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1 1-1 1) ) 3-1-1
2 ) ) (1)
3 ()
4 1-- 1) H H10.0 1) 10.0 ) H 4) H3.0 3) 1) ) ) N0 kn / m 3) 4 H8.0 4) -9-5 (1) )
5 () (3) kN L
6 5.0 kn / m 1-5 3)(6) kn / m 10 kn / m (4) i=0/(50+ ) =415m i= =0.3 i= i=0.3 i=0.4 (5) -3 PA K A h q c K P K h' c K p p p A P A PP K A KP φ kn / m kn / m K tan A 45 / tan 45 / K P h kn / m h' kn / m γ h h' kn / m q kn / m kn / m 3-1-6
7 1--5 P A 0.3 h q P a 0.3 h () () kn / m N Hm 3-1-7
8 a=1 5.0m>3.0m 1 a N q10 kn / m. q/ (m) 1--8 H= ' ' (a) (b) ABD 3-1-8
9 (6) kN 3) (1) kn / m 3 3 W =10.0 kn / m W =10.3 kn / m - () (3) kn/
10 (4) -9 k H k H 0 BH 0.3 3/ 4 k H k H 0 BH 30 3/ 4 k H η 3 kn / m k H 0 η1 η B 0 / B0 B f η4 B f 30 3 kn / m k H 0 E0 k H E 0 BH B H 10 E BH k H 1--7 kn / m E 10C kn / m α 0 C kn / m α α 0 α E O, ) 1--8 H H 60 E cm 30cm
11 5) (1) k SS 400 SM 490 l () () l l r r 18 r l 9 [ (l /r-18) 1.5 1,00,000 l 9 6,700 l/r r r l 79 [185-1.l /r-16] 1.5 1,00,000 l 79 5,000 l/r r 1.5 l () () l b l b l b 30 [140-.4( l b -4.5)] l b 30 [ ( l b -4.0)] SS400 σ σ c caz σ bagy 1 σ bcy σ c σ eay σ bao σ 1 σ bcz c σ eaz 1 σ c 1 σ σ bcy c σ eay 1 σ σ bcz c σ eaz σ cal σc N/ mm σ, σ bcy bcz N/ mm σcaz σbagy N/ mm t (N/ mm )
12 AcAw (Ac(cm )Aw(cm ) ) σbao σcal 10N/ mm 10N/ mm 13.1t σ eay, σ eaz N/ mm ) σeay 1,00,000/ ' r y σeaz 1,00,000/ ' r z ' r y, r z b t b t SM400SMA400 (N/ mm ) SM
13 () (N/ mm ) SY95 SY (3) 1--1 (N/ mm ) SKY400 SKY (4) 4.4 JIS G 3536 PC PC PC JIS G 3109 PC PC (5) 51mm (N/ mm ) SR35 SD95A SD95B SD
14 (6) (SS400 ) (B10T) (N/ mm ) SS400 (10) SS400-6 (7) (N/ mm )
15 1--3 1).3() (1) () (3)
16
17 (4) a. b. a
18 b. 10 a ( , , ,000 5,000 10, b. (4)b a : : ,000 4,000 5, ,000 10, , b
19 3-1-19
20 a. a-a (7) (5) a. b. (4) a
21 b. (6) = (7)
22 (8) ) (1) a. b. 3-1-
23
24
25
26 3-1-6
27 3) (1)
28 3-1-8
29 () 3-1-9
30 1--1 () N
31 (3) / ) SY SY SKY SKY SS SWRH SWRS / SS ( 40mm ) ( 40mm ) SS ( 40mm ) ( 40mm )
32
33 (4) φ= k/ sat () v v50 50 v 170( v70) 1.7( v0.7 v
34 1--5 N 5 e. K h =0.1 (5) sat 10 w sat K h Kh sat w
35 (6) No A B 7.1 a
