ρ ( ) sgv + ρwgv γ sv + γ wv γ s + γ w e e γ ρ g s s γ s ( ) + γ w( ) Vs + V Vs + V + e + e + e γ γ sa γ e e n( ) + e γ γ s ( n) + γ wn γ s, γ w γ γ +

Size: px
Start display at page:

Download "ρ ( ) sgv + ρwgv γ sv + γ wv γ s + γ w e e γ ρ g s s γ s ( ) + γ w( ) Vs + V Vs + V + e + e + e γ γ sa γ e e n( ) + e γ γ s ( n) + γ wn γ s, γ w γ γ +"

Transcription

1 σ P σ () n σ () n σ P ) σ ( σ P σ σ σ + u V e m w ρ w gv V V s m s ρ s gv s

2 ρ ( ) sgv + ρwgv γ sv + γ wv γ s + γ w e e γ ρ g s s γ s ( ) + γ w( ) Vs + V Vs + V + e + e + e γ γ sa γ e e n( ) + e γ γ s ( n) + γ wn γ s, γ w γ γ + γ w σ σ + u γ we we w waer γ σ γ γ sa oal, γ T W T W V V V W s W W γ V γ wv W W γ V γ wv ( γ γ w) V γ V γ γ γ w V γ W W ( γ w γ w) V + ( γ s γ w) Vs ( γ s γ w) Vs

3 W V s γ s γ ( γ w s γ w) ( γ s γ w)( ) V V + e + e + e γ s e γ w e γ w γ + w + e + e + e + e γ γ w γ γ V W W γ V ( γ + γ w) V γ V + γ wv V γ V V γ wv V γ d h u γ w h A A A γ A σ γ σ γ γ + γ w σ + u u u γ w

4 σ γ σ γ d σ γ + γ w d γ + γ w + γ w d γ + γ w ( + d) γ w ( + d) u σ σ + u σ u σ γ σ γ u γ w u γ w ( + d) σ P A area ~ A A ~ σ γ γ + γ w σ + u

5 σ σ ~ γ ( ) + + γ w ~ γ ( ) + γ w ( ) + + γ w ~ γ ( ) + + γ w ~ γ ~ γ γ w u σ σ ~γ ( ) + ~ γ γ σ γ + σ ~ A ~ A A ~ σ ~ γ ( ~ ) + + γ w ~ γ ( ~ ) + γ w ( ~ ) + + γ w ~ γ ( ~ ) + + γ ~ w γ ~ w u A ~ σ σ ~γ ( ~ ) + γ γ ~ γ ~ γ ( ~ ) σ γ + A A ~ σ u σ γ σ γ + u γ w u γ ~ w

6 P A area P A area ~ A A A ~ A A ~ σ u σ γ σ γ σ γ + u γ w u γ w ~ + u γ ~ w

7 σ γ σ γ + γ w d d γ w d σ ( ) γ σ ( ) γ γ w d d σ () dσ σ ( ) + d σ ( ) γ d d γ d + d dσ γ σ ( + d) d dσ σ ( ) + d d σ ( ) γ + C σ ( ) C σ ( ) γ w d σ ( ) γ + γ w d

8 γ γ γ sa 3kN/m 3kN/m 3 σ 6kN / m γ kn / m 3 γ 3 w kn/m 3 σ 9 (m) γ 3 5kN / m 3 γ kn / m u σ 9 σ 5kN / m σ kn / m σ u d u σ u σ 9 (m)

9 P d k ( P / A) ( k d / A)

10 P P kx σ Eε k σ E x ε m ε m ε ε log ) m ε e e e ( V V ) ( e e ) ε V + e

11 log e e e e Cc log e a C c a elog Cc a elog m a m ( e e ) e ε ε m ε + e + e e m ε a + e + e e m ( d) dε m d dε m d m dσ Teraghi m K E dσ E dε dε m d ( m dσ ) G dτ G dγ dε m dσ m K dσ m K dε SI kn/m (kpa), MN/m (MPa) SI m / kn(kpa - ), m /MN (MPa - )

12 elog e log c C s C s C c c Casagrande Virgin Comression line

13 A D B O C E F O A A A O A B C OC C B B D E OF OE EF

14 9 e- log c

15 f U ρ ρ ) ( ) ( ) ( U f ρ ( ρ f ρ ( ρ (m)

16 ρ f m σ ρ f εd m σ d m d m : σ ε m e ~ log e c log e e e Cs e C c e log c e e Cc log C s < c e e Cs log Cc C c Cs C s Cs e ~ log Cs

17 e V V V ( + e ) ( + e) e e ( e e ) e e V e ε ε V + e V V e e ε e e e f d d V + e ρ ε + e + e de dε + e c e e Cc log e e Cc log( + ) + e e e Cc log + Cc log( + ) Cc log e C d c + ρ f log d + e + e ρ f C c log + + e ) e e ( c V + e V + e e e e

18 + c C c C s C log s + ρ f ( + c ) + e < c + > c e c + log e e e e Cs log e ( e ) + e e ρ f + e Cs + log c e Cc + e log C c log { C c s + Cc c c + } e c c e e c e e e m, C c, Cs ρ( U ( ρ f ρ f U ( ρ( ρ f ρ f

