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1 SAW 14 2 M3622
2 i SAW SAW
3 5 SAW Wedge SAW Wedge SAW ii
4 ( ) 1) 2) 3) ( ) - 1 -
5 1 1-2 SAW 4) SAW SAW 3 4 SAW 2 5 SAW 2 SAW
6 2 2 5) 128Y X LiNbO3 LiNbO3 2-1 (surface acoustic wave:saw) (interdigital transducer:idt) SAW λ λ/
7 x 2 x Lord Rayleigh 1 9% /5 ( ) LiNbO3 2-2 x1 (x3 ) xi ui u = A e i i αω υx e ω j ωt υ 3 x 1 ( i = 1 ~ 3) i (=13) υ α x3 x
8 2 α 3ω α pω = υx 3 υx 3 1 u1 F1 e pe e ω j ωt υx u = 1 α 3ω α pω F 1 = υx 1 3 υx 3 1 u1 j e e e α 3 p ω j ωt υx p =-F2/F1 F1F2 u3 u SAW 128Y X LiNbO3 µm 4µm2 IDT 2-3 SAW 2-4 LiNbO3 396 m/s SAW f υ λ υ f = λ 4µm 9.6 MHz - 5 -
![2 2-3 SAW LiNbO 3 : [mm] t = 1 IDT 16 43 2 IDT :](/docs-images/101/150733999/images/9-0.jpg "[mm] 9 16 8.")
9 2 2-3 SAW LiNbO 3 : [mm] t = 1 IDT IDT : [mm] : aluminum : µm : 4 µm SAW - 6 -
10 SAW (HEWLETT PACKARD IMPEDANCE/GAIN- PHASE ANALYZER 4194A) 2-5 LiNbO3 (G) 9.59 MHz ml G G G 2 SAW ml 9.59 MHz 9.59 MHz - 7 -
11 2 G [S] B G [MHz] B [S] 2-5 () G [S] B [MHz] G (a).1 ml 5-5 B [S] G [S] B [MHz] G (b).2 ml 5-5 B [S] G [S] B [MHz] G 5-5 B [S] G [S] B [MHz] (c).3 ml (d).4 ml G 5-5 B [S] 2-6 SAW ( ) - 8 -
12 2 mist Fluid SAW device IDT 15 G 15 G [S] 5 B 5 B [S] [MHz] SAW ( ) - 9 -
13 MHz 1 khz 1 msec 9.59 MHz 2-8 IDT LiNbO3 8 V-p 1 khz (1 msec) 2-8 (LDVLaser Doppler Vibrometer, Polytec OFV 51,OFV27) A f V V = 2πfA
14 2 2-6 V-p 1 khz G [nm] [m/sec] [V -p ] 2-9 [nm] [m/sec] [MHz]
15 SAW SAW 2-11 ( ) θr θ R = sin 1 V W / V R VR VW θr =23 θ R
16 (IDT) 128 Y X (MHz) ( ) IDT IDT
17 ( ) θ R (1) (5) (A) (C) ( ) υ
18 3 (A) (B) (C) (1) (2) (3) (4) (5) T c t
19 3 φ 3-4 x x ( ) z xz 2 2 φ φ + = 2 2 x z φ υ ρ σλ g λ πσ υ = g 2 2 π + ρλ λ = 2π / k λ = 2π / k
20 3 λ 2πσ υ (3.1) ρλ τ υ λ = υτ (3.1) λ υ = = τ 2πσ ρλ 3 λ 2πσ = 2 τ ρ fe fk τ = 1 f k 3 2πσ λ = (3.2) 2 ρf k fe fk f = n/ 2 k f e n 1 n = f k = f e / 2 ()
21 8πσ λ = 2 ρf e d λ κ 1 3 8πσ d = κ 2 (3.3) ρf e d fe 2/3 fe d 3-5 (3.3) κ 3-5 khz MHz MHz 5 MHz (3.3) κ = 1. MHz 3µm [µ] k k 1 M M [Hz]
22 4 SAW 4 SAW 3 2 SAW SAW IDT (SAW ) SAW SAW SAW SAW SAW SAW 2 SAW A B Normal
