2001 3
|
|
- きみえ よせ
- 5 years ago
- Views:
Transcription
1 2001 3
2 : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 43 i
3 5.4 : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 79 2 : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 121 ii
4 1 1.1, [34] ( 12 ) ( ) [30][31][32][33][34] 3 2 ( ) 3 2 [23] [35] (2 2.1 )
5 1.1: ( ) ( ) ( ) : 2 2
6 1.2: = N / Nn 2 3 [35] 2 1 3
7 1.2: 3 (-:,=:,N:,/:,+: ) / - = N = = / N N / / / - - / - / - - N N / - / / / / = = / / / / / = / - N N / / - / = = = / N N / / N N / / / - = = = / - - N N / / - / / / = = / - - N / = = N N / / - - / = = / - - / / - = N N / / / - - / N / - / = = / - - N N / - - / - = = / - / / - N N / - = = / / - / N N / / - / = = = / - / = = N N / / / / / / / = = / - - / N N / - - = / - - / / = = N N / / / - - / = / - N N / / - - = / / / - / = / - / = = N N / / = = / N / = = = / N N / / / / - - = / - = = = / - / / N / / - = = / - - / = = = / = N N / - - / / = = N N / / = = / - - / + - / = = / / - / N N / = N N / + - / - / / / = N N / / / / = = / - - = / / - / = = / / - - N N / - = / - - N N / / - - / / / / - - / - - / - = = N N / - = = / / / = = N N / / / N / = = / - - = = / / - - N N / / = / / N N / - / - = / / - / / = = N N / - - / / - / - = / N N / / + = = N = / / - N N / / - - = = / - / / = = / / - = / N N / / / = N N / / - = = / / - - / - = = N N / - / / / - = = N N / / / = = / / - / - = = N N / - - / - - / / N N / - - / / / / = = / / - N N / = / - = = / = = / - - / / / - / - - N N / = = / - - / - N N / = = / - = / - N N / - = = / - = / / - + / N N / - - = = = / - - / - / : =: N:
8 1.3: 2 (-:,Nn:,/:,+: ) / - Nn + 1 N n / / - - / - N n / + - / - N n N n / N n / / / N n N n / / / N n N n / / / - - N n N n / / / N / - - N n / - - / N n / / - - N n / - / / / N n N n / / / / / / / - / - / / / n / / - N n N n / / - N n N n / - / - N n N n / / - / / - - / / N n N n / - / - N n N n / N n / / / / N n N n / - - / N n / / / N n / / N n / N n / - / N n / / - - N n / N n / / / / N n N n / N n / / - N n N n / / / - / / N n N n / - / / N N n / / / N n / / + N n / - - / N n / - / - - N n / / - N n N n / / - - / N n / - / / / - / - N n / n / / - / / N n N n / / / N n / / - - / N n N n N n / / / - - N n / - - / - N n / - - N n / - - / - - / / N n / / - N n / - / / N n / + + N n / - / N n / - / N n / / - - / / - - / N n / / / N n / - / N n n / - / / / - - N n / - - / / - N n / / / N n N / N n / / + N n / / / N n / - - N n / / N n / N n / N n / - - N n / / / N n N n / / - / / / / / / / - N n / - - N n / - - / N n / / - N n / / - N n / - - / - - / N n / - / - - N n N n / / / - - N n N n / / / N n / / - N n / - - N n / - / - - N n / / / / - N n / / N n N n / / / N n N n / / / - - N n N n / - + N n / - - N n / - - / - N n / - + / / n N n / N n / / / / N n / / / / N n N N n / / / - - / N n N n / / / - - N n / + - N n / N n / N n / / - - N n / - - N n / / - / / / N n N n / / N n / / N n / / - N n / N n / / / / / N n N n / - - / / N n N n / - / - - / N / / / - N n / - - N n / / / - / N n N n / N n / / - - N n / - / - N n N n / - / / N n / - - N n / / / - N n / / - - / - N n N n / - - / N n N n / / / N n N n / / - + N n / - - N n / / / / N n / N n N n / - + / N n / - - N n / - - N n / / / / / / N n N n / / N n N n / / / / / N n / N n N n / / / N n N n / + / / / + + / + N n / / N n / / / / / N n N n / - / / N n N n n / / / / - + / N n N n / N n / - - / N n N n / / - / / / - - / - / / / - - / - / / / - - / - / / / - - / : Nn:
9 j Φ ΦΦß i ρ ρ ρ= 1.3: ( ) [29][35][36][37][38][39] 6
10 [39] [36] [36][38] 1.4 Smith-Daniels,Schweikhert and Smith-Daniels[14] Siferd and Benton[13],Li and Benton[5] Miller[8] 1 Warner[16] 3 (3 ) Warner Miller Warner Musa and Saxena[9], Rosenbloom and Goertzen[12], Venkataraman and Brusco[15] Arther and Ravindran[1] 3 1 7
11 1 1 [2][6] 7 [7][12] 7 [11] 7 14 [3][4][8][15][16] [2][10][11][16] 3 [1][4][6][10][11][16] 2 [2][3] Millar and Kiragu[7] [28] , [20] 22 [34] [23]
12 ( ) ( )
13 [19] A 6.8 (40 ) 1 30 (
14 4 4 2 (85.2 ) B ( ) ( ) ( ) (2 ) 12
15 2.1: ( ) (1) (2) (3) 2.2: ( ) (1) (2) (3) 13
16 2.3: (1) 4 (2) (3) C ( ) ( )
17 2.4: (1) (2) 15
18 2.5: (3 ) (1) (2) (3) 4 2.6: (2 ) (1) (2) 2 7 (3)
19 : (1) (2) (3) D (3) (1)(2)(4) E (2 )
20 2.8: (1) (2) (3) (4) ( ) 2 4 ( 8 ) (1) 6 (2) 24 (3) 22 (4)
21 [23] ( 8 ) (34 ) 16 (43 ) 2 (2.1 ) 8 2 ( 3 ) A ( ) 3 ( 6 ) [34]
22 ( ) B ( ) ( )
23 2.9: (1 ) ( ) 2.10:
24 (a) (b) (a) (b) ( ) 22
25 ( ) ( ) (float nurse) [4][7][15] 2 ( ) 23
26 ( ) ( 1) ( 2) ( 3) ( 4) ( 5)
27 [21][22][26] m n w M = f 1, 2,:::, mg : N = f1,2,:::,ng : W = f 1, 2,:::, wg : R = frjr g G r = fiji r g, r 2 R F 1 = f(i; j; k);i2 M; j 2 N; k 2 W j i j k g F 0 = f(i; j; k);i2 M; j 2 N; k 2 W j i j k g P h = f(k 1 ;k 2 ;:::;k h );k 1 ;k 2 ;:::;k h 2 W j k 1 ;k 2 ;:::;k h g, h 2f2; 3;:::g Q h = f(k; u; v);k2 W;u;v 2f0; 1; 2;:::gj k, h u v g, h 2f2; 3;:::g d jk ;j 2 N; k 2 W : j k a rjk ;r 2 R; j 2 N; k 2 W : j k r b rjk ;r 2 R; j 2 N; k 2 W : j k r c ik ;i2 M; k 2 W : i k e ik ;i2 M; k 2 W : i k x ijk ;i2 M; j 2 N; k 2 W : i j k 1, S = fsjs g f s (x ijk ; i 2 M ; j 2 N ; k 2 W );s2 S : x ijk s ( ) 25
28 1 X min f s (x ijk ;i2 M; j 2 N; k 2 W ) (3.0) s2s subject to X i2m x ijk d jk j 2 N; k 2 W (3.1) X a rjk» x ijk» b rjk i2g r r 2 R; j 2 N; k 2 W (3.2) X c ik» x ijk» e ik j2n i 2 M; k 2 W (3.3) x ijk = fi (i; j; k) 2 F fi ; fi 2f0; 1g (3.4) hx ff=1 u» X k2w x i j+ff 1 kff» h 1 i 2 M; j 2f1;:::;n h +1g; (3.5) hx ff=1 (k 1 ;k 2 ;:::;k h ) 2 P h ; h 2f2; 3;:::g x i j+ff 1 k» v i 2 M; j 2f1;:::;n h +1g; (3.6) (k; u; v) 2 Q h ; h 2f2; 3;:::g x ijk =1 i 2 M; j 2 N (3.7) x ijk =0or 1 i 2 M; j 2 N; k 2 W (3.8) (3.0) (3.1) j k (3.2) j k r (3.3) i k (3.4) i j k (fi =1) k (fi =0) (3.5) j h (3.6) j h k (3.7) i j 1 (3.8) x ijk (3.1) 2 (3.2) 3 (3.3) 4 (3.4) 5 (3.5) (3.7) (3.1) (3.2) (3.3) (3.7) 26