19 ε h k u k ( ) w γ ε k γ w u ε σ dε m dσ m σ σ u ( + ) σ u ε u m u u k c ( c ) mγ w σ (, σ σ / σ / σ σ u σ u h + γ w γ w i k i

20 k w σ γ σ ε d m d m σ ε m k w ε γ ε ) ( m k w ε γ ε w c m k γ c ε ε ) ( ), ( ), ( P u + σ ) ( P P u + ) ( σ + u σ σ + u σ c ε ε m σ ε c σ σ ) ( u c P u ), ( ) ( ), ( V P u + V u V P u + ) ( V c V

21 u u u u u u u u u u c u(, Z( ) T ( Z( ) T ( c Z ( ) T ( T ( Z ( ) cons. ( A ) c T ( Z( ), T ( A ct( Z ( ) A Z( ) T ( C ex( A c Z ( ) C cos A + C3 sin A u u(, ( C4 cos A + C5 sin A) ex( A c u(, u(, u(, C4 ex( A c C u(, C5 sin A ex( A c sin A n A n A 4

22 n n u(, C sin ex( c n n n u(, Bn sin ex( c n B n u (,) P n u(,) Bn sin P n n sin {( n n n n Bn sin )sin } d ( P sin ) d n n n ( Bn sin sin ) d ( P sin ) n Bn ( P sin ) d d * sinmxsinnxdx δ δ mn mn ( m n ) ( m n ) B n n P n P d ( sin ) cos n n ( ) {( ) } P n P n+ {( ) + } n P (, ) n n n u + {( ) + }sin ex( c n n 4P (m + ) (m + ) sin ex( c ( ) m m +

23 u u c u(, ( C cos A + C sin A) ex( A c u(, u(, u(, C ex( A c C u(, AC cos A ex( A c cos A n ( n ) A A (n ) (n ) (n ) {( Bn sin )sin } d ( P sin ) d n (n ) (n ) u(, C sin ex( c 4 (n ) (n ) u(, B n Bn sin ex( c n n 4 (n ) u (,) P u(,) Bn sin P n (n ) sin (n ) Bn sin d (n ) P sin d B n u (n ) Bn ( P sin P ) d (n ) 4P B n (n ) 4P ( ) ( ) (, ) n n u sin ex( c ( ) n n 4 4P (n + ) (n + ) sin ex( c ( ) n n + 4

24 P M c sin ex( P ) M sin MZ ex( M T ) n M n M ( n + ) c M T Z u(, u(, u(, C ex( A c C u(, C sin A ex( A c sin A n A n A n n ) u(, Bn sin ex( c n 4 n u (,) P u(,) Bn sin P n n sin n n n {( Bn sin )sin } d ( P sin ) d n Bn sin n d n P sin d P n+ Bn {( ) + } P n+ Bn {( ) } n n + P (, ) n n n u + {( ) + }sin ex( c n n 4 m c 4P (m + ) (m + ) sin ex( (m + ) 4 ( n + ) c M T Z P sin MZ ex( M T n M ) )

25 u u u c u(, u(, h k u ki k γ w Teraghi u (,)

26 u u u(, c u(, u (,) u(, n P M sin MZ ex( M ( n + ) T ) M T c Z u / Z / T. u / T. T T Z /

27 ) 4 ) ( ex( ) ( sin ), ( c n n B u n n ) ( 4 n B n n B u n n ) ( sin,) ( M M B n B n B n 5 sin sin 3 3 sin sin sin 4 sin n n n n3 n5 n u n5.6 ) ( sin 4 λ 3 4 λ 5 4 λ

28 n (n ) ex( c 3 λ 4 4 ex( λn T ) λn ( n ) 4 λ λ 9 λ 5 64 M T n c 4 sin ex( 4 T ) n ) ex( λn T 4 T c T k c c m γ w k m

29 ρ( U ρ f ε(, m σ (, m { P( u(, } P( ρ ( ε(, d m { P( u(, } d m P( m u(, d f u(, ) ρ m P P P ( ) P P P ρ f ρ P( P ( > ) ρ( m P m u(, d ρ f m u(, d U ρ f m u(, d ρ( U m u(, d / mp u(, d ρ f ρ f P ) P Teraghi u(, sin MZ ex( M T ) n M u(, d U ( T ) P ex( M M n n M T ) ex( M T )

30 U ( T ) ex( M T ) n M T 5% 9% U(%) U(%) T c * UT T c T T c m c. - (cm /s) 9% T (sec) 49(days). c T cm cm m 8% 3 8% c 3 c T 3 (min) 5.7(years)

31 d 6cm, cm 9.8, 9.6, 39., 78.5, 57, 34, 68, 56 kn/m 6, 9,, 8, 3, 4sec,,.5,, 3, 5, 7,, 5,, 3, 4min,,.5,, 3, 6,, 4 hrs

