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( x, y) ( 0, c) A m/ θ x y t ( x, y) x = At cosθ, 1 2 1 g 2 sinθ 2 y = gt + At sinθ + c y = x + x + c = ax + bx + c t 2 2 2 ( Acosθ ) cosθ x y 2 ax + bx + c ( R, S) 2 R S = -ax + bx + c 1 ( b ± b 4 ( ) ) 2 + a c S 2a R 1 ( b b 4 ( ) ) 2 + a c S A 2 cos g 2 θ sinθ cosθ 2a sin θ 2g( c S) + A = 2 2 cos θ A cos θ + cosθ sinθ + g 2 2 2 + sin 2 2 2g( c S) θ + A R A θ c S 2 2 A cosθ 2sinθ A sin 2θ R = R A g g 18m, 30m, 50m, 60m, 70m, 90m () 78
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3 1 = 3 3 2 = 9 2mod7 3 3 = 2 3 = 6 3 4 = 6 3 = 18 4mod7 3 5 = 4 3 = 12 5mod7 3 6 = 5 3 = 15 1mod7 3, 2, 6, 4, 5, 1 5 S.K. K.W. a = 7 M = 2 31 1 5 X i = 7 X i 1 mod (2 31 1) IBM RANDU 1970 X i = 65539X i 1 mod 2 31 (1) S. K. Park and K. W. Miller, 1988, Random number generators: Good ones are hard to find, Communication of the ACM, Vol.31, pp.1192-1201 85
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L N( t) = 1+ αt me L S t L N(t) L 1972 1985 1972 1977 1982 3 127,085,000 20 dn dt = b( 1 an( t)) N( t) dn dn adn ( 1 an ) N = bdt N + 1 an = bdt log N log(1 an) = bt C C bt log( 1 an ) / N = bt + C 1/ N a = e C bt bt N = 1/( a + e ) = L /(1 + me ) L = 1/ a, m 1 e a C = 113
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