29 3.1 i x ijk i x ijk (3.3) (3.7)... x ijk... (3.1)(3.2) HY H H@ H@ H Ψ... x ijk : i j k 0-1 (3.3)(3.4)(3.5)(3.6)(3.7) 3.1: 1 5 ( 6 ) ( 3 ) ( 4 ) ( ) 4 ( +1) 1 (3.6) (3.6) (3.5) ( ) (3.5) (3.6) (3.5) k x ijk k P k 0 2W;k6=k 0 x ijk 0 (3.5) 27
30 (3.1) (3.8) A = f(r 1 ;r 2 ;j;k;g);r 1 ;r 2 2 R; j 2 N; k 2 W j j k r 1 r 2 g g X i2g r 1 x ijk X i2g r 2 x ijk» g (r 1 ;r 2 ;j;k;g) 2 A (3.9) (3.1) ( ) G r = M r (3.2) 2 [25] n ( 1 (3.3) (3.4) (3.5) (3.6) (3.7) ) i 2 M P i q 2 P i ffi iqjk (j k 1 0) 1 x ijk i q iq ( q 1 0) x ijk = X q2p i ffi iqjk iq i 2 M; j 2 N; k 2 W (3.10) X q2p i iq =1 i 2 M (3.11) 1 (3.0) (3.2) 2 f 0 s iq s 2 S 0 ( ) 28
31 2 X min fs( 0 iq ;q 2 P i ;i2 M) (3.12) s2s subject to X X ffi iqjk iq d jk i2m q2p i j 2 N; k 2 W (3.13) X X a rjk» ffi iqjk iq» b rjk q2p i r 2 R; j 2 N; k 2 W (3.14) X i2g r iq =1 q2p i i 2 M (3.15) iq =0or 1 i 2 M; q 2 P i (3.16) (3.12) (3.13) j k (3.14) j k r (3.15) i 1 (3.16) iq ( ) ( 1 (3.3) (3.7) ) 2 P i d jk a rjk b rjk 29
32 ... iq... iq : i q 0-1 (3.13)(3.14)» = Z} Z Z Z = 1 Z (3.15) 1 3.2:
33 2 [24] 1 (3.5) (3.6) (3.5) (3.6) (1) 7 1 (2) ( ) (3)1 ( 3 4 ) 3 1 ( 1 ) 1 2 (1)(2)(3) 3 4 (3.5) (3.6) (3.3) (3.4) ( ) (3.13) (3.14) A B (1)(2)(3) (8+4+3) 2=30 AB (2+1+1) 2= (8+4+3) 30 Ξ 21 = 21: (2+1+1) 30 Ξ 21 = 5:
34 (3.14) (3.14) 2 (3.14) d jk a rjk m ( ) ( ) 2 32
35 [21] 33
36 ( ) [26] q 2 P i ;i 2 M ( 2 (3.13) (3.14) ) ( 1 (3.3) (3.7) ) 1 (3.1) (3.8) i 2 M : i i i ( ) ( ) 2 (3.13) (3.14) w jk ;u rjk ;v rjk 0 ff jk ;ff+ jk ;fi rjk ;fi+ rjk ;fl rjk ;fl+ rjk 0 i i0 q;q 2 P i 0;i 0 2 M; i 0 6= i 0 1 i 2 M
37 X X X X X X X min w jk ff jk + j2n k2w r2g subject to X X i 0 2M q2p i 0 X X i 0 2G r q2p i 0 X X i 0 2G r q2p i 0 X j2n k2w u rjk fi rjk + X r2g j2n k2w v rjk fl + rjk (4.1) ffi i0 qjk i0 q + ff jk ff + jk = d jk j 2 N; k 2 W (4.2) ffi i0 qjk i0 q + fi rjk fi + rjk = a rjk r 2 R; j 2 N; k 2 W (4.3) ffi i0 qjk i0 q + fl rjk fl + rjk = b rjk r 2 R; j 2 N; k 2 W (4.4) iq =1 q2p i (4.5) iq =0or1 q 2 P i (4.6) ff jk ;ff+ jk 0 j 2 N; k 2 W (4.7) fi rjk ;fi+ rjk ;fl rjk ;fl+ rjk 0 r 2 R; j 2 N; k 2 W (4.8) i i i i q 2 P i (3.13) (3.14) ( ) (ff jk ff+ jk fi rjk fi+ rjk fl rjk fl+ rjk ) 0 35
38 ( ) y Ω Ωffi : 2 n jrj n 2 jrj r j k jRj(j 1) + jrj(k 1) + r 36
39 4 ( ) ( ) ( ) S i2m P i 1 ( ) m ( ) 1 ( ), = P i ( ) = ,0,0,0,1,1,0,0 ( 29 )
40 v Q QQQ Q QQQ v v Qv A A A AA AA AA A A A AA AA AA v v v v v v v v v ΠE Π EE Π Π E EE Π Π Π ΠE EE E EE Π Π Π ΠE EE E EE Π Π Π ΠE EE E EE Π Π Π ΠE EE Π Π Π Π Π Π Π Π Π vvvvvvvvvvvvvvvvvvvvvvvvvvv Π Π Π Π Π Π Π Π Π 6 E EE Π Π Π ΠE EE E EE Π Π Π ΠE EE E EE Π Π Π ΠE EE E EE Π Π Π ΠE EE E EE 4.2: v Q QQQ Q QQQ v v Qv A A Q A AA AA AA A A A AA AA AA v v v v v v v v v Π E Π EE Π Π E EE Π E Π EE Π Π E EE Π E Π EE Π Π E EE ΠE Π EE Π Π E EE Π Π Π ΠE EE Π Π Π Π Π Π Π Π Π Π vvvvvvvvvvvvvvvvvvvvvvvvvvv yyyπ yπ Πy Π Π Πy Π Π E EE Π Π Π ΠE EE E EE Π E Π EE Π Π E EE 6 Π Π Π ΠE EE E EE Π Π Π ΠE EE E EE 4.3: 38
41 2 3 3 ( ) ( 4.3 ) ( ) ( ) 27 6 m m m ( ) 39
42 (1.1 )
43 5.2 2 ( 2 (3.13) (3.14) ) 3 2 P i ;i2 M w jk ;u rjk ;v rjk W = fnight; dayg 2 1 q 2 P i ;i 2 M (i; j; k) 2 F q 2 P i ;i2 M ffi iqjk j ffi iqj night 1 j 0 ffi iqj day j 1 j (3.7) (4.2)(4.3)(4.4) 5 ( P k2w ffi iqjk» 1;j 2 N; q 2 P i ;i2 M.) 41
44 5.1: N n N n / N n N n / N n / z } 4 z } 3 5.2: 3 Nn:,/:, : N n / N n / N n / N n / N n / z } 3 w jk ;u rjk ;v rjk v rj day q 2 P i ;i2 M 5 i : / N n / N n / / N n / / N n / N n / / q 2 P i ;i2 M ffi iqj night ;j 2 N j ffi iqj day =
45 w j night, u rj night, v rj night P 8i 2 M; P i P P i ;i2 M q 0 ( ) ( ) q 0 P i P i Big i Big Pk2W maxf0;c ik P j2n ffi iq0 jkg iq0 X X X min w jk ff jk + j2n k2w r2g X j2n X k2w u rjk fi rjk + X r2g 43 X X j2n k2w v rjk fl + rjk
46 +Big X k2w maxf0;c ik X j2n ffi iq0 jkg iq0 (5.1) 1 TL i z i z Λ i q (counter ) exchanged iq ( 6) TL ( 5) ( ) exchanged iq 1 ( 1 8) 0. P P 1. P P i 2 M P i exchanged iq = 1;q 2 P i 2. i 2 M q 0 P i = P i [fq 0 g 3. i 2 M q 0 q i = q 0 4. counter =1 5. i 2 M TABU i = fqjexchanged iq counter TLg[fq i g q i q 2 (P i n TABU i ) z i i iq =0;q 2 TABU i 6. z Λ = min i2m z i i q Λ q i q 0 = q i ;q i = q Λ q 0 = q 0 P i = P i nfq 0 g exchanged iq 0 = counter counter = counter z Λ =0 q i ;i2 M 5 8. i 2 M P i exchanged iq = 1;q 2 P i 9. i 2 M q 0 P i = P i [fq 0 g 10. i 2 M q 0 q i = q 0 44
47 11. counter =1 12. z Λ = ABC B 1 ( 19) 2 3 C 1 ( 28) P i P ffi iqj night ;j 2 N ffi iqj day ;j 2 N ( 19 8 ) (3.0) (3.8) P i 45
48 N n / N n / N n / N n / N n /? N n / N n / / N n / N n / N n / z } N n / N n / N n / N n / / / N n / z } 2 5.1: Nn:,/:, : 46
49 : / / / N n / + / 2 / / / / * / / * 3 N n / / / / 4 N n / / N n / / A 5 N n / 6 n / N n / 7 + N n / + / / 8 / / N n / + + / / x 9 N n / + + N n / / 10 / + + / 11 / / / N n / + / / 12 N n / / / / 13 / / N n / / / N n / 14 N n / / / B 15 n / N n / + / N n / 16 N n / N n / N n / 17 / / N n / / / N n / / / 21 / / 22 / / N n / / 23 N n / + / x C 24 n / + N n / + 25 / + N n / N n / N n / 26 / / / / N n / N n + 27 / N n / / + / + 28 N n / + (Nn:, :,+:,/:,*:,x: ) 47
50 5.5: A B C
51 w jk ;u rjk ;v rjk v rj day ;r 2 R; j 2 N TL z Λ = P 4.9 P Sun SS
52 5.6: / Nn + 1 n / / + N n / N n / N n / / N n / / N n / N n / / N n / N n / N n / / / N n / / N n / N n / / / N n / N / N n / N n / N n / / N n / / N n / N n / N n / N n / / / N n / / / / N n / N n / N n / N n / / + N n / / N n / / / N n / N n N n / N n / / N n / / / N n / N n / N n / / / + N n / N n / / N n / / / N n / / N n / N n / N n / N n / N n / + N n / N n / / / / / N n / / N n / N n / N n / N n / N / N n / N n / / N n / N n / N n / N n / / / / / N n / N n / N n / + N n / N n / / N n / / N n / N n / N n / N n / / / N n / N n / N n / + N n / / / N n / N n / / N n / N n / + N n / N n / / N n / / / N n / / N n / N n / N n / / N n / N n / N n / N n / / N n / N n / N n / N n / / N n / N n / / N n / N n / / + N n / N n / / N n / N n N n / + / / N n / N n / N n / n / / N n / N n / N n / N n / N / N n + / N n / / / N n / N n / n / / / N n / + / N n / + N n / N n / / / N n / N n / : Nn:
53 5.7: A B C
54 5.8: / Nn + 1 n / / / / + N n / N n / N n / / N n / / N n / N n / / N n / N n / / N n / / / N n / / N n / / N n / / / / N n / / N / N n / N n / N n / / N n / / N n / / / N n / / / N n / / / N n / / / N n / / / / N n / N n / N n / / / N n / / / / + N n / / N n / / / N n / / / N n / / / + + N n / N n / / N n / / / N n / N n / N n / / / + N n / / N n / / N n / / / / N n / / N n / / / N n / / / N n / N n / N n / + / N n / N n / / / / / N n / / / N n / / N n / N n / / / N n / N / N n / N n / / N n / / N n / / N n / / N n / / / / / / N n / / N n / / N n / / + N n / / N n / / N n / / N n / N n / N n / N n / / / / N n / N n / / / N n / / + N n / / / N n / / N n / / / N n / / N n / / + N n / N n / / N n / / / / / / / / + + / / / / N n / / N n / / N n / N n / / N n / / N n / / N n / N n / / / N n / / / N n / N n / N n / / N n / / N n / / N n / / / N n / / / + N n / / N n / / / N n / N n / N n / + / / N n / / / N n / N n / n / / N n / / N n / N n / / N n / / N / N n + / N n / / / / / N n / N n / / n / / / N n / + / N n / + / N n / N n / / / / / / N n / / N n / / / : Nn:
55
56 6 [27] ( ) q 2 P i ;i2 M (5 5.1 ) ,4,5,6,8,9,11,12,18,
57 N n / N n / N n / N n / N n /? N n / N n / / N n / N n / N n / z } N n / N n / N n / N n / / / N n / z } N n / N n / / N n / N n / N n / z }? ( ) N n / N n / / N n / N n / N n / 6.1: Nn:,/:, : 55
58 6.1: ( ) / Nn + 1 n / / N n / + N n / N n / N n / / N n / / N n / N n / / N n / N n / N n / / / N n / / N n / N n / / N n / N / / / N n / N n / / N n / N n / N n / N n / N n / N n / / / N n / / N n / N n / N n / / / N n / / + N n / / N n / / / N n / N n N n / + + N n / N n / N n / / / N n / / / N n / + N n / N n / / N n / N n / / N n / / / N n / N n / N n / N n / + N n / N n / / / / / N n N n / / N n / N n / N n / / N n / N n / / N n / N n / N n / N n / / / / / N n / N n / N n / / / + N n / N n / / N n / N n / N n / N n / N n / / / N n / N n / N n / / / + N n / N n / N n / / N n / + N n / N n / / N n / / / / N n / / N n / N n / N n / / N n / N n / N n / N n / / N n / N n / N n / N n / / N n / N n / / N n / N n / / + N n / N n / / N n / N n N n / + / / N n / N n / N n / n / / N n / N n / N n / N n / N / N n + / N n / / / N n / N n / n / / / N n / + / N n / + N n / N n / / / N n / N n / N : Nn: ( : Nn:2 +: /: ) 56
59 q 2 P i 1 P i2m jp i j q i q 5.4 ( 6.1) 97% ( ) 1 1 ( ) : Nn / / N n / N n / N n / N n / (1) / / N n / N n / N n / N n / N n / (2) N n / N n / N n / N n / / / N n / 4 1 (9 ) ( ) (1) (2) 1 (9 ) 57
60 q i q Λ 2 ( ) q q 0 nx j=1 jffi iqj night ffi iq0 j nightj (6.1) (0,2,4,...) 1 1 (1,3,5,...) 2 (2,4,8,...) 6.2 (1) (2) 1 (1) (2) ( 6.1) ( ) 1 47, w jk ;u rjk ;v rjk 5.4 v rj day 0 1 TL =
61 6.2: 1 6.3: 2 59
62 (P i ) : ( 1) : ( 2) , % 98% 60
63 6.5: 1 2 ( ) : 61
64 6.3 DIFF i P i q i DIFF ~ Pi k = night ~ Pi ~P i = fqj nx j=1 jffi iqjk ffi iq i jkj»diff; q 2 P i g (6.2) q 2 P i q i DIFF ~ Pi ITE ITE= P P 1. P P i 2 M P i exchanged iq = 1;q 2 P i 2. i 2 M q 0 q i = q 0 3. i 2 M ~ Pi = P i counter =1 4. i 2 M TABU i = fqjexchanged iq counter TLg[fq i g q i q 2 ( ~ Pi n TABU i ) z i 5. z Λ = min i2m z i i q Λ q i q 0 = q i ;q i = q Λ Pi ~ ( Pi ~ = fqj P n j=1 jffi iqjk ffi iqi jkj» DIFF; q 2 P i g) exchanged iq 0 = counter counter = counter z Λ =0 q i ;i2 M counter ITE 4 62
65 DIFF DIFF = 10 DIFF =1; 2; 3; DIFF = GATEWAY G6-266(OS:FreeBSD2.2.2) 6.6: (DIFF =1; 2; 3; 10) ( ) DIF F (78) (34) 18.0 (972) (47) 31.4 (972) 10( ) 71.3 (47) (972) 6.5: (DIFF =1 10) 1 DIFF 3 2 DIFF 2 DIFF
66 DIFF DIFF =1 1 2 DIFF = (ITE = z Λ =7) 1 ( 1 ) ( 6.4 ) DIFF DIFF 1 2 DIFF DIFF 2 1 DIFF ~ Pi q i q 2 P i q i DIFF ~ Pi DIF F DIF F 64
67 TL w jk ;u rjk ;v rjk DIFF TL ( ) w jk ;u rjk ;v rjk (w j day = u rj day = 1;v rj day = 0 w j night = u rj night = v rj night 1 5 ) TL TL TL ( 1 ) 65
68 6.6: TL 30 ( 1) 6.7: TL 30 ( 2) 66
69 6.8: ( 1 TL 30) 6.9: ( 1 TL 50) 67
70 6.10: ( 2 TL 30) 6.11: ( 2 TL 50) 68
71 2 3.5 ( )
72 70
73 OR NEC USA, NEC America SVP OR 71
74 72
75 [1] Jeffrey L. Arther and A. Ravindran. A multiple objective nurse scheduling model. AIIE transactions, Vol. 13, No. 1, pp , [2] Peter C. Bell, Genevieve Hay, and Y. Liang. A visual interactive decision support system for workforce (nurse) scheduling. INFOR, Vol. 24, No. 2, pp , [3] Kathryn A. Dowsland. Nurse scheduling with tabu search and strategic oscillation. European Journal of Operational Research, Vol. 106, No. 2 3, pp , [4] Brigitte Jaumard, Fr ed eric Semet, and Tsevi Vovor. A generalized linear programming model for nurse scheduling. European Journal of Operational Research, Vol. 107, No. 2, pp. 1 18, [5] L. X. Li and W. C. Benton. Performance measurement criteria in health care organization: Review and future research directions. European Journal of Operational Research, Vol. 93, No. 3, pp , [6] Joe D. Megeath. Successful hospital personnel scheduling. Interfaces, Vol. 8, No. 2, pp , [7] Harvey H. Millar and Mona Kiragu. Cyclic and non-cyclic scheduling of 12 h shift nurses by network programming. European Journal of Operational Research, Vol. 104, No. 3, pp , [8] Holmen E. Miller, William P. Pierskalla, and Gustave J. Rath. Nurse scheduling using mathematical programming. Operations Research, Vol. 24, No. 5, pp , [9] A. A. Musa and U.Saxena. Scheduling nurses using goal-programming techniques. IIE transactions, Vol. 16, No. 3, pp , [10] Irem Ozkarahan and James Bailey. Goal programming model subsystem of a flexible nurse scheduling support system. IIE Transactions, Vol. 20, No. 3, pp , [11] Sabah U. Randhawa and Darwin Sitompul. A heuristic-based computerized nurse scheduling system. Computer & Operations Research, Vol. 20, No. 8, pp ,