32 elog ) P c C c c m ε m ε / k c m γ w Cc c

33 log d d d d9 d

34

untitled

untitled 9118 154 B-1 B-3 B- 5cm 3cm 5cm 3m18m5.4m.5m.66m1.3m 1.13m 1.134m 1.35m.665m 5 , 4 13 7 56 M 1586.1.18 7.77.9 599.5.8 7 1596.9.5 7.57.75 684.11.9 8.5 165..3 7.9 87.8.11 6.57. 166.6.16 7.57.6 856 6.6.5

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

(1.2) 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 information

all.dvi

all.dvi 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

More information

[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

More information

66 σ σ (8.1) σ = 0 0 σd = 0 (8.2) (8.2) (8.1) E ρ d = 0... d = 0 (8.3) d 1 NN K K 8.1 d σd σd M = σd = E 2 d (8.4) ρ 2 d = I M = EI ρ 1 ρ = M EI ρ EI

66 σ σ (8.1) σ = 0 0 σd = 0 (8.2) (8.2) (8.1) E ρ d = 0... d = 0 (8.3) d 1 NN K K 8.1 d σd σd M = σd = E 2 d (8.4) ρ 2 d = I M = EI ρ 1 ρ = M EI ρ EI 65 8. K 8 8 7 8 K 6 7 8 K 6 M Q σ (6.4) M O ρ dθ D N d N 1 P Q B C (1 + ε)d M N N h 2 h 1 ( ) B (+) M 8.1: σ = E ρ (E, 1/ρ ) (8.1) 66 σ σ (8.1) σ = 0 0 σd = 0 (8.2) (8.2) (8.1) E ρ d = 0... d = 0 (8.3)

More information

untitled

untitled GeoFem 1 1.1 1 1.2 1 1.3 1 2 2.1 2 2.2 3 2.3 FEM 5 (1) 5 (2) 5 (3) 6 2.4 GeoFem 7 2.5 FEM 16 2.6 19 2.7 26 3.1 33 3.2 35 3.3 GeoFem 36 3.4 48 3.5 49 A A1 A2 A3 A4 A5 A6 A7 GeoFem GeoFem CRS GeoFem GeoFem

More information

NETES No.CG V

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

More information

y = x x R = 0. 9, R = σ $ = y x w = x y x x w = x y α ε = + β + x x x y α ε = + β + γ x + x x x x' = / x y' = y/ x y' =

y = x x R = 0. 9, R = σ $ = y x w = x y x x w = x y α ε = + β + x x x y α ε = + β + γ x + x x x x' = / x y' = y/ x y' = y x = α + β + ε =,, ε V( ε) = E( ε ) = σ α $ $ β w ( 0) σ = w σ σ y α x ε = + β + w w w w ε / w ( w y x α β ) = α$ $ W = yw βwxw $β = W ( W) ( W)( W) w x x w x x y y = = x W y W x y x y xw = y W = w w

More information

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

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

More information

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)

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

More information

(1) 1.1

(1) 1.1 1 1 1.1 1.1.1 1.1 ( ) ( ) ( ) { ( ) ( ) { ( ) ( ) { ( ) ( ) { ( ) ( ) { ( ) ( ) ( ) ( ) ( ) 2 1 1.1.2 (1) 1.1 1.1 3 (2) 1.2 4 1 (3) 1.3 ( ) ( ) (4) 1.1 5 (5) ( ) 1.4 6 1 (6) 1.5 (7) ( ) (8) 1.1 7 1.1.3

More information

1 I 1.1 ± e = = - = C C MKSA [m], [Kg] [s] [A] 1C 1A 1 MKSA 1C 1C +q q +q q 1

1 I 1.1 ± e = = - = C C MKSA [m], [Kg] [s] [A] 1C 1A 1 MKSA 1C 1C +q q +q q 1 1 I 1.1 ± e = = - =1.602 10 19 C C MKA [m], [Kg] [s] [A] 1C 1A 1 MKA 1C 1C +q q +q q 1 1.1 r 1,2 q 1, q 2 r 12 2 q 1, q 2 2 F 12 = k q 1q 2 r 12 2 (1.1) k 2 k 2 ( r 1 r 2 ) ( r 2 r 1 ) q 1 q 2 (q 1 q 2

More information

: , 2.0, 3.0, 2.0, (%) ( 2.

: , 2.0, 3.0, 2.0, (%) ( 2. 2017 1 2 1.1...................................... 2 1.2......................................... 4 1.3........................................... 10 1.4................................. 14 1.5..........................................

More information

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.   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

More information

橡博論表紙.PDF

橡博論表紙.PDF 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

More information

v v = v 1 v 2 v 3 (1) R = (R ij ) (2) R (R 1 ) ij = R ji (3) 3 R ij R ik = δ jk (4) i=1 δ ij Kronecker δ ij = { 1 (i = j) 0 (i

v v = v 1 v 2 v 3 (1) R = (R ij ) (2) R (R 1 ) ij = R ji (3) 3 R ij R ik = δ jk (4) i=1 δ ij Kronecker δ ij = { 1 (i = j) 0 (i 1. 1 1.1 1.1.1 1.1.1.1 v v = v 1 v 2 v 3 (1) R = (R ij ) (2) R (R 1 ) ij = R ji (3) R ij R ik = δ jk (4) δ ij Kronecker δ ij = { 1 (i = j) 0 (i j) (5) 1 1.1. v1.1 2011/04/10 1. 1 2 v i = R ij v j (6) [

More information

TOP URL 1

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.............................