36 b ) (1) () =0E =0=0 0=0 a. P K h q c K (1--1) A A i i A K A cos 0 cos sin 1 0 sin cos 0 0 (1--) b. P K h q c K (1--3) P P i i P K P cos 0 cos sin 1 0 sin cos (1--4)
37 c. P o K o PA i h i q Ko 1 sin Ko k/ PP k/ k/ K A K P K o hi q i 0 K h K h k/ k/ k/ () = tan K h 1 K h d. (1--1)(1--3) (1--1) P A P A =0 e. 10m K =0 (1--1)(1--) 10m 10m K =0 1--1(1--) f
38 a. b c. b Westergaard P wd 7 Kh w he y (1--5) 8 7 Pwd Pwd Kh whe 1 (1--6) 3 L wd h (1--7) e
39 Kh w he y k/ (7) a. () M M F s d r F 1--5 s (1--8) M d M r kn kn b (a)(b) (1-9)(1-10) M M M M (1--9) d de w we pa pae pp M M M M M M (1--10) ppe e wd M d M de M w M we M pa M pae kn/ kn/ (1--1)(1--) kn/ M pp M ppe (1--3)(1--4) kn/ 10 0 M e M wd kn/ ( )kN/
40 (a) (b) c. M M 1 d / H r ro M sp (1--11) M kn/ ro d M kn/ sp H M ro (1--1)
41 M ro 1 6 m R m H 3 m (1--1) m h i H m H d B / H m B h k/ m (1--13) m R m (3 cos )sin (1--14) R m ( K EP K EA ) 3 cot EP 1 cot EA cot EP 1 cot EA K : EP K EA EP : EA M sp M sp M sp1 M sp =( ) kn/ M sp1 M sp a = spkn/ = P h kn/ N/ pu pu
42 Z sp P pu h pu / kn// P pu a. F F / F s r d (1--16) F s F d F r 1--6 k/ k/ b (a)(b) (a) (b) F = F + d w F pa F d = F we F pae e F F wd F r = F + F s pp F r = F F se ppe F = C s B W tan F = C se B W e tan 3-1-4
43 F w F we F pa F pae Fe Fwd F pp F ppe F F s se k/ k/ k/ k/ k/ k/ k/ k/ a b. (1--17)(1--18) (a) (b) F s V Qu D f B e (1--17) 1 Qu Be C Nc D f N q 1 1 B e N r (1--18)
44 F s 1--7 Qu k/ V k/ B e m Be B e B B () e () B e B M V B kn/ =0.3 D / =1.0 f B e C k/ D f 1 (m) k/ k/ N, N, N c q M B r H B H e tan a H B / V k/ k/ N
45 1--37 N c N q K=
46 F s W sin C K h W cos y 1 W R R K h ( P wh W sin tan h P wv v P wd wd ) (1--19) F s 1--8 R C W W y K h P wh k/ k/ k/ k/ P wv k/ h v P wh P wv P wd wd k/ P wd (8) a
47 b (1) 1--40() (1) () 9.1 F M / M s M AF M PF PF PA P P AF (1--0) A P (1--1) w P (1--) M PF M AF D P P kn kn () kn / P P P () P A kn / P A A () P w kn /
48 P w w ( ) F s C (1--3) C i hi i h i k/ k/ () a b. KH
49 c..9 AE K s kn// S A E S k/ a M max Z z sp (1--4) a / M max N/ z z 1-- 4) Z sp / (1--5) a T (1--5) A A T a 5 / ) (1--8) M TL = 10 (1--6) M = P L 4 (1--7) M T L kn N ()