76 [12] E. S. Rosenbloom and N. F. Goertzen. Cyclic nurse scheduling. European Journal of Operational Research, Vol. 31, No. 1, pp , [13] Sue Perrott Siferd and W. C. Benton. Workforce staffing and scheduling: Hospital nursing specific models. European Journal of Operational Research, Vol. 60, No. 3, pp , [14] Vicki L. Smith-Daniels, Sharon B. Schweikhert, and Dwight E. Smith-Daniels. Capacity management in health care services:review and future research directions. Decision Sciences, Vol. 19, No. 4, pp , [15] R Venkataraman and Mj Brusco. An integrated analysis of nurse staffing and scheduling policies. Omega, Vol. 24, No. 1, pp , [16] D. Michael Warner. Scheduling nursing personnel according to nursing preferense : A mathematical programming approach. Operations Research, Vol. 24, No. 5, pp , [17],,.. 36, pp , [18],,.. 37, pp , [19],,,,,.., Vol. 71, No. 10, pp , [20], , pp , [21],,.., Vol. 41, No. 8, pp , [22], , pp , [23],.. ( ), [24] , pp , [25],.. OR, pp ,
77 [26],. 2. Journal of Operations Research Society of Japan, Vol. 41, No. 4, pp , [27]. 2. Journal of Operations Research Society of Japan, Vol. 43, No. 3, pp , [28].., Vol. 44, No. 11, pp , [29]. 5., Vol. 3, No. 5, pp , [30]. 59., [31]. 62., [32]. 2., [33]. 5., [34]. 8., [35].. Nursing Today, Vol. 12, No. 5, [36]. 4., Vol. 3, No. 4, pp , [37]. 3., Vol. 3, No. 3, pp , [38]. 1., Vol. 3, No. 1, pp , [39]. 2., Vol. 3, No. 2, pp ,
78 1 2.3 A : ( ) ( )
79 B. [17] [18] 7.1 (a) 1 (b) 5 (c) 7.1: 3 80
80 (a) 1 (b) 5 5 (c) 3 (1 ) 30 ( ) ( 10 2 ) (1) 5 1 (2) (3) (d) (e) (f) 1 1 (g) 5 7 ( ) 5 (h) (i) ( ) ( 24 ) ( 32 ) 81
81 4 5 5 ( 3 )
82 ( ) 1 C (1) (2) (3) (4) (5) (6) (7) (1)
83 (2) (3) (4) ( ) (5) (6) ( ) (7) ( ) 84
84 [19]
85 5 ( ) (12 42 ) : ( )
86 7.2: ( ) ( ) ( ) ( ) ( )
87 7.3:
88 7.4:
89 7.3: (1) (2) (3)
90
91 7.4: (1) (1 6 ) (3 11 ) ( ) (2) (3)
92 7.5: ( ) (1) (2) (3) ( ) 93
93 : ( ) (1) (2) (3) ( )
94 7.7: (1) (2) (3) 29 ( ) 7.8: (1) (2)
95 (2 )
96 7.9: (3 ) (1) (2) (3) ( ) 97
97 7.10: (2 ) (1) (2) 7 2 (3)
98 : (1) 31 (2) 1 1 (3)
99 : (1) ( ) (2) (3) (4)
100 : (1) ( ) (2) (3) (4)
101
102 7.14: (1) (2) (3) (4) ( ) (5)
103 27 ( ) (1) 6 (2) 24 (3) 22 (4)
104 [23] : (3 1 2 ) ( 8 ) ( ) ( ) ( )
105 7.16:
106 :
107 7.6:
108
109 (
110 [1,2,3]7 [1,2]4 [2,3]8 [1,3]5 [2,3,5]1 111
111
112 7.17:
113 7.18:
114 7.19:
115 :
116 7.21:
117 : ( ) : ( ) (3 ) (2 )
118 : ( )
119 7.25: ( ) 2 3 ( ) 21 ) ( ) ( ) ( ) 120
120 (DIF F = 1) 4 1 (DIF F = 2)
1 n 1 1 2 2 3 3 3.1............................ 3 3.2............................. 6 3.2.1.............. 6 3.2.2................. 7 3.2.3........................... 10 4 11 4.1..........................
More information149 (Newell [5]) Newell [5], [1], [1], [11] Li,Ryu, and Song [2], [11] Li,Ryu, and Song [2], [1] 1) 2) ( ) ( ) 3) T : 2 a : 3 a 1 :
Transactions of the Operations Research Society of Japan Vol. 58, 215, pp. 148 165 c ( 215 1 2 ; 215 9 3 ) 1) 2) :,,,,, 1. [9] 3 12 Darroch,Newell, and Morris [1] Mcneil [3] Miller [4] Newell [5, 6], [1]
More information7 π L int = gψ(x)ψ(x)φ(x) + (7.4) [ ] p ψ N = n (7.5) π (π +,π 0,π ) ψ (σ, σ, σ )ψ ( A) σ τ ( L int = gψψφ g N τ ) N π * ) (7.6) π π = (π, π, π ) π ±
7 7. ( ) SU() SU() 9 ( MeV) p 98.8 π + π 0 n 99.57 9.57 97.4 497.70 δm m 0.4%.% 0.% 0.8% π 9.57 4.96 Σ + Σ 0 Σ 89.6 9.46 K + K 0 49.67 (7.) p p = αp + βn, n n = γp + δn (7.a) [ ] p ψ ψ = Uψ, U = n [ α
More informationnewmain.dvi
数論 サンプルページ この本の定価 判型などは, 以下の URL からご覧いただけます. http://www.morikita.co.jp/books/mid/008142 このサンプルページの内容は, 第 2 版 1 刷発行当時のものです. Daniel DUVERNEY: THÉORIE DES NOMBRES c Dunod, Paris, 1998, This book is published
More informationTOP URL 1
TOP URL http://amonphys.web.fc.com/ 3.............................. 3.............................. 4.3 4................... 5.4........................ 6.5........................ 8.6...........................7
More informationCVaR
CVaR 20 4 24 3 24 1 31 ,.,.,. Markowitz,., (Value-at-Risk, VaR) (Conditional Value-at-Risk, CVaR). VaR, CVaR VaR. CVaR, CVaR. CVaR,,.,.,,,.,,. 1 5 2 VaR CVaR 6 2.1................................................
More informationt = h x z z = h z = t (x, z) (v x (x, z, t), v z (x, z, t)) ρ v x x + v z z = 0 (1) 2-2. (v x, v z ) φ(x, z, t) v x = φ x, v z
I 1 m 2 l k 2 x = 0 x 1 x 1 2 x 2 g x x 2 x 1 m k m 1-1. L x 1, x 2, ẋ 1, ẋ 2 ẋ 1 x = 0 1-2. 2 Q = x 1 + x 2 2 q = x 2 x 1 l L Q, q, Q, q M = 2m µ = m 2 1-3. Q q 1-4. 2 x 2 = h 1 x 1 t = 0 2 1 t x 1 (t)
More informationA, B, C. (1) A = A. (2) A = B B = A. (3) A = B, B = C A = C. A = B. (3)., f : A B g : B C. g f : A C, A = C. 7.1, A, B,. A = B, A, A A., A, A
91 7,.,, ( ).,,.,.,. 7.1 A B, A B, A = B. 1), 1,.,. 7.1 A, B, 3. (i) A B. (ii) f : A B. (iii) A B. (i) (ii)., 6.9, (ii) (iii).,,,. 1), Ā = B.. A, Ā, Ā,. 92 7 7.2 A, B, C. (1) A = A. (2) A = B B = A. (3)
More informationpenalty cost. back log KM hq + cm + Q 2 2KM Q = h economic order quantity, EOQ Wilson 2
logistics 1 penalty cost. back log KM hq + cm + Q 2 2KM Q = h economic order quantity, EOQ Wilson 2 Wilson lot size lot-size formula Kotler[15], p602 Scarf [15] / s,s Veinott [18] 3 + + x d(x) f(x) x h
More informationX線-m.dvi
X Λ 1 X 1 O Y Z X Z ν X O r Y ' P I('; r) =I e 4 m c 4 1 r sin ' (1.1) I X 1sec 1cm e = 4:8 1 1 e.s.u. m = :1 1 8 g c =3: 1 1 cm/sec X sin '! 1 ß Z ß Z sin 'd! = 1 ß ß 1 sin χ cos! d! = 1+cos χ (1.) e
More informationd ϕ i) t d )t0 d ϕi) ϕ i) t x j t d ) ϕ t0 t α dx j d ) ϕ i) t dx t0 j x j d ϕ i) ) t x j dx t0 j f i x j ξ j dx i + ξ i x j dx j f i ξ i x j dx j d )
23 M R M ϕ : R M M ϕt, x) ϕ t x) ϕ s ϕ t ϕ s+t, ϕ 0 id M M ϕ t M ξ ξ ϕ t d ϕ tx) ξϕ t x)) U, x 1,...,x n )) ϕ t x) ϕ 1) t x),...,ϕ n) t x)), ξx) ξ i x) d ϕi) t x) ξ i ϕ t x)) M f ϕ t f)x) f ϕ t )x) fϕ
More information新製品開発プロジェクトの評価手法
CIRJE-J-60 2001 8 A note on new product project selection model: Empirical analysis in chemical industry Kenichi KuwashimaUniversity of Tokyo Junichi TomitaUniversity of Tokyo August, 2001 Abstract By
More informationn ξ n,i, i = 1,, n S n ξ n,i n 0 R 1,.. σ 1 σ i .10.14.15 0 1 0 1 1 3.14 3.18 3.19 3.14 3.14,. ii 1 1 1.1..................................... 1 1............................... 3 1.3.........................