More information

V(x) m e V 0 cos x π x π V(x) = x < π, x > π V 0 (i) x = 0 (V(x) V 0 (1 x 2 /2)) n n d 2 f dξ 2ξ d f 2 dξ + 2n f = 0 H n (ξ) (ii) H

V(x) m e V 0 cos x π x π V(x) = x < π, x > π V 0 (i) x = 0 (V(x) V 0 (1 x 2 /2)) n n d 2 f dξ 2ξ d f 2 dξ + 2n f = 0 H n (ξ) (ii) H 199 1 1 199 1 1. Vx) m e V cos x π x π Vx) = x < π, x > π V i) x = Vx) V 1 x /)) n n d f dξ ξ d f dξ + n f = H n ξ) ii) H n ξ) = 1) n expξ ) dn dξ n exp ξ )) H n ξ)h m ξ) exp ξ )dξ = π n n!δ n,m x = Vx)

More information

土木工事共通仕様書(その2)

土木工事共通仕様書(その2) 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 1 2 3 22 578 582 27 4 5 6 567 7 21 8 9 (9), 10 11 12 13 14 (1) (2) 16 532 35 15 (3) (4) (1) (1) 16 (4) () () () 17 () 18 170 19 20 21 10 22 23 24 25 26 27

More information

http://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 information

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 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

More information

all.dvi

all.dvi 72 9 Hooke,,,. Hooke. 9.1 Hooke 1 Hooke. 1, 1 Hooke. σ, ε, Young. σ ε (9.1), Young. τ γ G τ Gγ (9.2) X 1, X 2. Poisson, Poisson ν. ν ε 22 (9.) ε 11 F F X 2 X 1 9.1: Poisson 9.1. Hooke 7 Young Poisson G

More information

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

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. +

More information

LLG-R8.Nisus.pdf

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 =

More information

8 300 mm 2.50 m/s L/s ( ) 1.13 kg/m MPa 240 C 5.00mm 120 kpa ( ) kg/s c p = 1.02kJ/kgK, R = 287J/kgK kPa, 17.0 C 118 C 870m 3 R = 287J

8 300 mm 2.50 m/s L/s ( ) 1.13 kg/m MPa 240 C 5.00mm 120 kpa ( ) kg/s c p = 1.02kJ/kgK, R = 287J/kgK kPa, 17.0 C 118 C 870m 3 R = 287J 26 1 22 10 1 2 3 4 5 6 30.0 cm 1.59 kg 110kPa, 42.1 C, 18.0m/s 107kPa c p =1.02kJ/kgK 278J/kgK 30.0 C, 250kPa (c p = 1.02kJ/kgK, R = 287J/kgK) 18.0 C m/s 16.9 C 320kPa 270 m/s C c p = 1.02kJ/kgK, R = 292J/kgK

More information

29 4 ... 1... 1... 1... 2... 3... 4.... 4... 4... 7... 8... 8... 8... 8...12...14...14...14...16...18...18...19...21... 42...42...42....42....46....49...51....51....51... 52...52...52...53 I. I. I. I.

More information

29

29 9 .,,, 3 () C k k C k C + C + C + + C 8 + C 9 + C k C + C + C + C 3 + C 4 + C 5 + + 45 + + + 5 + + 9 + 4 + 4 + 5 4 C k k k ( + ) 4 C k k ( k) 3 n( ) n n n ( ) n ( ) n 3 ( ) 3 3 3 n 4 ( ) 4 4 4 ( ) n n

More information

meiji_resume_1.PDF

meiji_resume_1.PDF β β β (q 1,q,..., q n ; p 1, p,..., p n ) H(q 1,q,..., q n ; p 1, p,..., p n ) Hψ = εψ ε k = k +1/ ε k = k(k 1) (x, y, z; p x, p y, p z ) (r; p r ), (θ; p θ ), (ϕ; p ϕ ) ε k = 1/ k p i dq i E total = E

More information

PowerPoint プレゼンテーション

PowerPoint プレゼンテーション 003.10.3 003.10.8 Y 1 0031016 B4(4 3 B4,1 M 0 C,Q 0. M,Q 1.- MQ 003/10/16 10/8 Girder BeamColumn Foundation SlabWall Girder BeamColumn Foundation SlabWall 1.-1 5mm 0 kn/m 3 0.05m=0.5 kn/m 60mm 18 kn/m

