17 ( :52) α ω 53 (2015 ) 2 α ω 55 (2017 ) 2 1) ) ) 2 2 4) (α β) A ) 6) A (5) 1)
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1 3 3 1 α ω 53 (2015 ) 2 α ω 55 (2017 ) 2 1) ) ) 2 2 4) (α β) A ) 6) A (5) 1) Évariste Galois( ) 2) Joseph-Louis Lagrange( ) 18 3),Niels Henrik Abel( ) 4) 1
2 Q (α) (α β) 2 α + β II II 2 ax 2 + bx + c = 0 2 α, β α + β = b, αβ = c a a 1 2 2x 2 4x + 3 = 0 2 α, β (1) (α + 2) (β + 2) (2) β α + α β (3) (α β) 2 (4) α 3 β 3 2 7) 1(3)(α β) 2 8) 5) Felix Christian Klein( ) 6) Plato(B.C.427-B.C.347) 5 7) Albert Girard( ) 8) α β 2 2
3 n n 2 α, β α + β, αβ 2 3 α, β, γ 1 x 1 n n a 1, a 2, a 3,, a n 1, a n n x n 1 x n 2 x n 3 k=1 n 1 i,j n a k n a i a j 1 i,j,k n a i a j a k n x n p ( 1) p a i1 a i2 a ip 1 i 1,i 2,,i p n ( 1) n a 1 a 2 a 3 a n 1 a n n n n n 9) 10) 11) 12) 13) 19 14) 9) Gottfried Wilhelm Leibniz( ) 10) Leonhard Euler( )18 11) Carolus Fridericus Gauss( ) 12) Georg Ferdinand Ludwig Philipp Cantor( ) 13) Julius Wilhelm Richard Dedekind( ) 14) 3
4 2 C n a n x n +a n 1 x n 1 +a n 2 x n 2 + +a 2 x 2 +a 1 x+a 0 = 0 C n a 0, a 1, a 2,, a n C a n x n + a n 1 x n 1 + a n 2 x n a 2 x 2 + a 1 x + a 0 = a n (x r 1 ) (x r 2 ) (x r n ) r 0, r 1, r 2,, r n C 3 3 ax 3 + bx 2 + cx + d = 0 α, β, γ x, y, z 4 x, y (1) xy 2 z 3 x 2 yz 3 (2) xyz (3) xy + yz + zx (4) x 2 y + y 2 z + z 2 x 5 x yy zz x (1) xy 2 z 3 x 3 yz 2 (2) xyz (3) xy + yz + zx (4) x 2 y + y 2 z + z 2 x x yy zz x 15) 4(3) 5(4) x, y x 2 y + y 2 z + z 2 x xy 2 + yz 2 + zx 2 x yy zz x x 2 y + y 2 z + z 2 x x 2 y + y 2 z + z 2 x x, y, z x, y, z 6 3! = 6 4(1) 5(1) xy 2 z 3 x 2 y + y 2 z + z 2 x 6 2 β α 2 (β α) 2 15) C(3) 4
5 16) 3 D (3) 3 x, y, z 6 x, y, z xy 2 + z xy 2 + z xy 2 + z 120 x y y z z x x y z x xy 2 + z ( ) 240 x z y x z y x z y x xy 2 + z ( ) x x y z z y y z xy 2 + z ( ) 16) D (3) 5
6 y y x z z x x z xy 2 + z ( ) z z x y y x x y xy 2 + z ( ) 7 x 2 y + y 2 z + z 2 x 6 x 2 y + y 2 z + z 2 x ( ) 120 x 2 y + y 2 z + z 2 x ( ) 240 x 2 y + y 2 z + z 2 x ( ) x x 2 y + y 2 z + z 2 x ( ) y x 2 y + y 2 z + z 2 x ( ) z x 2 y + y 2 z + z 2 x ( ) x 2 y + y 2 z + z 2 x x, y, z xy 2 + yz 2 + zx 2 x 2 y + y 2 z + z 2 x 17) 3 f x 1, x 2,, x n f x 1, x 2,, x n s 1, s 2,, s n x 1, x 2,, x n f s 1, s 2,, s n 17) kenkyubu/kokai-koza/h16-mukai.pdf 6