50 M a Z (1--8) Z a / (9) F s L1 h 1 and L h (1--9) F s L 1, L () 1, ()
51 1--4 1) (1) m 3 / m cm / m () 10kN/m =
52 1. A P P / A =P yp / a a = / / (a) (b)
53 0.5m 0.5m 3.0m 0kN/m (3) 6 a. 3m b. c k d. e. a. 10kN/ 3 3 b. 18kN/ m 16kN/ m c
54 ) 1. (1) (4) =.5/ 0 0 (m) (m -1 ) 4 k H B 4EI H (kn/m 3 )/ 1-- 3)(4) (m) (kn/m ) (m 4 ) 100 / 0 =.5/.5/
55 a. 10kN/m b. M P (1 h ) 1 exp( tan h0 ) 0 (knm) (kn) (m) (m -1 ) 3 = () () () () 1 (1 h0 ) P 3 EI (1 EI h0 ) PH
56 3 4 ph 30EI ( -1 ) 0 () k (kn/m ) p ( 4 ) () (kn /) p 6 M H (knm) () (3) 3) -9 (1) P p y p P a y a
57
58 H
59 ) (4) () t 6M b a a () (1000 ) (N/ ) W (N) 8 () (N/) bt a (N/ ) (= /) (N) () a (N/ ) (3)
60 (a) 1--54(b) ()
61 1--54(a)
62 kN/m } % 1-5 4) (5) / /
63 (4) =/cos (kn) (kn) ()
64 abc R R R a b c R R R R R R ) -9 (1) (a) (b) () ( 1 )
65 1-- ) (5) 9.0kN/m ) (4) (a) 1--63(b)
66 s = M max Z s max (N/ ) (N/m) ( 3 /) / 1 = / 1 = = 4 5w 384EI () = K R () (kn/m) (kn/ ) ( 4 ) = 1 w 1 (kn)} (kn/m)
67 / 1 = 1 /= / (kn/m) H (kn/m 3 ) hp =H H 1-- 3) (4) H kn/m 3 ) H 5,0000,000 15,00030,000 0,00040,000 40,00060, ()
68 / () a. = 3 t = 3 =(n1n) (kn) n 1 1 = S x SY 1 50 x (kn) XY (kn) N = ( w w ) (kn) n x 1 x x y y x y
69 wxw y x=y=0.5 (kn/m) N3 Nt (kn) (kn) (knm) n1 n (kn) (kn) () b. b (kn /m ) M b f b Z c (kn /m ) N c f c A f b b f c c 1.0 ( 3 ) ( ) fb (kn/m ) fc (kn /m ) ) (1) c k k ( 1 m 1 ( m) )
70 1 kh kn/ 3 () kn/ 3 ( 4 ) c ) (5) (3) N 1 w / cos (kn) (m) w (kn/m) 1 ()
71 R a = 1 W R b = 3 W R c = 3 4 W a W (kn/) R R R abc (kn/) b c () (4) -9-3 Terzaghi Terzaghi / Terzaghi F s W u F ( F 1.) s W d (kn /m ) s
72 (kn /m ) d hw u whw (kn /m 3 ) () w (kn /m 3 ) () pwa ( whw / ) d / p wb p p wb wa u 1.57 whw 4 = ( B / d ) = {( L / B) 0.37} / 0..( D d ) =1.6 () 1--74(b) k1k 3-1-7
73 -9-3 ()1 () h h d w h () h d hw () ()
74 N N b N 3.14 N 5.14 b b b N b H c 3.14 N b (kn /m 3 ) () (kn /m ) N b ( M ) ( M ) d r F s M M r d x π / 0 α c (Z) x W xd θ ( α π ) () (kn /m ) = kn /m ()
75 (kn) = (kn /m ) (kn /m 3 ) () Fs ( Fs 1.) F s M M r d x ( H xc x q ) x ( H ) c q