More information

1 y(t)m b k u(t) ẋ = [ 0 1 k m b m x + [ 0 1 m u, x = [ ẏ y (1) y b k m u

1 y(t)m b k u(t) ẋ = [ 0 1 k m b m x + [ 0 1 m u, x = [ ẏ y (1) y b k m u ( ) LPV( ) 1 y(t)m b k u(t) ẋ = [ 0 1 k m b m x + [ 0 1 m u, x = [ ẏ y (1) y b k m u m 1 m m 2, b 1 b b 2, k 1 k k 2 (2) [m b k ( ) k 0 b m ( ) 2 ẋ = Ax, x(0) 0 (3) (x(t) 0) ( ) V (x) V (x) = x T P x >

More information

untitled

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 =

More information

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.   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)

More information

n 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 information

The Physics of Atmospheres CAPTER :

The 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 information

c y /2 ddy = = 2π sin θ /2 dθd /2 [ ] 2π cos θ d = log 2 + a 2 d = log 2 + a 2 = log 2 + a a 2 d d + 2 = l

c y /2 ddy = = 2π sin θ /2 dθd /2 [ ] 2π cos θ d = log 2 + a 2 d = log 2 + a 2 = log 2 + a a 2 d d + 2 = l c 28. 2, y 2, θ = cos θ y = sin θ 2 3, y, 3, θ, ϕ = sin θ cos ϕ 3 y = sin θ sin ϕ 4 = cos θ 5.2 2 e, e y 2 e, e θ e = cos θ e sin θ e θ 6 e y = sin θ e + cos θ e θ 7.3 sgn sgn = = { = + > 2 < 8.4 a b 2

More information

pdf

pdf 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

More information

( ) e + e ( ) ( ) e + e () ( ) e e Τ ( ) e e ( ) ( ) () () ( ) ( ) ( ) ( )

( ) e + e ( ) ( ) e + e () ( ) e e Τ ( ) e e ( ) ( ) () () ( ) ( ) ( ) ( ) 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

More information

( ) Note (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

( ) Note (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 ( ) 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 ( - )

More information

数学の基礎訓練I

数学の基礎訓練I I 9 6 13 1 1 1.1............... 1 1................ 1 1.3.................... 1.4............... 1.4.1.............. 1.4................. 3 1.4.3........... 3 1.4.4.. 3 1.5.......... 3 1.5.1..............

More information

f(x) = f(x ) + α(x)(x x ) α(x) x = x. x = f (y), x = f (y ) y = f f (y) = f f (y ) + α(f (y))(f (y) f (y )) f (y) = f (y ) + α(f (y)) (y y ) ( (2) ) f

f(x) = f(x ) + α(x)(x x ) α(x) x = x. x = f (y), x = f (y ) y = f f (y) = f f (y ) + α(f (y))(f (y) f (y )) f (y) = f (y ) + α(f (y)) (y y ) ( (2) ) f 22 A 3,4 No.3 () (2) (3) (4), (5) (6) (7) (8) () n x = (x,, x n ), = (,, n ), x = ( (x i i ) 2 ) /2 f(x) R n f(x) = f() + i α i (x ) i + o( x ) α,, α n g(x) = o( x )) lim x g(x) x = y = f() + i α i(x )

More information

³ÎΨÏÀ

³ÎΨÏÀ 2017 12 12 Makoto Nakashima 2017 12 12 1 / 22 2.1. C, D π- C, D. A 1, A 2 C A 1 A 2 C A 3, A 4 D A 1 A 2 D Makoto Nakashima 2017 12 12 2 / 22 . (,, L p - ). Makoto Nakashima 2017 12 12 3 / 22 . (,, L p

More information

all.dvi

all.dvi 5,, Euclid.,..,... Euclid,.,.,, e i (i =,, ). 6 x a x e e e x.:,,. a,,. a a = a e + a e + a e = {e, e, e } a (.) = a i e i = a i e i (.) i= {a,a,a } T ( T ),.,,,,. (.),.,...,,. a 0 0 a = a 0 + a + a 0

More information

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 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

More information

I

I I 6 4 10 1 1 1.1............... 1 1................ 1 1.3.................... 1.4............... 1.4.1.............. 1.4................. 1.4.3........... 3 1.4.4.. 3 1.5.......... 3 1.5.1..............

More information

Note.tex 2008/09/19( )

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..................................

More information

19 σ = P/A o σ B Maximum tensile strength σ % 0.2% proof stress σ EL Elastic limit Work hardening coefficient failure necking σ PL Proportional

19 σ = P/A o σ B Maximum tensile strength σ % 0.2% proof stress σ EL Elastic limit Work hardening coefficient failure necking σ PL Proportional 19 σ = P/A o σ B Maximum tensile strength σ 0. 0.% 0.% proof stress σ EL Elastic limit Work hardening coefficient failure necking σ PL Proportional limit ε p = 0.% ε e = σ 0. /E plastic strain ε = ε e

More information

211 kotaro@math.titech.ac.jp 1 R *1 n n R n *2 R n = {(x 1,..., x n ) x 1,..., x n R}. R R 2 R 3 R n R n R n D D R n *3 ) (x 1,..., x n ) f(x 1,..., x n ) f D *4 n 2 n = 1 ( ) 1 f D R n f : D R 1.1. (x,