23 4 SAW SAW 4-1 Normal A B IDT SAW IDT SAW
24 4-2 4 SAW A B 4-3 G Q G 15 G [S] 5 B 5 B [S] [MHz] (a) A G 15 G [S] 5 B 5 B [S] [MHz] (b) B
25 4 SAW 4-1 A B G Q A 9.59 MHz 11.1 ms B 9.59 MHz 12.7 ms LDV 4-4 SAW 4 µm LDV LDV LDV µm MHz 1 khz y IDT LDV 3 mm y SAW IDT
26 A [mn] A [mn] 3 4 SAW 18 2 A θ [mm] 3 (a) A 2 A θ [mm] (b) B θ [] θ []
27 4 SAW 4-3 SAW MHz 1 khz (2 CH) (1 khz) 2 CH 9.59 MHz 2 CH 2 2 EN MODEL 24L RF POWER AMPLIFIER WAVE FACTORY HEWLETT PACKARD WF A CH1 CH1 CH2 Iwatsu DS-8812 CH2 CH1 CH
28 4 SAW VrmsI G 2 W = IV rms = GV rms 1 khz 9.59 MHz W/9.59 SAW 2 (1) (.1 ml.15 ml) SAW
29 4 SAW IDT 4-8 (a) (DOW CORNING : HIGH VACUUM GREASE) 4-8 (b)(c) SAW A [mn] A [mn] 3 (a) 18 2 A θ [mm] 3 (b) 2 A θ [mm] (c) θ [] θ []
30 4 SAW 4-8 (2) MHz 1 khz mm Normal 1.27 mm mm [ml/min] [mm]
31 (3) 4 SAW MHz 1 khz 1.27 mm MHz 9.59 MHz [ml/min] MHz [W]
32 4 SAW / (3) 4-11 (a) 4-11 (b) 4-11 (b) 2 IDT θ (a) [V -p ] (b)
33 4 SAW (4) 2 SAW (a) (b) (c) 9.59 MHz 1 khz 1.27 mm 2 23 (a).12. (b) [ml/min] [Wh] (c)
34 4 SAW (5) 5 mm MHz 1 khz 1.27 mm 4-13 [mm] mm 2.5 cm [W]
35 4 SAW (6) 4-14 (a) 1 mm He-Ne 4-14 (b) 4-14 (b) 6 W.25 msec IDT 3.3 mm IDT 4 m/s.8 µsec He-Ne 4. (a) [msec] [Wh] (b)
36 (8) 4 SAW Normal
37 (7) 4 SAW ml ml 4-15 N/m.5.4 [ml/min] : 5.4 W [N/m]
38 4 SAW 4-4 SAW 2 Normal 1.27 mm SAW ( )
39 5 SAW 5 SAW 4 2 SAW SAW 2 SAW IDT 3 2 Wedge IDT 3 2 Wedge Wedge SAW SAW 2 2 SAW IDT C D Wedge
40 5 SAW Wedge C SAW D SAW IDT IDT SAW 9.57 MHz 9.57 MHz (a) 1 mm 1 mm 1 mm mm LiNbO 3 (a) SAW 5-1 Wedge SAW
41 5 SAW (1) 5-1 C D 5-2 G Q G [S] G B [S] 5 B [MHz] (a) C G [S] G B [S] 5 B [MHz] (b) D C D G Q C 9.57 MHz. ms 81. D 9.57 MHz 11. ms
42 5 SAW (2) LDV C 5-3 x y u v D y MHz 1 khz SAW SAW x y u v A [mn] A [mn] 3 IDT θ A [mm] (a) C y θ A [mm] (b) D y θ [] θ [] 5-4 (1)
43 A [mn] A [mn] 3 2 θ 5 SAW [mm] (c) C u θ A [mm] (d) C v A 18 θ [] θ [] 5-4 (2) 5-4 (1) (a)(b) y (b).5 mm (2) (c) u - 4 -
44 5 SAW 5-4 (2) (d) v Wedge 9.57 MHz 1 khz 1.27 mm SAW LDV
45 5 SAW (1) Wedge 2 (2) 18 SAW [ml/min] [Wh]
46 5 SAW (2) 5-6 Wedge [W] [mm]