76 ( ) W u 1 1 F s w h w h h Fs F s 1.1 (kn /m ) (kn /m ) 1 (kn /m 3 ) h1 h hw () w (kn /m3 ) () F s
77 5) (1) () mm (3) Kranz
78 1--81(a) max R h 1--81(b) E W E E tan tan( rh ah 1h ) max Rh 1 Eah tan E1 h E tan( rh ) Ea Pb (kn/m) (kn/m) (kn/m) max R h F s R E max ah h Fs Eah (kn/m) () () () A
79 = ()
80 (1) T d R cos cos T d (kn /) (kn /m) (m) () ()= (4) (1) ()
81 310 a A f T d D F a s a () A Td f Fs Da () () (kn) 1.5 () (kn/ )} (kn/ ) 10 0 N C
82 (5) 18N/ ( sa T U d a sa ) sa () Td (kn) ()PC PC a (N/ ) (N/ ) (6) 3-1-8
83 (7) ( T d )( T a ) ( T a )( T as )( T ag ) a. ( T as ) ( T as )( T us )( T ys ) ( T us ) 0.65 T us ( T ys ) 0.80 T ys 6.6 b. ( T ag ) ( T ag ) ( T ug ) Tug
84 ()
85
86
87 ) ()9. 1 (1) 1-3- () cm 3 /sec cm 3 /sec
88 () Hz 60Hz m 3 /min m 3 /min kw () m 3 /min m 3 /min kw ) (1) ()
89 a. Terzaghi 1.9D 10 cm / sec) b. Hazen CD 10 cm / sec) D10 C1/cms c. reager() (mm) cm/sec 0(mm) cm/sec
90 () ( ) (4) ()
91 a. Q 4kH 9L 1 Q (m3/secm) k (m/sec) H (m) L1 (m) A.Casagrande () b. Q kh L d 0.86d Q (m3/secm) k (m/sec) H (m) d L (m) (m) ()
92 c. 4k H 9L b Q 1 k H L 1 d Q (m3/secm) k (m/sec) k b (m/sec) H (m) d L1 (m) (m) () Q S k f H d h d hd 1 Q (m3/secm) k f (m/sec) H (m) d S h1 h (m) (m) (m) (m) ()
93 (5) 9. a. b. a. 0 () 0 () b () 1 1, a
94 b. Kusakin 575 s Seichardt m/sec c > >1, ,
95 () () a ()
96 ). Q kh.3 log R r 10 h 0 0 Q (m3/sec) k (m/sec) r0 (m) h0 (m) R (m) H (m) () Q kh h0 t 0.5r0 h0 4.3log R r H h t Q (m3/sec) k (m/sec) r (m) H (m) 0 h (m) R (m) 0 t (m) ()
97 Q 4kr H h 0 0 () Q kdh h.3log R r Q (m3/sec) k (m/sec) d (m) H (m) h (m) R (m) 0 r0 (m) ()
98 . Q kdh.3 log 10 R r 0 h0 G Kozenyde Gle Kozeny G l d 1 7 r cos l l d 0 Q (m3/sec) k (m/sec) d (m) H (m) h (m) R (m) 0 r (m) l (m) 0 () b ()
99 ). Q kh R h0 L Q (m3/sec) L (m) k (m/sec) H (m) h (m) R (m) 0 () (1) Q kh 0 L.3log R r 10 0 Q (m3/sec) L (m) k R (m/sec) (m) H (m) 0 r0 1/(m) () ()
100 . kh h0 H h0 Q L R H R / H3 Q (m3/sec) L (m) k (m/sec) H (m) h (m) R (m) 0 () Q k dh R 0 h L Q (m3/sec) k (m/sec) d (m) H (m) h (m) L (m) 0 R (m) ()