7 n a n x n + a n 1 x n 1 + a n 2 x n a 2 x 2 + a 1 x + a 0 = 0 n n (1) a n x n +a n 1 x n 1 +a n 2 x n 2 + +a 2 x 2 +a 1 x+a 0 = 0 x 1, x 2,, x n (2) x 1, x 2,, x n ax 2 + bx + c = 0 α, β α, β (1) α + β = (2) αβ = (3) (α + β) 2 = (4) α 2 + β 2 = (5) (α β) 2 = (6) α β = (7) α = (8) β = α β α β β α (α β) 2 = α 2 2αβ + β 2 2 a, b, c ( α + ωβ + ω 2 γ ) ( α + ωβ + ω 2 γ 9 (1) ( α + ωβ + ω 2 γ ) (2) ( α + ωβ + ω 2 γ ( α + ωβ + ω 2 γ ) 6 ( α + ωβ + ω 2 γ ( α + ωβ + ω 2 γ )3 = ( α 3 + β 3 + γ 3) + 3ω ( α 2 β + β 2 γ + γ 2 α ) + 3ω 2 ( αβ 2 + βγ 2 + γα 2) + 6αβγ ( α + ωβ + ω 2 γ αβγ 7 α 2 β + β 2 γ + γ 2 α αβ 2 + βγ 2 + γα 2 7
8 18) ( α + ωβ + ω 2 γ ) 3 2 α β x 1, x 1, x n x i, x j i < j x i x j x 1, x 2 x 1 x 2 3 x 1, x 2, x 3 (x 1 x 2 ) (x 1 x 3 ) (x 2 x 3 ) x 1, x 2, x 3, x 4 3 (x 1 x 2 ) (x 1 x 3 ) (x 2 x 3 ) x 1 x 2 (x 1 x 2 ) x 1 x 2 (x 2 x 1 ) ( 1 k (x 1 x k ) (x 2 x k ) (x 2 x k ) (x 1 x k ) (x 1 x 2 ) ( 1) ( 1) ( 1) 3 ( 1) 12 6 (1) (2) 120 (3) 240 (4) x (5) y (6) z 18) D (3) C (3) 8
9 x 1 x 2 x 1 x x 1, x 2,, x n n n 2 α β n ( 1) x 3 + ax 2 + bx + c = 0 α, β, γ a, b, c (1) α + β + γ = (2) αβ + βγ + γα = (3) αβγ = x 3 + ax 2 + bx + c = 0 α, β, γ a, b, c (1) α 2 + β 2 + γ 2 = (2) α 2 β 2 + β 2 γ 2 + γ 2 α 2 = (3) αβ 2 + βγ 2 + γα 2 + α 2 β + β 2 γ + γ 2 α = 3 2 a, b, c 15 3 (α β) (α γ) (β γ) a, b, c (1) (α β) (β γ) β a, b (2) (β γ) (γ α) γ a, b (3) (γ α) (α β) α a, b (4) 2 {(α β) (α γ) (β γ)} 2 {(α β) (α γ) (β γ)} 2 = {(α β) (β γ) (γ α)} 2 (i) α 2 β 2 γ 2 = (ii) αβγ (αβ + βγ + γα) = (iii) αβγ (α + β + γ) = 9
10 (iv) αβ 2 + βγ 2 + γα 2 + α 2 β + β 2 γ + γ 2 α = (v) α 2 β 2 + β 2 γ 2 + γ 2 α 2 = (vi) α 2 + β 2 + γ 2 = (vii) α + β + γ = (viii) αβ + βγ + γα = (ix) αβγ = (5) (α β) (α γ) (β γ) a, b, c 16 ω ω 2 + ω + 1 = 0 3 x 3 + ax 2 + bx + c = 0 3 α, β, γ D = (α β) (α γ) (β γ) (i) D = (α β) (α γ) (β γ) (ii) ( α + ωβ + ω 2 γ a, b, c, D (iii) ( α + ω 2 β + ωγ a, b, c, D (iv) (α + β + γ) + ( α + ωβ + ω 2 γ ) + ( α + ω 2 β + ωγ ) = 3α 3 (v) a = 0, b = p, c = q (3) 3 19) ) ) ) 23) ) ) x 3 + px + q = ω x = 3 q ( q q ( q , ω 3 q ( q ω 2 3 q ( q , ω 2 3 q ( q ω q ( q ) D (3) 21) C (3) 22) 4 S (4) 23) 4 A (4) 24) 5 S (5) 25) 5 A (5) 10
11 α ω [1] Coxeter,H,S,M, (), (),, [2] Sautor,M, (),,, [3], 30,, [4] Klein,F., (), 20 5,, [5], 14,, [6],,, [7],,, [8],, 2011vol39-4,pp38-58,, [9],,, [10], 13,, [11],,, [12],, 2 α ω 53, pp47-57, [13], α ω 55, pp.54-65,
ax 2 + bx + c = n 8 (n ) a n x n + a n 1 x n a 1 x + a 0 = 0 ( a n, a n 1,, a 1, a 0 a n 0) n n ( ) ( ) ax 3 + bx 2 + cx + d = 0 4