More information

,,..,. 1

,,..,. 1 016 9 3 6 0 016 1 0 1 10 1 1 17 1..,,..,. 1 1 c = h = G = ε 0 = 1. 1.1 L L T V 1.1. T, V. d dt L q i L q i = 0 1.. q i t L q i, q i, t L ϕ, ϕ, x µ x µ 1.3. ϕ x µ, L. S, L, L S = Ld 4 x 1.4 = Ld 3 xdt 1.5

More information

2003 12 11 1 http://www.sml.k.u-tokyo.ac.jp/members/nabe/lecture2003 http://www.sml.k.u-tokyo.ac.jp/members/nabe/lecture2002 nabe@sml.k.u-tokyo.ac.jp 2 1. 10/ 9 2. 10/16 3. 10/23 ( ) 4. 10/30 5. 11/ 6

More information

Γ Ec Γ V BIAS THBV3_0401JA THBV3_0402JAa THBV3_0402JAb 1000 800 600 400 50 % 25 % 200 100 80 60 40 20 10 8 6 4 10 % 2.5 % 0.5 % 0.25 % 2 1.0 0.8 0.6 0.4 0.2 0.1 200 300 400 500 600 700 800 1000 1200 14001600

More information

1 1.1 Excel Excel Excel log 1, log 2, log 3,, log 10 e = ln 10 log cm 1mm 1 10 =0.1mm = f(x) f(x) = n

1 1.1 Excel Excel Excel log 1, log 2, log 3,, log 10 e = ln 10 log cm 1mm 1 10 =0.1mm = f(x) f(x) = n 1 1.1 Excel Excel Excel log 1, log, log,, log e.7188188 ln log 1. 5cm 1mm 1 0.1mm 0.1 4 4 1 4.1 fx) fx) n0 f n) 0) x n n! n + 1 R n+1 x) fx) f0) + f 0) 1! x + f 0)! x + + f n) 0) x n + R n+1 x) n! 1 .

More information

( ) ± = 2018

( ) ± = 2018 30 ( 3 ) ( ) 2018 ( ) ± = 2018 (PDF ), PDF PDF. PDF, ( ), ( ),,,,., PDF,,. , 7., 14 (SSH).,,,.,,,.,., 1.. 2.,,. 3.,,. 4...,, 14 16, 17 21, 22 26, 27( ), 28 32 SSH,,,, ( 7 9 ), ( 14 16 SSH ), ( 17 21, 22

More information

Part () () Γ Part ,

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

More information

1 1.1 ( ). z = a + bi, a, b R 0 a, b 0 a 2 + b 2 0 z = a + bi = ( ) a 2 + b 2 a a 2 + b + b 2 a 2 + b i 2 r = a 2 + b 2 θ cos θ = a a 2 + b 2, sin θ =

1 1.1 ( ). z = a + bi, a, b R 0 a, b 0 a 2 + b 2 0 z = a + bi = ( ) a 2 + b 2 a a 2 + b + b 2 a 2 + b i 2 r = a 2 + b 2 θ cos θ = a a 2 + b 2, sin θ = 1 1.1 ( ). z = + bi,, b R 0, b 0 2 + b 2 0 z = + bi = ( ) 2 + b 2 2 + b + b 2 2 + b i 2 r = 2 + b 2 θ cos θ = 2 + b 2, sin θ = b 2 + b 2 2π z = r(cos θ + i sin θ) 1.2 (, ). 1. < 2. > 3. ±,, 1.3 ( ). A

More information

B

B B YES NO 5 7 6 1 4 3 2 BB BB BB AA AA BB 510J B B A 510J B A A A A A A 510J B A 510J B A A A A A 510J M = σ Z Z = M σ AAA π T T = a ZP ZP = a AAA π B M + M 2 +T 2 M T Me = = 1 + 1 + 2 2 M σ Te = M 2 +T

More information

1 12 *1 *2 (1991) (1992) (2002) (1991) (1992) (2002) 13 (1991) (1992) (2002) *1 (2003) *2 (1997) 1

1 12 *1 *2 (1991) (1992) (2002) (1991) (1992) (2002) 13 (1991) (1992) (2002) *1 (2003) *2 (1997) 1 2005 1 1991 1996 5 i 1 12 *1 *2 (1991) (1992) (2002) (1991) (1992) (2002) 13 (1991) (1992) (2002) *1 (2003) *2 (1997) 1 2 13 *3 *4 200 1 14 2 250m :64.3km 457mm :76.4km 200 1 548mm 16 9 12 589 13 8 50m

More information

/02/18

/02/18 3 09/0/8 i III,,,, III,?,,,,,,,,,,,,,,,,,,,,?,?,,,,,,,,,,,,,,!!!,? 3,,,, ii,,,!,,,, OK! :!,,,, :!,,,,,, 3:!,, 4:!,,,, 5:!,,! 7:!,,,,, 8:!,! 9:!,,,,,,,,, ( ),, :, ( ), ( ), 6:!,,, :... : 3 ( )... iii,,

More information

Q & A Q A p

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

More information

,. Black-Scholes u t t, x c u 0 t, x x u t t, x c u t, x x u t t, x + σ x u t, x + rx ut, x rux, t 0 x x,,.,. Step 3, 7,,, Step 6., Step 4,. Step 5,,.