101 . Q kdh h0 L R d Q (m3/sec) k (m/sec) d (m) H (m) h (m) L (m) R (m) ()
102
103 / Ch C ( h 0. h )( W B 0.09) C 3/ Cbh h h ( B d h ) W BW B W 3 / CBh C h (1 ) h W W1(m) ε=0 W>1(m) ε=0.55(w1) h = (m) hb/3 h = b (m) h = (m) hw hb /4 B =0.51.(m) W = (m) B =0.56.3(m) W = (m) b = (m) bw / B 0.06 B 0.5(m) W =0.3.5(m) ) 9. (1)
104 () 5) m m 10m 1) (1) () (3) (4) ). ). 3)
105 ) (1) () (3) (4) ()9.. 3) )
106 4) Seichart q w w s 15 1 m 3 /sec w m/sec () ) m 3 /sec m 3 /sec
107 6) (1) l n kd l n H x h x H h kd l n l n x x m 3 /sec m/sec χ χ χ H ()
108 () l n K l n H h x x H h H H l n l n x x m 3 /sec m/sec χ χ χ 7) H h πkd l n l n (x1x 0 x r n 1 w ) 0 H h 0 H H l n l n (x 1 x x n 1 χ χ χ W r w Q m 3 /sec m/sec 8)
109 9) q q 4)5) 4) q q 10) m m 3 /min 5.511kW ) )
110 3) 9. (1) () (3) (4) q.0m NO YES =.0m ) )
111 5) m 3 /min ) m 3 /min m 3 /min 7) 0.8.0m a m m 8) m 3 /min m 3 /min m
112 m 3 /min 18m 7.5kW kPa 7.5 9) m m m m 3 () () ()
113
114 1-5 1) ) (3)
115 (4) -11 6% 6% (5) [ [ (6) ) a. 1-- ) (3) b. 1-- ) (3) c
116 1-5- k (kn) (kn)
117 q W B T kn / m q 0.5 W B T kn / m kn kn 1 kn / m. 1/ q W B T 1 W 0.75 T B kn / m kn kn kn / m
118 q W 1 kn / 0.9 T B m q W kn / 0.9 T B m kn kn q1 q kn / m 1-- ) (4) a b
119 c.. d. 4) -11 (1) ()
120 1-5-3 (kn/m ) (3)
121 a P 1.0 P y P y P kn
122 b. /400.5 δ δ 3 P0 48EI 4 5W M max 0 384EI 9.6EI 3-1-1
123 M max (m) (kn) (m) ( 4 ) (kn/m ) P0 (kn) Wo 8M max (kn/) (4)
124 () () n S a R S a A a S a () () ( ) a (N/ )
125 (5) 3m a. R 1 n a R u Ra (kn) R R u q u d Ru = A U i f i (kn) (m ) qd (kn/m ) U i (m) (m) f i (kn/m ) N
126 q d (kn/m ) f i (kn/m ) q d =00α fi 10 N c Nc N fi N c N c fi N s αβ N N 1 N 40 N1 N N c N s m kN/m 150kN/m α β m U= U= = U
127 b.. H 0 H n H 0 H n (kn) (kn) = β 0 0 M m H 0 1 ( h) exp( tan 1 1 ) h M 0 (knm) M m (knm) () β (m -1 ) rad
128 4 k H D 4EI k H (kn/m 3 ) 1-- 3(4) () (kn/m ) ( 4 ) 3 ( ) 3 1EI 0 δ () ( I ) ( I y ) x () () M 0 0 m 0 ( h) exp( 3 ( h) 1/ tan ) δ δ
129 c (6) c n A σc (N/ ) () 1-5- ( ) = c n A cos σc (N/ ) () 1-5- ( ) α ( 1-5- ) 1-5- =
130 1-5- 5) 7. φ48.6=.4 φ48.6=
131 ) ) 1)) 3) 3) (1).'