20 20.0 ( ) 8 y = ax 2 + bx + c 443 ax 2 + bx + c = 0 20.1 20.1.1 n 8 (n ) a n x n + a n 1 x n 1 + + a 1 x + a 0 = 0 ( a n, a n 1,, a 1, a 0 a n 0) n n ( ) ( ) ax 3 + bx 2 + cx + d = 0 444 ( a, b, c, d
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変 位 変位とは 物体中のある点が変形後に 別の点に異動したときの位置の変化で あり ベクトル量である 変位には 物体の変形の他に剛体運動 剛体変位 が含まれている 剛体変位 P(x, y, z) 平行移動と回転 P! (x + u, y + v, z + w) Q(x + d x, y + dy, z + dz) Q! (x + d x + u + du, y + dy + v + dv, z +
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1998 6 25 ( ) 1 10 1982 10 28 37/7 1990 12 14 45/94 (WHO) 1 1989 12 8 NGO (ECE) 3 1995 10 25 ECE 1991 2 25 1992 3 17 1998 6 4 1 2 1. 2. a b c (a) (b) d 17 3. a b (a) c (b) 4. 5. 3 1. 2. 3. 4. 5. 6. 7.
2620149 3 8 2 198802 492/ 198802 492 1 4 5 JISJIS X 0208 : 1997 JIS JIS X 0213:2004 http://www.pref.hiroshima.lg.jp/site/monjokan/ 1... 1 1... 1 2... 2 3... 2 4... 2 5... 3 6... 3 7... 4 8... 4 2... 4
Step2 入門
ii iii iv v vi NEC Corporation 1999 vii C O N T E N T S PART 1 PART 2 PART 3 viii PART 4 ix C O N T E N T S PART 5 x PART 6 xi C O N T E N T S PART 7 xii PART 8 PART 9 xiii C O N T E N T S xiv xv PART
n 2 + π2 6 x [10 n x] x = lim n 10 n n 10 k x 1.1. a 1, a 2,, a n, (a n ) n=1 {a n } n=1 1.2 ( ). {a n } n=1 Q ε > 0 N N m, n N a m
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1 1 1 + 1 4 + + 1 n 2 + π2 6 x [10 n x] x = lim n 10 n n 10 k x 1.1. a 1, a 2,, a n, (a n ) n=1 {a n } n=1 1.2 ( ). {a n } n=1 Q ε > 0 N N m, n N a m a n < ε 1 1. ε = 10 1 N m, n N a m a n < ε = 10 1 N
2 7 V 7 {fx fx 3 } 8 P 3 {fx fx 3 } 9 V 9 {fx fx f x 2fx } V {fx fx f x 2fx + } V {{a n } {a n } a n+2 a n+ + a n n } 2 V 2 {{a n } {a n } a n+2 a n+
R 3 R n C n V??,?? k, l K x, y, z K n, i x + y + z x + y + z iv x V, x + x o x V v kx + y kx + ky vi k + lx kx + lx vii klx klx viii x x ii x + y y + x, V iii o K n, x K n, x + o x iv x K n, x + x o x
x V x x V x, x V x = x + = x +(x+x )=(x +x)+x = +x = x x = x x = x =x =(+)x =x +x = x +x x = x ( )x = x =x =(+( ))x =x +( )x = x +( )x ( )x = x x x R
V (I) () (4) (II) () (4) V K vector space V vector K scalor K C K R (I) x, y V x + y V () (x + y)+z = x +(y + z) (2) x + y = y + x (3) V x V x + = x (4) x V x + x = x V x x (II) x V, α K αx V () (α + β)x
1981 i ii ➀ ➁ 61
(autism) 1943 60 1981 i ii ➀ ➁ 61 DSM- 4 3 29 99 DSM- 62 1 2 3 4 4 vi 63 64 ix x xi 204 3 65 176 90 3 79 66 DSM- 82 67 68 ➀ ➁ ➂ 69 34 5 70 JR 71 i 1944 ii iii 28 72 iv 48 v ➀ vi PHP 39 vii 176 viii ➄ 77