More informationuntitled
c 645 2 1. GM 1959 Lindsey [1] 1960 Howard [2] Howard 1 25 (Markov Decision Process) 3 3 2 3 +1=25 9 Bellman [3] 1 Bellman 1 k 980 8576 27 1 015 0055 84 4 1977 D Esopo and Lefkowitz [4] 1 (SI) Cover and
More information商学 63‐1・2☆/5.冨田
70 1 Donabedian1980 Parasuraman, Berry, and Zeithaml1988 71 1Donabedian Donabedian1980 2 1 1 2 2 Donabedian1980 Donabedian1980 3 1 3 Donabedian1980Donabedian1982 Donabedian1985 Donabedian1966 72 1 Donabedian1968,
More informationE E E E E 9001700 113 114 0120-109217 E E E E E E E EE E E EE E E E E E E E E E E E E E E E E E E E E E E E E 9001700 113 114 0120-109217 9001700 113 114 0120-109217 E E E E E E E E E E
More informationSL-8号電話機 取扱説明書
E E E E E E 0120-109217 9001700 113 114 E E E E E E E E E E E E EE E E EE E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E 9001700 113 114 0120-109217 9001700 113
More informationV 0 = + r pv (H) + qv (T ) = + r ps (H) + qs (T ) = S 0 X n+ (T ) = n S n+ (T ) + ( + r)(x n n S n ) = ( + r)x n + n (d r)s n = ( + r)v n + V n+(h) V
I (..2) (0 < d < + r < u) X 0, X X = 0 S + ( + r)(x 0 0 S 0 ) () X 0 = 0, P (X 0) =, P (X > 0) > 0 0 H, T () X 0 = 0, X (H) = 0 us 0 ( + r) 0 S 0 = 0 S 0 (u r) X (T ) = 0 ds 0 ( + r) 0 S 0 = 0 S 0 (d r)
More information1 Abstract 2 3 n a ax 2 + bx + c = 0 (a 0) (1) ( x + b ) 2 = b2 4ac 2a 4a 2 D = b 2 4ac > 0 (1) 2 D = 0 D < 0 x + b 2a = ± b2 4ac 2a b ± b 2
1 Abstract n 1 1.1 a ax + bx + c = 0 (a 0) (1) ( x + b ) = b 4ac a 4a D = b 4ac > 0 (1) D = 0 D < 0 x + b a = ± b 4ac a b ± b 4ac a b a b ± 4ac b i a D (1) ax + bx + c D 0 () () (015 8 1 ) 1. D = b 4ac
More information28 Horizontal angle correction using straight line detection in an equirectangular image
28 Horizontal angle correction using straight line detection in an equirectangular image 1170283 2017 3 1 2 i Abstract Horizontal angle correction using straight line detection in an equirectangular image
More informationChap10.dvi
=0. f = 2 +3 { 2 +3 0 2 f = 1 =0 { sin 0 3 f = 1 =0 2 sin 1 0 4 f = 0 =0 { 1 0 5 f = 0 =0 f 3 2 lim = lim 0 0 0 =0 =0. f 0 = 0. 2 =0. 3 4 f 1 lim 0 0 = lim 0 sin 2 cos 1 = lim 0 2 sin = lim =0 0 2 =0.
More informationx, y x 3 y xy 3 x 2 y + xy 2 x 3 + y 3 = x 3 y xy 3 x 2 y + xy 2 x 3 + y 3 = 15 xy (x y) (x + y) xy (x y) (x y) ( x 2 + xy + y 2) = 15 (x y)
x, y x 3 y xy 3 x 2 y + xy 2 x 3 + y 3 = 15 1 1977 x 3 y xy 3 x 2 y + xy 2 x 3 + y 3 = 15 xy (x y) (x + y) xy (x y) (x y) ( x 2 + xy + y 2) = 15 (x y) ( x 2 y + xy 2 x 2 2xy y 2) = 15 (x y) (x + y) (xy
More information77
O r r r, F F r,r r = r r F = F (. ) r = r r 76 77 d r = F d r = F (. ) F + F = 0 d ( ) r + r = 0 (. 3) M = + MR = r + r (. 4) P G P MX = + MY = + MZ = z + z PG / PG = / M d R = 0 (. 5) 78 79 d r = F d
More information1 P2 P P3P4 P5P8 P9P10 P11 P12
1 P2 P14 2 3 4 5 1 P3P4 P5P8 P9P10 P11 P12 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 & 11 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 1! 3 2 3! 4 4 3 5 6 I 7 8 P7 P7I P5 9 P5! 10 4!! 11 5 03-5220-8520
More information2 2 MATHEMATICS.PDF 200-2-0 3 2 (p n ), ( ) 7 3 4 6 5 20 6 GL 2 (Z) SL 2 (Z) 27 7 29 8 SL 2 (Z) 35 9 2 40 0 2 46 48 2 2 5 3 2 2 58 4 2 6 5 2 65 6 2 67 7 2 69 2 , a 0 + a + a 2 +... b b 2 b 3 () + b n a
More information1. 2 P 2 (x, y) 2 x y (0, 0) R 2 = {(x, y) x, y R} x, y R P = (x, y) O = (0, 0) OP ( ) OP x x, y y ( ) x v = y ( ) x 2 1 v = P = (x, y) y ( x y ) 2 (x
. P (, (0, 0 R {(,, R}, R P (, O (0, 0 OP OP, v v P (, ( (, (, { R, R} v (, (, (,, z 3 w z R 3,, z R z n R n.,..., n R n n w, t w ( z z Ke Words:. A P 3 0 B P 0 a. A P b B P 3. A π/90 B a + b c π/ 3. +
More informationMAIN.dvi
01UM1301 1 3 1.1 : : : : : : : : : : : : : : : : : : : : : : 3 1.2 : : : : : : : : : : : : : : : : : : : : 4 1.3 : : : : : : : : : : : : : : : : : 6 1.4 : : : : : : : : : : : : : : : 10 1.5 : : : : : :
More informationlinearal1.dvi
19 4 30 I 1 1 11 1 12 2 13 3 131 3 132 4 133 5 134 6 14 7 2 9 21 9 211 9 212 10 213 13 214 14 22 15 221 15 222 16 223 17 224 20 3 21 31 21 32 21 33 22 34 23 341 23 342 24 343 27 344 29 35 31 351 31 352
More information行列代数2010A
(,) A (,) B C = AB a 11 a 1 a 1 b 11 b 1 b 1 c 11 c 1 c a A = 1 a a, B = b 1 b b, C = AB = c 1 c c a 1 a a b 1 b b c 1 c c i j ij a i1 a i a i b 1j b j b j c ij = a ik b kj b 1j b j AB = a i1 a i a ik
More informationVol. 52 No ,332,000 1,638, ,774 8 A ,11, II. A. % % B. 500 A A N=353
2015. 10 209 25 A A 120 33% 101,829 34,473 24% 22% 6% : I. 1992 1 2 100% 3 2011 10.9% 0.1% 7.5% 0.6% 4 4 Li 2013 5 1990 2010 26 210 Vol. 52 No. 4 2 1,332,000 1,638,000 6 7 19 105,774 8 A 33 1 653 4 5 794
More informationver Web
ver201723 Web 1 4 11 4 12 5 13 7 2 9 21 9 22 10 23 10 24 11 3 13 31 n 13 32 15 33 21 34 25 35 (1) 27 4 30 41 30 42 32 43 36 44 (2) 38 45 45 46 45 5 46 51 46 52 48 53 49 54 51 55 54 56 58 57 (3) 61 2 3
More informationuntitled
18 1 2,000,000 2,000,000 2007 2 2 2008 3 31 (1) 6 JCOSSAR 2007pp.57-642007.6. LCC (1) (2) 2 10mm 1020 14 12 10 8 6 4 40,50,60 2 0 1998 27.5 1995 1960 40 1) 2) 3) LCC LCC LCC 1 1) Vol.42No.5pp.29-322004.5.
More information( ) ( ) 1729 (, 2016:17) = = (1) 1 1
1729 1 2016 10 28 1 1729 1111 1111 1729 (1887 1920) (1877 1947) 1729 (, 2016:17) 12 3 1728 9 3 729 1729 = 12 3 + 1 3 = 10 3 + 9 3 (1) 1 1 2 1729 1729 19 13 7 = 1729 = 12 3 + 1 3 = 10 3 + 9 3 13 7 = 91
More information2019 1 5 0 3 1 4 1.1.................... 4 1.1.1......................... 4 1.1.2........................ 5 1.1.3................... 5 1.1.4........................ 6 1.1.5......................... 6 1.2..........................