,. Black-Scholes u t t, x c u 0 t, x x u t t, x c u t, x x u t t, x + σ x u t, x + rx ut, x rux, t 0 x x,,.,. Step 3, 7,,, Step 6., Step 4,. Step 5,,. 9 α ν β Ξ ξ Γ γ o δ Π π ε ρ ζ Σ σ η τ Θ θ Υ υ ι Φ φ κ χ Λ λ Ψ ψ µ Ω ω Def, Prop, Th, Lem, Note, Remark, Ex,, Proof, R, N, Q, C [a, b {x R : a x b} : a, b {x R : a < x < b} : [a, b {x R : a x < b} : a,

More information

1 12 ( )150 ( ( ) ) x M x 0 1 M 2 5x 2 + 4x + 3 x 2 1 M x M 2 1 M x (x + 1) 2 (1) x 2 + x + 1 M (2) 1 3 M (3) x 4 +

1 12 ( )150 ( ( ) ) x M x 0 1 M 2 5x 2 + 4x + 3 x 2 1 M x M 2 1 M x (x + 1) 2 (1) x 2 + x + 1 M (2) 1 3 M (3) x 4 + ( )5 ( ( ) ) 4 6 7 9 M M 5 + 4 + M + M M + ( + ) () + + M () M () 4 + + M a b y = a + b a > () a b () y V a () V a b V n f() = n k= k k () < f() = log( ) t dt log () n+ (i) dt t (n + ) (ii) < t dt n+ n

More information

基礎数学I

基礎数学I I & II ii ii........... 22................. 25 12............... 28.................. 28.................... 31............. 32.................. 34 3 1 9.................... 1....................... 1............

More information

23 1 Section ( ) ( ) ( 46 ) , 238( 235,238 U) 232( 232 Th) 40( 40 K, % ) (Rn) (Ra). 7( 7 Be) 14( 14 C) 22( 22 Na) (1 ) (2 ) 1 µ 2 4

23 1 Section ( ) ( ) ( 46 ) , 238( 235,238 U) 232( 232 Th) 40( 40 K, % ) (Rn) (Ra). 7( 7 Be) 14( 14 C) 22( 22 Na) (1 ) (2 ) 1 µ 2 4 23 1 Section 1.1 1 ( ) ( ) ( 46 ) 2 3 235, 238( 235,238 U) 232( 232 Th) 40( 40 K, 0.0118% ) (Rn) (Ra). 7( 7 Be) 14( 14 C) 22( 22 Na) (1 ) (2 ) 1 µ 2 4 2 ( )2 4( 4 He) 12 3 16 12 56( 56 Fe) 4 56( 56 Ni)

More information

chap9.dvi

chap9.dvi 9 AR (i) (ii) MA (iii) (iv) (v) 9.1 2 1 AR 1 9.1.1 S S y j = (α i + β i j) D ij + η j, η j = ρ S η j S + ε j (j =1,,T) (1) i=1 {ε j } i.i.d(,σ 2 ) η j (j ) D ij j i S 1 S =1 D ij =1 S>1 S =4 (1) y j =

More information

untitled

untitled 0 ( L CONTENTS 0 . sin(-x-sinx, (-x(x, sin(90-xx,(90-xsinx sin(80-xsinx,(80-x-x ( sin{90-(ωφ}(ωφ. :n :m.0 m.0 n tn. 0 n.0 tn ω m :n.0n tn n.0 tn.0 m c ω sinω c ω c tnω ecω sin ω ω sin c ω c ω tn c tn ω

More information

A = A x x + A y y + A, B = B x x + B y y + B, C = C x x + C y y + C..6 x y A B C = A x x + A y y + A B x B y B C x C y C { B = A x x + A y y + A y B B

A = A x x + A y y + A, B = B x x + B y y + B, C = C x x + C y y + C..6 x y A B C = A x x + A y y + A B x B y B C x C y C { B = A x x + A y y + A y B B 9 7 A = A x x + A y y + A, B = B x x + B y y + B, C = C x x + C y y + C..6 x y A B C = A x x + A y y + A B x B y B C x C y C { B = A x x + A y y + A y B B x x B } B C y C y + x B y C x C C x C y B = A

More information

TOP URL 1

TOP URL   1 TOP URL http://amonphys.web.fc2.com/ 1 30 3 30.1.............. 3 30.2........................... 4 30.3...................... 5 30.4........................ 6 30.5.................................. 8 30.6...............................