47 5 SAW (2) IDT IDT IDT IDT SAW
48 5 SAW 5-2 Wedge SAW SAW 2 2 SAW IDT E F Wedge2 Wedge_2 E F IDT IDT SAW 9.74 MHz SAW 9.74 MHz (a) 5-9 (1) Wedge2-45 -
49 5 SAW 1 mm 3 1 mm (b) SAW 5-9 (2) Wedge2-46 -
50 5 SAW (1) G Q G [S] G B [S] 5 B [MHz] (a) E G [S] G B [S] 5 B [MHz] (b) F E F G Q E 9.74 MHz 13.5 ms 1.3 F 9.74 MHz 13.4 ms
51 5 SAW (2) LDV 5-11 y u 5-12 SAW u y IDT A [mn] A θ θ [] A [mn] 3 (a) E y 18 2 A θ (b) F y θ [] 5-12 (1) EF
52 5 SAW A [mn] A θ θ [] (c) E u A [mn] 3 18 θ 2 A (d) F u θ [] 5-12 (2) EF 5-12 (1) (a)(b) (2) (c)(d) Wedge
53 5 SAW Wedge MHz 1 khz 1.4 mm (1) 5-13 Normal Wedge 2 Wedge [ml/min] [W] [W]
54 5 SAW [ml/min] Wedge [] 7 W (2) W mm Wedge2 mm [mm] [W]
55 5 SAW (3) Wedge2 5 mm µm MHz µm µm 5-16 ( )
56 5 SAW 5-3 SAW IDT 3 2 Wedge IDT 3 2 Wedge Normal 5-17 Wedge Wedge2 Wedge Normal 1 4 W Wedge
57 Wedge MHz 9.74 MHz 5 SAW [ml/min] Normal Wedge 9.59 MHz 9.59 MHz 9.57 MHz 9.57 MHz.2 [mm] [W] 5-17 () [W] 5-18 ( ) 5-3 Normal Wedge Wedge
58 SAW SAW SAW SAW IDT 3 2 Wedge IDT 3 2 Wedge2 2 3 Wedge Wedge SAW
59 6 SAW SAW SAW SAW SAW IDT IDT SAW
60 James R Friend SAW
61 1) Japan Hardcopy '99(1999) 2) () (1993) 3) (199) 4) SAW 5) US95-2pp. 1-8 (1995) 6) (1978) 7) (1983) 8) 15 (1993) 9) (1988)
62 (1), J. Friend,,, " 2 ", (2), J. Friend,,, " SAW ", (3), J. Friend,,, " SAW ",
63 IDT (1) (2) 2 Al φ.1 mm 8m Cr cm Pa CrAl - 6 -
64 (3) 9 3 ( ) (4) 6 LiNbO3 128Y-cut X XY 8 2 ( ) (5) 1 CrAl AlCr
65 Table 1 The kind of etching liquids : = 2 : 1 cc 2 17 g 5 cc
64 3 g=9.85 m/s 2 g=9.791 m/s 2 36, km ( ) 1 () 2 () m/s : : a) b) kg/m kg/m k
63 3 Section 3.1 g 3.1 3.1: : 64 3 g=9.85 m/s 2 g=9.791 m/s 2 36, km ( ) 1 () 2 () 3 9.8 m/s 2 3.2 3.2: : a) b) 5 15 4 1 1. 1 3 14. 1 3 kg/m 3 2 3.3 1 3 5.8 1 3 kg/m 3 3 2.65 1 3 kg/m 3 4 6 m 3.1. 65 5
LLG-R8.Nisus.pdf
d M d t = γ M H + α M d M d t M γ [ 1/ ( Oe sec) ] α γ γ = gµ B h g g µ B h / π γ g = γ = 1.76 10 [ 7 1/ ( Oe sec) ] α α = λ γ λ λ λ α γ α α H α = γ H ω ω H α α H K K H K / M 1 1 > 0 α 1 M > 0 γ α γ =
微分積分 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. このサンプルページの内容は, 初版 1 刷発行時のものです.
