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Mount Usu / Sarobetsu postmined peatland
From left: Crater basin in 1986 and 2006. Cottongrass / Daylily
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Principle of optimality (最適性原理)= Bellman equation, discovered by Richard Bellman (1953)= dynamic programming equation Bellman, Richard Ernest (1920–1984) 

Boole George (18151864, England)
differential equations and algebraic logic Boolean algebraAxiom
1' = 0 → 1' = 1'•1 = 1•1' = 0 a + 1 = 1 → a + 1 = a + (a + a') = (a + a) + a' = a + a' = 1 a•0 = 0•a = 0 → a•0 = 0•a, a•0 = a(aa') = (aa)a' = aa' = 0 a + ab = a → a + ab = a•1 + ab = a(1 + b) = a•1 = a a(a + b) = a → a(a + b) = aa + ab = a + ab = a a(a + b + c) = a → aa + ab + ac = (aa + ab) + ac = a + ac = a a + bc = (a + b)(a + c) → a + bc = a(a + b + c) + bc = a(a + b) + ac + bc = a(a + b) + c(a + b) // Q Solve simultaneous equation a + x = 1, ax = 0A (x = a') is a root because of axiomatic system (a + a' =1)
set x_{0} as a root 
Law. De Morgan's law (1)→ (ab)' = a' + b'Pr. (a' + b') + ab = (a' + b' + a)(a' + b' + b) = (b' + 1)(a' + 1) = 1•1 = 1
while (a' + b')ab = a'ab + b'ab = 0•b + 0•a = 0 + 0 = 0 Law. de Morgan's law (2)→ (a + b)' = a'b'Pr. (a + b)' = [(a')' + (b')']' = [(a'b')']' = a'b' // Table. Case that Boolean algebra that has only specific factors (0, 1) + 0 1 • 0 1 '    0 0 1 0 0 0 0 1 1 1 1 1 0 1 1 0 Table. Set {a, b} → subset φ, U = {a, b}, {a}, {b} 0 = π, 1 = U, 2 = {a}, 3 = {b} + 0 1 2 3 • 0 1 2 3 '    0 0 1 2 3 0 0 0 0 0 0 1 1 1 1 1 1 1 0 1 2 3 1 0 2 2 1 2 1 2 0 2 2 0 2 3 3 3 1 1 3 3 0 3 0 3 3 2 
1969 Thompson K: developing the OS for minicomputer PDP7 (DEC)
= beginning of UNIX Ex. ATT System V, UCB BSD, IBM AIX 1973 Richie D: unix kernel rewritten by C language1991.10.5 Linus T (Finland): opned Linux distributed freely, independent of unixOS system → becoming popular EWS (engineering workstation)
Past: office computer = EWS ↔ personal computer (PC)
Present:
one of the UNIX OSs, developed by Univercity of Carfornia, Berkeley
characterzied by highspec job control projects and standards of six computer items, including desktop and network environments, drawn up common API proposed by UNIX vendors 