the^? ddi ngu+o+.c tho+`i
gian dda^u, nhu+ng ma` cha? ha.n ba'c la^'y 1 die^?m o+? high level song
ro^`i ha. ca'i variable gi` ddo' xuo^'ng mo^.t ca'ch ddo^.t ngo^.t,
thu+? ho?i ddie^?m ddo' cha.y ddi dda^u? Trong Zeeman model thi` no' se~
bi. ma('c la.i o+? bo+` ne^'u kho^ng la`m 1 ca'i jump xuo^'ng low level.
(hay co' the^? ba'c va` tui ddang nghi~ dde^'n hai models kha'c nhau?).
Tui vie^'t complex analysis cho vui tho^i chu+' tu+'c nhie^n ca'i ma(.t
Riemann ma` ddem va`o model love thi` co`n do+? ho+n nu+~a.

Tui ddoa'n ca'i 'hie^.u u+'ng con bu+o+'m' co' trong va^.t ly' tu+` la^u
tru+o+'c khi o^ng Zeeman la`m catastroph theory. ca'i hie^.u u+'ng con
bu+o+'m co' the^? ti`m tha^'y trong dynamical systems du+o+'i da.ng ca'c
he^. hyperbolic. No'i no^m na ca'c he^. hyperbolic la` ca'c he^.
very initial-value-sensitive, "sai mo^.t ly ddi mo^.t da(.m" (the
distance between 2 points grows exponentially with time). Geodesic flows
on negative-curvature manifolds are examples of hyperbolic systems.

Ca'c ba'c co' bie^'t vi` sao "du+. ba'o tho+`i tie^'t" hay tha`nh "du+.
la'o tho+`i tie^'t" kho^ng? Chi'nh vi` ca'c cha^'t lo?ng, cha^'t khi'
hay ta.o tha`nh hyperbolic systems dda^'y. A` ma` ca'c he^. hyperbolic
thi` luo^n co' positive entropy. Nhu+ng ca'i na`y cha('c pha?i vie^'t 1
posting rie^ng vi` da`i do`ng la('m, ddu.ng dde^'n ca? symbolic dynamics
nu+~a, ma` ca'i symbolic dynamics tui tha^'y co' the^? co' 1 functor
ba('n kinh di.ch va`o no' cu~ng ne^n.

Ba'c Thanh Tung  vie^'t ve^` fuzzy logic "sang tra'i mo^.t bu+o+'c,
ro^`i la.i sang pha?i 1 bu+o+'c..." xem ra cu~ng gio^'ng kinh di.ch va`
symbolic dynamics ghe^. Ca'm o+n ba'c Thanh Tung, nho+` ba'c ma` nay 
thi` tui hie^?u fuzzy logic la` gi` ro^`i. 
No' la` tu+` ghe'p nhu+ng co' nghia~ mo+'i va` ba^y gio+` ra^'t 
mo^'t, cu~ng nhu+ tu+` quantum group trong toa'n y' ma`

Cheers, Zung

Fuzzy logic not fuzzy nor logic - Le^'u tu+?