More informationLINEAR ALGEBRA I Hiroshi SUZUKI Department of Mathematics International Christian University
LINEAR ALGEBRA I Hiroshi SUZUKI Department of Mathematics International Christian University 2002 2 2 2 2 22 2 3 3 3 3 3 4 4 5 5 6 6 7 7 8 8 9 Cramer 9 0 0 E-mail:hsuzuki@icuacjp 0 3x + y + 2z 4 x + y
More informationChap9.dvi
.,. f(),, f(),,.,. () lim 2 +3 2 9 (2) lim 3 3 2 9 (4) lim ( ) 2 3 +3 (5) lim 2 9 (6) lim + (7) lim (8) lim (9) lim (0) lim 2 3 + 3 9 2 2 +3 () lim sin 2 sin 2 (2) lim +3 () lim 2 2 9 = 5 5 = 3 (2) lim
More information量子力学 問題
3 : 203 : 0. H = 0 0 2 6 0 () = 6, 2 = 2, 3 = 3 3 H 6 2 3 ϵ,2,3 (2) ψ = (, 2, 3 ) ψ Hψ H (3) P i = i i P P 2 = P 2 P 3 = P 3 P = O, P 2 i = P i (4) P + P 2 + P 3 = E 3 (5) i ϵ ip i H 0 0 (6) R = 0 0 [H,
More information168. W rdrop. W rdrop ( ).. (b) ( ) OD W rdrrop r s x t f c q δ, 3.4 ( ) OD OD OD { δ, = 1 if OD 0
167 p (n) im p(n+1) im p (n+1) im p(n) im < ε (3.264) ε p (n+1) im 1 4 [1],, :, Vol.43, pp.14-21, 2001. [2] Rust, J., Optiml Replcement of GMC Bus Engines: An Empiricl Model of Hrold Zurcher, Econometric,
More information東アジアへの視点
8 8 1955 1 2 3 1. Sakamoto 2012 2012a b 8 8 2. 2.1 AGI Industrial Structure of the Prefectural Economy in Kyushu Area in Japan: Trend and Future Prediction 56th European Regional Science Association Congress
More informationWeb Stamps 96 KJ Stamps Web Vol 8, No 1, 2004
The Journal of the Japan Academy of Nursing Administration and Policies Vol 8, No 1, pp 43 _ 57, 2004 The Literature Review of the Japanese Nurses Job Satisfaction Research Which the Stamps-Ozaki Scale
More informationIPSJ SIG Technical Report 1,a) 1,b) 1,c) 1,d) 2,e) 2,f) 2,g) 1. [1] [2] 2 [3] Osaka Prefecture University 1 1, Gakuencho, Naka, Sakai,
1,a) 1,b) 1,c) 1,d) 2,e) 2,f) 2,g) 1. [1] [2] 2 [3] 1 599 8531 1 1 Osaka Prefecture University 1 1, Gakuencho, Naka, Sakai, Osaka 599 8531, Japan 2 565 0871 Osaka University 1 1, Yamadaoka, Suita, Osaka
More informationDirac 38 5 Dirac 4 4 γ µ p µ p µ + m 2 = ( p µ γ µ + m)(p ν γ ν + m) (5.1) γ = p µ p ν γ µ γ ν p µ γ µ m + mp ν γ ν + m 2 = 1 2 p µp ν {γ µ, γ ν } + m
Dirac 38 5 Dirac 4 4 γ µ p µ p µ + m 2 p µ γ µ + mp ν γ ν + m 5.1 γ p µ p ν γ µ γ ν p µ γ µ m + mp ν γ ν + m 2 1 2 p µp ν {γ µ, γ ν } + m 2 5.2 p m p p µ γ µ {, } 10 γ {γ µ, γ ν } 2η µν 5.3 p µ γ µ + mp
More informationHansen 1 2, Skinner 5, Augustinus 6, Harvey 7 Windle 8 Pels 9 1 Skinner 5 Augustinus 6 Pels 9 NL Harvey ML 11 NL
HANAOKA, Shinya 1 3 Hansen1, 2 1 2 3 Hansen 2 3 4 5 2 2.1 002 Vol.5 No.4 2003 Winter 3 4 2.2 Hansen 1 2, Skinner 5, Augustinus 6, Harvey 7 Windle 8 Pels 9 1 Skinner 5 Augustinus 6 Pels 9 NL Harvey 10 2.3
More informationdi-problem.dvi
2005/04/4 by. : : : : : : : : : : : : : : : : : : : : : : : : : : 2 2. : : : : : : : : : : : : : : : : : : : : : : 3 3. : : : : : : : : : : : : : : : : : : : : : : : : : 4 4. : : : : : : : : : : : : :
More information2016 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 1 16 2 1 () X O 3 (O1) X O, O (O2) O O (O3) O O O X (X, O) O X X (O1), (O2), (O3) (O2) (O3) n (O2) U 1,..., U n O U k O k=1 (O3) U λ O( λ Λ) λ Λ U λ O 0 X 0 (O2) n =
More informationohpmain.dvi
fujisawa@ism.ac.jp 1 Contents 1. 2. 3. 4. γ- 2 1. 3 10 5.6, 5.7, 5.4, 5.5, 5.8, 5.5, 5.3, 5.6, 5.4, 5.2. 5.5 5.6 +5.7 +5.4 +5.5 +5.8 +5.5 +5.3 +5.6 +5.4 +5.2 =5.5. 10 outlier 5 5.6, 5.7, 5.4, 5.5, 5.8,
More informationuntitled
0. =. =. (999). 3(983). (980). (985). (966). 3. := :=. A A. A A. := := 4 5 A B A B A B. A = B A B A B B A. A B A B, A B, B. AP { A, P } = { : A, P } = { A P }. A = {0, }, A, {0, }, {0}, {}, A {0}, {}.
More informationII No.01 [n/2] [1]H n (x) H n (x) = ( 1) r n! r!(n 2r)! (2x)n 2r. r=0 [2]H n (x) n,, H n ( x) = ( 1) n H n (x). [3] H n (x) = ( 1) n dn x2 e dx n e x2
II No.1 [n/] [1]H n x) H n x) = 1) r n! r!n r)! x)n r r= []H n x) n,, H n x) = 1) n H n x) [3] H n x) = 1) n dn x e dx n e x [4] H n+1 x) = xh n x) nh n 1 x) ) d dx x H n x) = H n+1 x) d dx H nx) = nh
More informationhttp://www.ike-dyn.ritsumei.ac.jp/ hyoo/wave.html 1 1, 5 3 1.1 1..................................... 3 1.2 5.1................................... 4 1.3.......................... 5 1.4 5.2, 5.3....................
More informationJAPAN MARKETING JOURNAL 111 Vol.28 No.32008
Vol.28 No.32008 JAPAN MARKETING JOURNAL 111 Vol.28 No.32008 JAPAN MARKETING JOURNAL 111 Vol.28 No.32008 JAPAN MARKETING JOURNAL 111 Vol.28 No.32008 JAPAN MARKETING JOURNAL 111 Vol.28 No.32008 JAPAN MARKETING
More informationJAPAN MARKETING JOURNAL 113 Vol.29 No.12009
JAPAN MARKETING JOURNAL 113 Vol.29 No.12009 JAPAN MARKETING JOURNAL 113 Vol.29 No.12009 JAPAN MARKETING JOURNAL 113 Vol.29 No.12009 JAPAN MARKETING JOURNAL 113 Vol.29 No.12009 Vol.29 No.12009 JAPAN MARKETING
More informationJAPAN MARKETING JOURNAL 110 Vol.28 No.22008
Vol.28 No.22008 JAPAN MARKETING JOURNAL 110 Vol.28 No.22008 JAPAN MARKETING JOURNAL 110 Vol.28 No.22008 JAPAN MARKETING JOURNAL 110 Vol.28 No.22008 JAPAN MARKETING JOURNAL 110 Vol.28 No.22008 JAPAN MARKETING
More informationI A A441 : April 15, 2013 Version : 1.1 I Kawahira, Tomoki TA (Shigehiro, Yoshida )
I013 00-1 : April 15, 013 Version : 1.1 I Kawahira, Tomoki TA (Shigehiro, Yoshida) http://www.math.nagoya-u.ac.jp/~kawahira/courses/13s-tenbou.html pdf * 4 15 4 5 13 e πi = 1 5 0 5 7 3 4 6 3 6 10 6 17
More information) a + b = i + 6 b c = 6i j ) a = 0 b = c = 0 ) â = i + j 0 ˆb = 4) a b = b c = j + ) cos α = cos β = 6) a ˆb = b ĉ = 0 7) a b = 6i j b c = i + 6j + 8)
4 4 ) a + b = i + 6 b c = 6i j ) a = 0 b = c = 0 ) â = i + j 0 ˆb = 4) a b = b c = j + ) cos α = cos β = 6) a ˆb = b ĉ = 0 7) a b = 6i j b c = i + 6j + 8) a b a b = 6i j 4 b c b c 9) a b = 4 a b) c = 7
More information+ 1 ( ) I IA i i i 1 n m a 11 a 1j a 1m A = a i1 a ij a im a n1 a nj a nm.....