微分積分 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. ttp://www.morikita.co.jp/books/mid/00571 このサンプルページの内容は, 初版 1 刷発行時のものです. i ii 014 10 iii [note] 1 3 iv 4 5 3 6 4 x 0 sin x x 1 5 6 z = f(x, y) 1 y = f(x)
医系の統計入門第 2 版 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. このサンプルページの内容は, 第 2 版 1 刷発行時のものです.
医系の統計入門第 2 版 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/009192 このサンプルページの内容は, 第 2 版 1 刷発行時のものです. i 2 t 1. 2. 3 2 3. 6 4. 7 5. n 2 ν 6. 2 7. 2003 ii 2 2013 10 iii 1987
空気の屈折率変調を光学的に検出する超指向性マイクロホン
23 2 1M36268 2 2 4 5 6 7 8 13 15 2 21 2 23 2 2 3 32 34 38 38 54 57 62 63 1-1 ( 1) ( 2) 1-1 a ( sinθ ) 2J D ( θ ) = 1 (1-1) kaka sinθ ( 3) 1-2 1 Back face hole Amplifier Diaphragm Equiphase wave surface
Microsoft Word - 学士論文（表紙）.doc
GHz 18 2 1 1 3 1.1....................................... 3 1.2....................................... 3 1.3................................... 3 2 (LDV) 5 2.1................................ 5 2.2.......................
Gauss Gauss ɛ 0 E ds = Q (1) xy σ (x, y, z) (2) a ρ(x, y, z) = x 2 + y 2 (r, θ, φ) (1) xy A Gauss ɛ 0 E ds = ɛ 0 EA Q = ρa ɛ 0 EA = ρea E = (ρ/ɛ 0 )e
7 -a 7 -a February 4, 2007 1. 2. 3. 4. 1. 2. 3. 1 Gauss Gauss ɛ 0 E ds = Q (1) xy σ (x, y, z) (2) a ρ(x, y, z) = x 2 + y 2 (r, θ, φ) (1) xy A Gauss ɛ 0 E ds = ɛ 0 EA Q = ρa ɛ 0 EA = ρea E = (ρ/ɛ 0 )e z
4‐E ) キュリー温度を利用した消磁：熱消磁
( ) () x C x = T T c T T c 4D ) ) Fe Ni Fe Fe Ni (Fe Fe Fe Fe Fe 462 Fe76 Ni36 4E ) ) (Fe) 463 4F ) ) ( ) Fe HeNe 17 Fe Fe Fe HeNe 464 Ni Ni Ni HeNe 465 466 (2) Al PtO 2 (liq) 467 4G ) Al 468 Al ( 468
128 3 II S 1, S 2 Φ 1, Φ 2 Φ 1 = { B( r) n( r)}ds S 1 Φ 2 = { B( r) n( r)}ds (3.3) S 2 S S 1 +S 2 { B( r) n( r)}ds = 0 (3.4) S 1, S 2 { B( r) n( r)}ds
127 3 II 3.1 3.1.1 Φ(t) ϕ em = dφ dt (3.1) B( r) Φ = { B( r) n( r)}ds (3.2) S S n( r) Φ 128 3 II S 1, S 2 Φ 1, Φ 2 Φ 1 = { B( r) n( r)}ds S 1 Φ 2 = { B( r) n( r)}ds (3.3) S 2 S S 1 +S 2 { B( r) n( r)}ds
C: PC H19 A5 2.BUN Ohm s law
C: PC H19 A5 2.BUN 19 8 6 3 19 3.1........................... 19 3.2 Ohm s law.................... 21 3.3.......................... 24 4 26 4.1................................. 26 4.2.................................
