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Fortran90/95 2. (p 74) f g h x y z f x h x = f x + g x h y = f y + g y h z = f z + g z f x f y f y f h = f + g Fortran 1 3 a b c c(1) = a(1) + b(1) c(
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2 K = f (x) K[[x]] = r f (x) r D = D (0, r) a D f (x) a D Figure X d : X X R 0 d(x, z) max{d(x, y), d(y, z)} x, y, z X (X, d) clopen 1.1. (X,
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C 1 -path x t x 1 (f(x u), dx u ) rough path analyi p-variation (1 < p < 2) rough path 2 Introduction f(x) = (fj i(x)) 1 i n,1 j d (x R d ) (n, d) Cb
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( ) (, ) arxiv: hgm OpenXM search. d n A = (a ij ). A i a i Z d, Z d. i a ij > 0. β N 0 A = N 0 a N 0 a n Z A (β; p) = Au=β,u N n 0 A
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f (x) f (x) f (x) f (x) f (x) 2 f (x) f (x) f (x) f (x) 2 n f (x) n f (n) (x) dn f f (x) dx n dn dx n D n f (x) n C n C f (x) x = a 1 f (x) x = a x >
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( [2], 1 p.38.) 1. [1] C R n y C u = (u 1,, u n ) α n u i y i > α i=1 n u i x i α, x C i=1 α 1 2 f(x) g(x) f(x) g(x) 1 ( 1 ) A B a b O a O b A B v a v
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kubostat2018d p.2 :? bod size x and fertilization f change seed number? : a statistical model for this example? i response variable seed number : { i
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9 8 7 (x-1.0)*(x-1.0) *(x-1.0) (a) f(a) (b) f(a) Figure 1: f(a) a =1.0 (1) a 1.0 f(1.0)
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(2018 2Q C) [ ] R 2 2 P = (a, b), Q = (c, d) Q P QP = ( ) a c b d (a c, b d) P = (a, b) O P ( ) a p = b P = (a, b) p = ( ) a b R 2 {( ) } R 2 x = x, y
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(2016 2Q H) [ ] R 2 2 P = (a, b), Q = (c, d) Q P QP = ( ) a c b d (a c, b d) P = (a, b) O P ( ) a p = b P = (a, b) p = ( ) a b R 2 {( ) } R 2 x = x, y
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Chapter (dynamical system) a n+1 = 2a n ; a 0 = 1. a n = 2 n f(x) = 2x a n+1 = f(a n ) a 1 = f(a 0 ), a 2 = f(f(a 0 )) a 3 = f(f(f(a
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k m m d2 x i dt 2 = f i = kx i (i = 1, 2, 3 or x, y, z) f i σ ij x i e ij = 2.1 Hooke s law and elastic constants (a) x i (2.1) k m σ A σ σ σ σ f i x
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M ω f ω = df ω = i ω idx i f x i = ω i, i = 1,..., n f ω i f 2 f 2 f x i x j x j x i = ω i x j = ω j x i, 1 i, j n (3) (3) ω 1.4. R 2 ω(x, y) = a(x, y
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1 1 Lambert Adolphe Jacques Quetelet ( ) [ ] 1 (1 ) n x 1, x 2,..., x n x a 1 a i a m f f 1 f i f m n 1.1 ( ( ))
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2 1,, x = 1 a i f i = i i a i f i. media ( ): x 1, x 2,..., x,. mode ( ): x 1, x 2,..., x,., ( ). 2., : box plot ( ): x variace ( ): σ 2 = 1 (x k x) 2
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p p p j h j j p p i k p d h p p p k l k k l k p k k k a k p a b k p i j p i p p a b c d e f g h i j k l m
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16) 12) 14) n x i, (1 i < n) x 1 = x 2 = = x n. (6) L = D A (1) D = diag(d 1,d 2,,d n ) n n A d i = j i a i j 9) 0 a 12 a 13 a 14 A = a 21 0 a
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