+ http://krishnathphysaitama-uacjp/joe/matrix/matrixpdf 1 ( ) I IA i i i 1 n m a 11 a 1j a 1m A = a i1 a ij a im a n1 a nj a nm (1) n m () (n, m) ( ) n m B = ( ) 3 2 4 1 (2) 2 2 ( ) (2, 2) ( ) C = ( 46
More informationJuly 28, H H 0 H int = H H 0 H int = H int (x)d 3 x Schrödinger Picture Ψ(t) S =e iht Ψ H O S Heisenberg Picture Ψ H O H (t) =e iht O S e i
July 8, 4. H H H int H H H int H int (x)d 3 x Schrödinger Picture Ψ(t) S e iht Ψ H O S Heisenberg Picture Ψ H O H (t) e iht O S e iht Interaction Picture Ψ(t) D e iht Ψ(t) S O D (t) e iht O S e ih t (Dirac
More informationBaba and Nobeoka CAE Computer Aided Engineering
Baba and Nobeoka, Baba and Nobeoka CAE Computer Aided Engineering Feitzinger and Lee, 1997 p p p p p p Ulrich, 1995 ; Sanchez and Mahoney, 1996 Baba, Y. and K. Nobeoka 1998 Towards Knowledge-based
More informationa) Extraction of Similarities and Differences in Human Behavior Using Singular Value Decomposition Kenichi MISHIMA, Sayaka KANATA, Hiroaki NAKANISHI a
a) Extraction of Similarities and Differences in Human Behavior Using Singular Value Decomposition Kenichi MISHIMA, Sayaka KANATA, Hiroaki NAKANISHI a), Tetsuo SAWARAGI, and Yukio HORIGUCHI 1. Johansson
More informationyoo_graduation_thesis.dvi
200 3 A Graduation Thesis of College of Engineering, Chubu University Keypoint Matching of Range Data from Features of Shape and Appearance Yohsuke Murai 1 1 2 2.5D 3 2.1 : : : : : : : : : : : : : : :
More informationDVIOUT-fujin
2005 Limit Distribution of Quantum Walks and Weyl Equation 2006 3 2 1 2 2 4 2.1...................... 4 2.2......................... 5 2.3..................... 6 3 8 3.1........... 8 3.2..........................
More informationi
i 3 4 4 7 5 6 3 ( ).. () 3 () (3) (4) /. 3. 4/3 7. /e 8. a > a, a = /, > a >. () a >, a =, > a > () a > b, a = b, a < b. c c n a n + b n + c n 3c n..... () /3 () + (3) / (4) /4 (5) m > n, a b >, m > n,
More information50. (km) A B C C 7 B A 0
49... 5 A B C. (. )?.. A A B C. A 4 0 50. (km) A B C..9 7. 4.5.9. 5. 7.5.0 4..4 7. 5.5 5.0 4. 4.. 8. 7 8.8 9.8. 8 5. 5.7.7 9.4 4. 4.7 0 4. 7. 8.0 4.. 5.8.4.8 8.5. 8 9 5 C 7 B 5 8 7 4 4 A 0 0 0 4 5 7 8
More informationn (1.6) i j=1 1 n a ij x j = b i (1.7) (1.7) (1.4) (1.5) (1.4) (1.7) u, v, w ε x, ε y, ε x, γ yz, γ zx, γ xy (1.8) ε x = u x ε y = v y ε z = w z γ yz
1 2 (a 1, a 2, a n ) (b 1, b 2, b n ) A (1.1) A = a 1 b 1 + a 2 b 2 + + a n b n (1.1) n A = a i b i (1.2) i=1 n i 1 n i=1 a i b i n i=1 A = a i b i (1.3) (1.3) (1.3) (1.1) (ummation convention) a 11 x
More informationX G P G (X) G BG [X, BG] S 2 2 2 S 2 2 S 2 = { (x 1, x 2, x 3 ) R 3 x 2 1 + x 2 2 + x 2 3 = 1 } R 3 S 2 S 2 v x S 2 x x v(x) T x S 2 T x S 2 S 2 x T x S 2 = { ξ R 3 x ξ } R 3 T x S 2 S 2 x x T x S 2
More informationOHP.dvi
7 2010 11 22 1 7 http://www.sml.k.u-tokyo.ac.jp/members/nabe/lecture2010 nabe@sml.k.u-tokyo.ac.jp 2 1. 10/ 4 2. 10/18 3. 10/25 2, 3 4. 11/ 1 5. 11/ 8 6. 11/15 7. 11/22 8. 11/29 9. 12/ 6 skyline 10. 12/13
More informationuntitled
C n π/n σ S n π/n v h N tc C S S S S S S S S S S S S S σ v S C σ v C σ v S. O. C / 8 Grou ABCABC EAAEA E AA - A- AE A - N C v EC C σ v σ v σ v 6 C C σ v σ v σ v X X A X - AXB B A B A B B A A C B C A B...
More informationτ τ
1 1 1.1 1.1.1 τ τ 2 1 1.1.2 1.1 1.1 µ ν M φ ν end ξ µ ν end ψ ψ = µ + ν end φ ν = 1 2 (µφ + ν end) ξ = ν (µ + ν end ) + 1 1.1 3 6.18 a b 1.2 a b 1.1.3 1.1.3.1 f R{A f } A f 1 B R{AB f 1 } COOH A OH B 1.3
More information@@ ;; QQ a @@@@ ;;;; QQQQ @@@@ ;;;; QQQQ a a @@@ ;;; QQQ @@@ ;;; QQQ a a a ; ; ; @ @ @ ; ; ; Q Q Q ;; ;; @@ @@ ;; ;; QQ QQ ;; @@ ;; QQ a a a a @@@ ;;; QQQ @@@ ;;; QQQ ;;; ;;; @@@ @@@ ;;; ;;; QQQ QQQ
More information福岡大学人文論叢47-3
679 pp. 1 680 2 681 pp. 3 682 4 683 5 684 pp. 6 685 7 686 8 687 9 688 pp. b 10 689 11 690 12 691 13 692 pp. 14 693 15 694 a b 16 695 a b 17 696 a 18 697 B 19 698 A B B B A B B A A 20 699 pp. 21 700 pp.
More informationOptical Flow t t + δt 1 Motion Field 3 3 1) 2) 3) Lucas-Kanade 4) 1 t (x, y) I(x, y, t)
http://wwwieice-hbkborg/ 2 2 4 2 -- 2 4 2010 9 3 3 4-1 Lucas-Kanade 4-2 Mean Shift 3 4-3 2 c 2013 1/(18) http://wwwieice-hbkborg/ 2 2 4 2 -- 2 -- 4 4--1 2010 9 4--1--1 Optical Flow t t + δt 1 Motion Field
More information日本看護管理学会誌15-2
The Journal of the Japan Academy of Nursing Administration and Policies Vol. 15, No. 2, PP 135-146, 2011 Differences between Expectations and Experiences of Experienced Nurses Entering a New Work Environment
More information1950 1970 1990 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 6,788 7,123 5,384 4,915 4,908 4,927 4,895 4,919 4,936 4,927 4,897 5,010 5,008 1,456 1
1950 1970 1990 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 6,788 7,123 5,384 4,915 4,908 4,927 4,895 4,919 4,936 4,927 4,897 5,010 5,008 1,456 1,616 927 824 826 821 813 808 802 803 801 808 806 18,483
More informationphs.dvi
483F 3 6.........3... 6.4... 7 7.... 7.... 9.5 N (... 3.6 N (... 5.7... 5 3 6 3.... 6 3.... 7 3.3... 9 3.4... 3 4 7 4.... 7 4.... 9 4.3... 3 4.4... 34 4.4.... 34 4.4.... 35 4.5... 38 4.6... 39 5 4 5....
More information31 33
17 3 31 33 36 38 42 45 47 50 52 54 57 60 74 80 82 88 89 92 98 101 104 106 94 1 252 37 1 2 2 1 252 38 1 15 3 16 6 24 17 2 10 252 29 15 21 20 15 4 15 467,555 14 11 25 15 1 6 15 5 ( ) 41 2 634 640 1 5 252
More information,..,,.,,.,.,..,,.,,..,,,. 2
A.A. (1906) (1907). 2008.7.4 1.,.,.,,.,,,.,..,,,.,,.,, R.J.,.,.,,,..,.,. 1 ,..,,.,,.,.,..,,.,,..,,,. 2 1, 2, 2., 1,,,.,, 2, n, n 2 (, n 2 0 ).,,.,, n ( 2, ), 2 n.,,,,.,,,,..,,. 3 x 1, x 2,..., x n,...,,
More informationuntitled
1 (1) (2) (3) (4) (1) (2) (3) (1) (2) (3) (1) (2) (3) (4) (5) (1) (2) (3) (1) (2) 10 11 12 2 2520159 3 (1) (2) (3) (4) (5) (6) 103 59529 600 12 42 4 42 68 53 53 C 30 30 5 56 6 (3) (1) 7 () () (()) () ()
More informationK E N Z U 2012 7 16 HP M. 1 1 4 1.1 3.......................... 4 1.2................................... 4 1.2.1..................................... 4 1.2.2.................................... 5................................