e a b a b b a a a 1 a a 1 = a 1 a = e G G G : x ( x =, 8, 1 ) x 1,, 60 θ, ϕ ψ θ G G H H G x. n n 1 n 1 n σ = (σ 1, σ,..., σ N ) i σ i i n S n n = 1,,
01 10 18 ( ) 1 6 6 1 8 8 1 6 1 0 0 0 0 1 Table 1: 10 0 8 180 1 1 1. ( : 60 60 ) : 1. 1 e a b a b b a a a 1 a a 1 = a 1 a = e G G G : x ( x =, 8, 1 ) x 1,, 60 θ, ϕ ψ θ G G H H G x. n n 1 n 1 n σ = (σ 1,
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[ ] [ ] [ ] [ ] [ ] [ ] ADC BS1 m1 PMT m2 BS2 PMT1 PMT ADC PMT2 α PMT α α = n ω n n Pn TMath::Poisson(x,[0]) 0.35 0.3 0.25 0.2 0.15 λ 1.5 ω n 2 = ( α 2 ) n n! e α 2 α 2 = λ = λn n! e λ Poisson Pn 0.1
http://www.ns.kogakuin.ac.jp/~ft13389/lecture/physics1a2b/ pdf I 1 1 1.1 ( ) 1. 30 m µm 2. 20 cm km 3. 10 m 2 cm 2 4. 5 cm 3 km 3 5. 1 6. 1 7. 1 1.2 ( ) 1. 1 m + 10 cm 2. 1 hr + 6400 sec 3. 3.0 10 5 kg
II (No.2) 2 4,.. (1) (cm) (2) (cm) , (
II (No.1) 1 x 1, x 2,..., x µ = 1 V = 1 k=1 x k (x k µ) 2 k=1 σ = V. V = σ 2 = 1 x 2 k µ 2 k=1 1 µ, V σ. (1) 4, 7, 3, 1, 9, 6 (2) 14, 17, 13, 11, 19, 16 (3) 12, 21, 9, 3, 27, 18 (4) 27.2, 29.3, 29.1, 26.0,
TOP 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.............................
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n n (n) (n) (n) (n) n n ( n) n n n n n en1, en ( n) nen1 + nen nen1, nen ( ) e + e ( ) ( ) e + e () ( ) e e Τ ( ) e e ( ) ( ) () () ( ) ( ) ( ) ( ) ( n) Τ n n n ( n) n + n ( n) (n) n + n n n n n n n n
(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
1. 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
![1. 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](/thumbs/101/149329485.jpg "1. 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()
[Ver. 0.2] 1 2 3 4 5 6 7 1 1.1 1.2 1.3 1.4 1.5 1 1.1 1 1.2 1. (elasticity) 2. (plasticity) 3. (strength) 4. 5. (toughness) 6. 1 1.2 1. (elasticity) } 1 1.2 2. (plasticity), 1 1.2 3. (strength) a < b F
50 2 I SI MKSA r q r q F F = 1 qq 4πε 0 r r 2 r r r r (2.2 ε 0 = 1 c 2 µ 0 c = m/s q 2.1 r q' F r = 0 µ 0 = 4π 10 7 N/A 2 k = 1/(4πε 0 qq
49 2 I II 2.1 3 e e = 1.602 10 19 A s (2.1 50 2 I SI MKSA 2.1.1 r q r q F F = 1 qq 4πε 0 r r 2 r r r r (2.2 ε 0 = 1 c 2 µ 0 c = 3 10 8 m/s q 2.1 r q' F r = 0 µ 0 = 4π 10 7 N/A 2 k = 1/(4πε 0 qq F = k r
) 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
positron 1930 Dirac 1933 Anderson m 22Na(hl=2.6years), 58Co(hl=71days), 64Cu(hl=12hour) 68Ge(hl=288days) MeV : thermalization m psec 100