132 () () (3) (4) () () ()
133 第３編 仮設工等 第１章 仮設工 コラム 河川工事の環境への影響低減対策 基本的考え方 仮設工については 周辺の自然環境に与える影響を回避 低減 代償する措置を講じることが望ましい できるだけ環境に対する影響を回避 低減 最小化 代償の順序に従って 段階を踏んでいき 生態系へ の開発のインパクトを最小化する ミチゲーション 環境を把握する 仮設構造物が生物の生息 生育環境に与える影響例 生息 生育地の損失 生息 生育地の分断 移動経路の分断 振動 騒音による影響 水質の悪化 その他 環境条件の変化 仮設計画のチェック 設計時点の仮設計画が現場の自然環境に適切かどうか確認する 影響低減の対策例 (1) 貴重種等の注目すべき生物が確認された場合には 生息 生育地を避けて仮設構造物を設置する () 準備工における周辺植生の伐採を最小限にとどめ 場合によっては移植する (3) 工事用道路の延長 幅員は最小限とし 必要に応じて粉じん対策や地盤に対する荷重を低減する (4) 土砂 濁水の流出防止対策を施す (5) 水中施工では 水域の攪乱を避け 水生生物に対する影響を低減するため 水域の攪乱を避け 土砂 濁 水の流出防止対策を図る (6) 生物の生息 生育環境の連続性やネットワークを確保する (7) 生物の生活史に配慮した施工工程計画を行う 樹林を避けて工事用道路を配置した例 搬入土を用いる際にシートを敷いて 土が混ざらないように配慮した例 仮設のろ過施設を設けて濁水 の流出を防止した例 河川と周辺環境の連続性とネットワーク 河川の生物の生息 生育環境の連続性 多自然型川づくり 施工と現場の工夫
134 第 3 編仮設工等第 1 章仮設工 参考文献 基準等の略称参考文献年月監修 編集 発行等 河川砂防 ( 調 ) 河川砂防技術基準調査編 H6.4 国土交通省 構造令改定解説 河川管理施設等構造令 H1.1 ( 社 ) 日本河川協会 例規集河川事業関係例規集 H7 ( 社 ) 日本河川協会 アンカー設計基準グラウンドアンカー設計 施工基準 同解説 H4.5 ( 社 ) 地盤工学会 二重式仮締切マニュアル 鋼矢板二重式仮締切設計マニュアル H13.5 ( 財 ) 国土技術研究センター 耐候性大型土のう 耐候性大型土のう積層工法 設計 施工 マニュアル マニュアル H4.3 ( 財 ) 土木研究センター 道示 ( 下部 ) 道路橋示方書 同解説 (Ⅳ 下部構造編 ) H4.3 ( 社 ) 日本道路協会 仮設工指針 道路土工仮設構造物工指針 H11.3 ( 社 ) 日本道路協会 仮設ガイドブック (Ⅰ) 土木工事仮設計画ガイドブック (Ⅰ) 平成 3 年改訂版 H3.3 ( 社 ) 全日本建設技術協会 仮設ガイドブック (Ⅱ) 土木工事仮設計画ガイドブック (Ⅱ) 平成 3 年改訂版 H3.3 ( 社 ) 全日本建設技術協会
(1) (kn/m 3 )
1 1 1.1 1.1.1 (1) 1.1 1.2 1.1 (kn/m 3 ) 77 71 24.5 23 21 8.0 22.5 2 1 1.2 N/m 2 2 m 3 m 2000 2200 2500 3000 (2) 1 A B B 1.3 1.5 1.1 T cm 1.1 3 1.3 L m L 4 L > 4 1.0 L 32 + 7 8 1.2 T 4 1 2 5.0 kn/m 2 3.
(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
NETES No.CG V
1 2006 6 NETES No.CG-050001-V 2007 5 2 1 2 1 19 5 1 2 19 8 2 i 1 1 1.1 1 1.2 2 1.3 2 2 3 2.1 3 2.2 8 3 9 3.1 9 3.2 10 3.3 13 3.3.1 13 3.3.2 14 3.3.3 14 3.3.4 16 3.3.5 17 3.3.6 18 3.3.7 21 3.3.8 22 3.4
Q & A Q A p
Q & A 2004.12 1 Q1. 12 2 A1. 11 3 p.1 1.1 2 Q2. A2. < > [ ] 10 5 15 (p.138) (p.150) (p.176) (p.167 ) 3 1. 4 1.6 1.6.1 (2) (p.6) Q3. 5 1 1:1.0 12 2 1:0.6 1:1.0 1:1.0 1:0.6 1:0.6 1:0.6 1:1.0 1:0.6 ( ) 1:1.0
untitled
- k k k = y. k = ky. y du dx = ε ux ( ) ux ( ) = ax+ b x u() = ; u( ) = AE u() = b= u () = a= ; a= d x du ε x = = = dx dx N = σ da = E ε da = EA ε A x A x x - σ x σ x = Eε x N = EAε x = EA = N = EA k =
1.500 m X Y m m m m m m m m m m m m N/ N/ ( ) qa N/ N/ 2 2
1.500 m X Y 0.200 m 0.200 m 0.200 m 0.200 m 0.200 m 0.000 m 1.200 m m 0.150 m 0.150 m m m 2 24.5 N/ 3 18.0 N/ 3 30.0 0.60 ( ) qa 50.79 N/ 2 0.0 N/ 2 20.000 20.000 15.000 15.000 X(m) Y(m) (kn/m 2 ) 10.000