More informationuntitled
8- My + Cy + Ky = f () t 8. C f () t ( t) = Ψq( t) () t = Ψq () t () t = Ψq () t = ( q q ) ; = [ ] y y y q Ψ φ φ φ = ( ϕ, ϕ, ϕ,3 ) 8. ψ Ψ MΨq + Ψ CΨq + Ψ KΨq = Ψ f ( t) Ψ MΨ = I; Ψ CΨ = C; Ψ KΨ = Λ; q
More information70 : 20 : A B (20 ) (30 ) 50 1
70 : 0 : A B (0 ) (30 ) 50 1 1 4 1.1................................................ 5 1. A............................................... 6 1.3 B............................................... 7 8.1 A...............................................
More information数学Ⅱ演習(足助・09夏)
II I 9/4/4 9/4/2 z C z z z z, z 2 z, w C zw z w 3 z, w C z + w z + w 4 t R t C t t t t t z z z 2 z C re z z + z z z, im z 2 2 3 z C e z + z + 2 z2 + 3! z3 + z!, I 4 x R e x cos x + sin x 2 z, w C e z+w
More informationThe Physics of Atmospheres CAPTER :
The Physics of Atmospheres CAPTER 4 1 4 2 41 : 2 42 14 43 17 44 25 45 27 46 3 47 31 48 32 49 34 41 35 411 36 maintex 23/11/28 The Physics of Atmospheres CAPTER 4 2 4 41 : 2 1 σ 2 (21) (22) k I = I exp(
More information1 Nelson-Siegel Nelson and Siegel(1987) 3 Nelson-Siegel 3 Nelson-Siegel 2 3 Nelson-Siegel 2 Nelson-Siegel Litterman and Scheinkman(199
Nelson-Siegel Nelson-Siegel 1992 2007 15 1 Nelson and Siegel(1987) 2 FF VAR 1996 FF B) 1 Nelson-Siegel 15 90 1 Nelson and Siegel(1987) 3 Nelson-Siegel 3 Nelson-Siegel 2 3 Nelson-Siegel 2 Nelson-Siegel
More information( ) ,
II 2007 4 0. 0 1 0 2 ( ) 0 3 1 2 3 4, - 5 6 7 1 1 1 1 1) 2) 3) 4) ( ) () H 2.79 10 10 He 2.72 10 9 C 1.01 10 7 N 3.13 10 6 O 2.38 10 7 Ne 3.44 10 6 Mg 1.076 10 6 Si 1 10 6 S 5.15 10 5 Ar 1.01 10 5 Fe 9.00
More information働く女性の母性健康管理、母性保護に関する法律のあらまし
17 1 3 3 12 3 13 10 19 21 22 22 23 26 28 33 33 35 36 38 39 1 I 23 2435 36 4/2 4/3 4/30 12 13 14 15 16 (1) 1 2 3 (2) 1 (1) (2)(1) 13 3060 32 3060 38 10 17 20 12 22 22 500 20 2430m 12 100 11 300m2n 2n
More information2 Recovery Theorem Spears [2013]Audrino et al. [2015]Backwell [2015] Spears [2013] Ross [2015] Audrino et al. [2015] Recovery Theorem Tikhonov (Tikhon
Recovery Theorem Forward Looking Recovery Theorem Ross [2015] forward looking Audrino et al. [2015] Tikhonov Tikhonov 1. Tikhonov 2. Tikhonov 3. 3 1 forward looking *1 Recovery Theorem Ross [2015] forward
More information(1) (2) (1) (2) 2 3 {a n } a 2 + a 4 + a a n S n S n = n = S n
. 99 () 0 0 0 () 0 00 0 350 300 () 5 0 () 3 {a n } a + a 4 + a 6 + + a 40 30 53 47 77 95 30 83 4 n S n S n = n = S n 303 9 k d 9 45 k =, d = 99 a d n a n d n a n = a + (n )d a n a n S n S n = n(a + a n
More informationVol. 32, Special Issue, S 1 S 17 (2011)
Vol. 32, Special Issue, S 1 S 17 (2011) e-mail:luke154@jcom.home.ne.jp 1. 1.1 7 1900 800 2 S2 1.2 19 1909 Herman Nilsson-Ehle F 2 F 3 1 3 2 3 4 E. M. East 1.3 Wilhelm Ludwig Johannsen 1900 19 574 5,494
More information2 (March 13, 2010) N Λ a = i,j=1 x i ( d (a) i,j x j ), Λ h = N i,j=1 x i ( d (h) i,j x j ) B a B h B a = N i,j=1 ν i d (a) i,j, B h = x j N i,j=1 ν i
1. A. M. Turing [18] 60 Turing A. Gierer H. Meinhardt [1] : (GM) ) a t = D a a xx µa + ρ (c a2 h + ρ 0 (0 < x < l, t > 0) h t = D h h xx νh + c ρ a 2 (0 < x < l, t > 0) a x = h x = 0 (x = 0, l) a = a(x,
More information1 filename=mathformula tex 1 ax 2 + bx + c = 0, x = b ± b 2 4ac, (1.1) 2a x 1 + x 2 = b a, x 1x 2 = c a, (1.2) ax 2 + 2b x + c = 0, x = b ± b 2
filename=mathformula58.tex ax + bx + c =, x = b ± b 4ac, (.) a x + x = b a, x x = c a, (.) ax + b x + c =, x = b ± b ac. a (.3). sin(a ± B) = sin A cos B ± cos A sin B, (.) cos(a ± B) = cos A cos B sin
More informationTitle 混合体モデルに基づく圧縮性流体と移動する固体の熱連成計算手法 Author(s) 鳥生, 大祐 ; 牛島, 省 Citation 土木学会論文集 A2( 応用力学 ) = Journal of Japan Civil Engineers, Ser. A2 (2017), 73 Issue
Title 混合体モデルに基づく圧縮性流体と移動する固体の熱連成計算手法 Author(s) 鳥生, 大祐 ; 牛島, 省 Citation 土木学会論文集 A2( 応用力学 ) = Journal of Japan Civil Engineers, Ser. A2 (2017), 73 Issue Date 2017 URL http://hdl.handle.net/2433/229150 Right
More information(1.2) T D = 0 T = D = 30 kn 1.2 (1.4) 2F W = 0 F = W/2 = 300 kn/2 = 150 kn 1.3 (1.9) R = W 1 + W 2 = = 1100 N. (1.9) W 2 b W 1 a = 0
1 1 1.1 1.) T D = T = D = kn 1. 1.4) F W = F = W/ = kn/ = 15 kn 1. 1.9) R = W 1 + W = 6 + 5 = 11 N. 1.9) W b W 1 a = a = W /W 1 )b = 5/6) = 5 cm 1.4 AB AC P 1, P x, y x, y y x 1.4.) P sin 6 + P 1 sin 45
More information2000年度『数学展望 I』講義録
2000 I I IV I II 2000 I I IV I-IV. i ii 3.10 (http://www.math.nagoya-u.ac.jp/ kanai/) 2000 A....1 B....4 C....10 D....13 E....17 Brouwer A....21 B....26 C....33 D....39 E. Sperner...45 F....48 A....53
More informationTOP URL 1
TOP URL http://amonphys.web.fc.com/ 1 19 3 19.1................... 3 19.............................. 4 19.3............................... 6 19.4.............................. 8 19.5.............................
More informationprime number theorem
For Tutor MeBio ζ Eite by kamei MeBio 7.8.3 : Bernoulli Bernoulli 4 Bernoulli....................................................................................... 4 Bernoulli............................................................................
More informationThe Journal of the Japan Academy of Nursing Administration and Policies Vol 7, No 2, pp 19 _ 30, 2004 Survey on Counseling Services Performed by Nursi
The Journal of the Japan Academy of Nursing Administration and Policies Vol 7, No 2, pp 19 _ 30, 2004 Survey on Counseling Services Performed by Nursing Professionals for Diabetic Outpatients Not Using
More information1. 4cm 16 cm 4cm 20cm 18 cm L λ(x)=ax [kg/m] A x 4cm A 4cm 12 cm h h Y 0 a G 0.38h a b x r(x) x y = 1 h 0.38h G b h X x r(x) 1 S(x) = πr(x) 2 a,b, h,π
. 4cm 6 cm 4cm cm 8 cm λ()=a [kg/m] A 4cm A 4cm cm h h Y a G.38h a b () y = h.38h G b h X () S() = π() a,b, h,π V = ρ M = ρv G = M h S() 3 d a,b, h 4 G = 5 h a b a b = 6 ω() s v m θ() m v () θ() ω() dθ()
More informationiBookBob:Users:bob:Documents:CurrentData:flMŠÍ…e…L…X…g:Statistics.dvi
4 4 9............................................... 3.3......................... 4.4................. 5.5............................ 7 9..................... 9.............................3................................4..........................5.............................6...........................
More informationSO(3) 7 = = 1 ( r ) + 1 r r r r ( l ) (5.17) l = 1 ( sin θ ) + sin θ θ θ ϕ (5.18) χ(r)ψ(θ, ϕ) l ψ = αψ (5.19) l 1 = i(sin ϕ θ l = i( cos ϕ θ l 3 = i ϕ
SO(3) 71 5.7 5.7.1 1 ħ L k l k l k = iϵ kij x i j (5.117) l k SO(3) l z l ± = l 1 ± il = i(y z z y ) ± (z x x z ) = ( x iy) z ± z( x ± i y ) = X ± z ± z (5.118) l z = i(x y y x ) = 1 [(x + iy)( x i y )
More information