positron 1930 Dirac 1933 Anderson m 22Na(hl=2.6years), 58Co(hl=71days), 64Cu(hl=12hour) 68Ge(hl=288days) 0.5 1.5MeV : thermalization 10 100 m psec 100psec nsec E total = 2mc 2 + E e + + E e Ee+ Ee-c mc
Part () () Γ Part ,
Contents a 6 6 6 6 6 6 6 7 7. 8.. 8.. 8.3. 8 Part. 9. 9.. 9.. 3. 3.. 3.. 3 4. 5 4.. 5 4.. 9 4.3. 3 Part. 6 5. () 6 5.. () 7 5.. 9 5.3. Γ 3 6. 3 6.. 3 6.. 3 6.3. 33 Part 3. 34 7. 34 7.. 34 7.. 34 8. 35
2.2 h h l L h L = l cot h (1) (1) L l L l l = L tan h (2) (2) L l 2 l 3 h 2.3 a h a h (a, h)
1 16 10 5 1 2 2.1 a a a 1 1 1 2.2 h h l L h L = l cot h (1) (1) L l L l l = L tan h (2) (2) L l 2 l 3 h 2.3 a h a h (a, h) 4 2 3 4 2 5 2.4 x y (x,y) l a x = l cot h cos a, (3) y = l cot h sin a (4) h a
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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
21 2 26 i 1 1 1.1............................ 1 1.2............................ 3 2 9 2.1................... 9 2.2.......... 9 2.3................... 11 2.4....................... 12 3 15 3.1..........
No δs δs = r + δr r = δr (3) δs δs = r r = δr + u(r + δr, t) u(r, t) (4) δr = (δx, δy, δz) u i (r + δr, t) u i (r, t) = u i x j δx j (5) δs 2
No.2 1 2 2 δs δs = r + δr r = δr (3) δs δs = r r = δr + u(r + δr, t) u(r, t) (4) δr = (δx, δy, δz) u i (r + δr, t) u i (r, t) = u i δx j (5) δs 2 = δx i δx i + 2 u i δx i δx j = δs 2 + 2s ij δx i δx j
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38 5 Cauchy.,,,,., σ.,, 3,,. 5.1 Cauchy (a) (b) (a) (b) 5.1: 5.1. Cauchy 39 F Q Newton F F F Q F Q 5.2: n n ds df n ( 5.1). df n n df(n) df n, t n. t n = df n (5.1) ds 40 5 Cauchy t l n mds df n 5.3: t
A (1) = 4 A( 1, 4) 1 A 4 () = tan A(0, 0) π A π
4 4.1 4.1.1 A = f() = f() = a f (a) = f() (a, f(a)) = f() (a, f(a)) f(a) = f 0 (a)( a) 4.1 (4, ) = f() = f () = 1 = f (4) = 1 4 4 (4, ) = 1 ( 4) 4 = 1 4 + 1 17 18 4 4.1 A (1) = 4 A( 1, 4) 1 A 4 () = tan
t = 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)
Note.tex 2008/09/19( )
1 20 9 19 2 1 5 1.1........................ 5 1.2............................. 8 2 9 2.1............................. 9 2.2.............................. 10 3 13 3.1.............................. 13 3.2..................................
基礎数学I
I & II ii ii........... 22................. 25 12............... 28.................. 28.................... 31............. 32.................. 34 3 1 9.................... 1....................... 1............