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20 3 Copyright (2007) by P.W.R.I. All rights reserved. No part of this book may be reproduced by any means, nor transmitted, nor translated into a machine language without the written permission of the
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Study on Retaining Wall Design For Circular Deep Shaft Undergoing Lateral Pressure During Construction 2003 3 Study on Retaining Wall Design For Circular Deep Shaft Undergoing Lateral Pressure During Construction
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振動と波動
Report JS0.5 J Simplicity February 4, 2012 1 J Simplicity HOME http://www.jsimplicity.com/ Preface 2 Report 2 Contents I 5 1 6 1.1..................................... 6 1.2 1 1:................ 7 1.3
[ ] 0.1 lim x 0 e 3x 1 x IC ( 11) ( s114901) 0.2 (1) y = e 2x (x 2 + 1) (2) y = x/(x 2 + 1) 0.3 dx (1) 1 4x 2 (2) e x sin 2xdx (3) sin 2 xdx ( 11) ( s
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[ ]. lim e 3 IC ) s49). y = e + ) ) y = / + ).3 d 4 ) e sin d 3) sin d ) s49) s493).4 z = y z z y s494).5 + y = 4 =.6 s495) dy = 3e ) d dy d = y s496).7 lim ) lim e s49).8 y = e sin ) y = sin e 3) y =
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1 2 2.1 (e ) (µ ) (τ ) ( (ν e,e ) e- (ν µ,µ ) µ- (ν τ,τ ) τ- ) ( ) ( ) ( ) (SU(2) ) (W +,Z 0,W ) * 1) [ ] [ ] [ ] ν e ν µ ν τ e µ τ, e R,µ R,τ R (2.1a) L ( ) ) * 2) W Z 1/2 ( - ) d u + e + ν e 1 1 0 0
W u = u(x, t) u tt = a 2 u xx, a > 0 (1) D := {(x, t) : 0 x l, t 0} u (0, t) = 0, u (l, t) = 0, t 0 (2)
3 215 4 27 1 1 u u(x, t) u tt a 2 u xx, a > (1) D : {(x, t) : x, t } u (, t), u (, t), t (2) u(x, ) f(x), u(x, ) t 2, x (3) u(x, t) X(x)T (t) u (1) 1 T (t) a 2 T (t) X (x) X(x) α (2) T (t) αa 2 T (t) (4)
1. 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. +
1 I
1 I 3 1 1.1 R x, y R x + y R x y R x, y, z, a, b R (1.1) (x + y) + z = x + (y + z) (1.2) x + y = y + x (1.3) 0 R : 0 + x = x x R (1.4) x R, 1 ( x) R : x + ( x) = 0 (1.5) (x y) z = x (y z) (1.6) x y =
Contents
Contents 6-1 6-2 780 630 440 385 355 325 295 205 80 1-1 1-2 1-3 1-4 1-5 1-6 1-7 1-8 1-9 1-10 1-11 1-12 1-13 1-14 1-15 1-16 1-17 1-18 1-19 1-20 1-21 1-22 1-23 1-24 1-25 1-26 1-27 1-28 1-29 1-30 MEMO G
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4 4. 4.. 5 5 0 A P P P X X X X +45 45 0 45 60 70 X 60 X 0 P P 4 4 θ X θ P θ 4. 0, 405 P 0 X 405 X P 4. () 60 () 45 () 40 (4) 765 (5) 40 B 60 0 P 0 0 + 60 = 90, 0 + 60 = 750 0 + 60 ( ) = 0 90 750 0 90 0
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