『共形場理論』
T (z) SL(2, C) T (z) SU(2) S 1 /Z 2 SU(2) (ŜU(2) k ŜU(2) 1)/ŜU(2) k+1 ŜU(2)/Û(1) G H N =1 N =1 N =1 N =1 N =2 N =2 N =2 N =2 ĉ>1 N =2 N =2 N =4 N =4 1 2 2 z=x 1 +ix 2 z f(z) f(z) 1 1 4 4 N =4 1 = = 1.3
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( ) Note 3 19 12 13 8 8.1 (e ) (µ ) (τ ) ( (ν e,e ) e- (ν µ, µ ) µ- (ν τ,τ ) τ- ) ( ) ( ) (SU(2) ) (W +,Z 0,W ) * 1) 3 * 2) [ ] [ ] [ ] ν e ν µ ν τ e µ τ, e R, µ R, τ R (1a) L ( ) ) * 3) W Z 1/2 ( - )
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,
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 +
最新耐震構造解析 ( 第 3 版 ) 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. このサンプルページの内容は, 第 3 版 1 刷発行時のものです.
最新耐震構造解析 ( 第 3 版 ) 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/052093 このサンプルページの内容は, 第 3 版 1 刷発行時のものです. i 3 10 3 2000 2007 26 8 2 SI SI 20 1996 2000 SI 15 3 ii 1 56 6
6 2 T γ T B (6.4) (6.1) [( d nm + 3 ] 2 nt B )a 3 + nt B da 3 = 0 (6.9) na 3 = T B V 3/2 = T B V γ 1 = const. or T B a 2 = const. (6.10) H 2 = 8π kc2
![6 2 T γ T B (6.4) (6.1) [( d nm + 3 ] 2 nt B )a 3 + nt B da 3 = 0 (6.9) na 3 = T B V 3/2 = T B V γ 1 = const. or T B a 2 = const. (6.10) H 2 = 8π kc2](/thumbs/92/109118076.jpg "6 2 T γ T B (6.4) (6.1) [( d nm + 3 ] 2 nt B )a 3 + nt B da 3 = 0 (6.9) na 3 = T B V 3/2 = T B V γ 1 = const. or T B a 2 = const. (6.10) H 2 = 8π kc2")
1 6 6.1 (??) (P = ρ rad /3) ρ rad T 4 d(ρv ) + PdV = 0 (6.1) dρ rad ρ rad + 4 da a = 0 (6.2) dt T + da a = 0 T 1 a (6.3) ( ) n ρ m = n (m + 12 ) m v2 = n (m + 32 ) T, P = nt (6.4) (6.1) d [(nm + 32 ] )a
II R n k +1 v 0,, v k k v 1 v 0,, v k v v 0,, v k R n 1 a 0,, a k a 0 v 0 + a k v k v 0 v k k k v 0,, v k σ k σ dimσ = k 1.3. k
II 231017 1 1.1. R n k +1 v 0,, v k k v 1 v 0,, v k v 0 1.2. v 0,, v k R n 1 a 0,, a k a 0 v 0 + a k v k v 0 v k k k v 0,, v k σ kσ dimσ = k 1.3. k σ {v 0,...,v k } {v i0,...,v il } l σ τ < τ τ σ 1.4.
II Time-stamp: <05/09/30 17:14:06 waki> ii
II waki@cc.hirosaki-u.ac.jp 18 1 30 II Time-stamp: ii 1 1 1.1.................................................. 1 1.2................................................... 3 1.3..................................................
1 (1) () (3) I 0 3 I I d θ = L () dt θ L L θ I d θ = L = κθ (3) dt κ T I T = π κ (4) T I κ κ κ L l a θ L r δr δl L θ ϕ ϕ = rθ (5) l
1 1 ϕ ϕ ϕ S F F = ϕ (1) S 1: F 1 1 (1) () (3) I 0 3 I I d θ = L () dt θ L L θ I d θ = L = κθ (3) dt κ T I T = π κ (4) T I κ κ κ L l a θ L r δr δl L θ ϕ ϕ = rθ (5) l : l r δr θ πrδr δf (1) (5) δf = ϕ πrδr