More information

TOP URL 1

TOP URL   1 TOP URL http://amonphys.web.fc.com/ 3.............................. 3.............................. 4.3 4................... 5.4........................ 6.5........................ 8.6...........................7

More information

(Compton Scattering) Beaming 1 exp [i (k x ωt)] k λ k = 2π/λ ω = 2πν k = ω/c k x ωt ( ω ) k α c, k k x ωt η αβ k α x β diag( + ++) x β = (ct, x) O O x

(Compton Scattering) Beaming 1 exp [i (k x ωt)] k λ k = 2π/λ ω = 2πν k = ω/c k x ωt ( ω ) k α c, k k x ωt η αβ k α x β diag( + ++) x β = (ct, x) O O x Compton Scattering Beaming exp [i k x ωt] k λ k π/λ ω πν k ω/c k x ωt ω k α c, k k x ωt η αβ k α x β diag + ++ x β ct, x O O x O O v k α k α β, γ k γ k βk, k γ k + βk k γ k k, k γ k + βk 3 k k 4 k 3 k

More information

IA hara@math.kyushu-u.ac.jp Last updated: January,......................................................................................................................................................................................

More information

[1.1] r 1 =10e j(ωt+π/4), r 2 =5e j(ωt+π/3), r 3 =3e j(ωt+π/6) ~r = ~r 1 + ~r 2 + ~r 3 = re j(ωt+φ) =(10e π 4 j +5e π 3 j +3e π 6 j )e jωt

[1.1] r 1 =10e j(ωt+π/4), r 2 =5e j(ωt+π/3), r 3 =3e j(ωt+π/6) ~r = ~r 1 + ~r 2 + ~r 3 = re j(ωt+φ) =(10e π 4 j +5e π 3 j +3e π 6 j )e jωt 3.4.7 [.] =e j(t+/4), =5e j(t+/3), 3 =3e j(t+/6) ~ = ~ + ~ + ~ 3 = e j(t+φ) =(e 4 j +5e 3 j +3e 6 j )e jt = e jφ e jt cos φ =cos 4 +5cos 3 +3cos 6 =.69 sin φ =sin 4 +5sin 3 +3sin 6 =.9 =.69 +.9 =7.74 [.]

More information

1

1 GL (a) (b) Ph l P N P h l l Ph Ph Ph Ph l l l l P Ph l P N h l P l .9 αl B βlt D E. 5.5 L r..8 e g s e,e l l W l s l g W W s g l l W W e s g e s g r e l ( s ) l ( l s ) r e l ( s ) l ( l s ) e R e r

More information

untitled

untitled .m 5m :.45.4m.m 3.m.6m (N/mm ).8.6 σ.4 h.m. h.68m h(m) b.35m θ4..5.5.5 -. σ ta.n/mm c 3kN/m 3 w 9.8kN/m 3 -.4 ck 6N/mm -.6 σ -.8 3 () :. 4 5 3.75m :. 7.m :. 874mm 4 865mm mm/ :. 7.m 4.m 4.m 6 7 4. 3.5

More information

熊本県数学問題正解

熊本県数学問題正解 00 y O x Typed by L A TEX ε ( ) (00 ) 5 4 4 ( ) http://www.ocn.ne.jp/ oboetene/plan/. ( ) (009 ) ( ).. http://www.ocn.ne.jp/ oboetene/plan/eng.html 8 i i..................................... ( )0... (

More information

untitled

untitled 1 th 1 th Dec.2006 1 1 th 1 th Dec.2006 103 1 2 EITC 2 1 th 1 th Dec.2006 3 1 th 1 th Dec.2006 2006 4 1 th 1 th Dec.2006 5 1 th 1 th Dec.2006 2 6 1 th 1 th Dec.2006 7 1 th 1 th Dec.2006 3 8 1 th 1 th Dec.2006

More information

6kg 1.1m 1.m.1m.1 l λ ϵ λ l + λ l l l dl dl + dλ ϵ dλ dl dl + dλ dl dl 3 1. JIS 1 6kg 1% 66kg 1 13 σ a1 σ m σ a1 σ m σ m σ a1 f f σ a1 σ a1 σ m f 4

6kg 1.1m 1.m.1m.1 l λ ϵ λ l + λ l l l dl dl + dλ ϵ dλ dl dl + dλ dl dl 3 1. JIS 1 6kg 1% 66kg 1 13 σ a1 σ m σ a1 σ m σ m σ a1 f f σ a1 σ a1 σ m f 4 35-8585 7 8 1 I I 1 1.1 6kg 1m P σ σ P 1 l l λ λ l 1.m 1 6kg 1.1m 1.m.1m.1 l λ ϵ λ l + λ l l l dl dl + dλ ϵ dλ dl dl + dλ dl dl 3 1. JIS 1 6kg 1% 66kg 1 13 σ a1 σ m σ a1 σ m σ m σ a1 f f σ a1 σ a1 σ m

More information

II Karel Švadlenka * [1] 1.1* 5 23 m d2 x dt 2 = cdx kx + mg dt. c, g, k, m 1.2* u = au + bv v = cu + dv v u a, b, c, d R

II Karel Švadlenka * [1] 1.1* 5 23 m d2 x dt 2 = cdx kx + mg dt. c, g, k, m 1.2* u = au + bv v = cu + dv v u a, b, c, d R II Karel Švadlenka 2018 5 26 * [1] 1.1* 5 23 m d2 x dt 2 = cdx kx + mg dt. c, g, k, m 1.2* 5 23 1 u = au + bv v = cu + dv v u a, b, c, d R 1.3 14 14 60% 1.4 5 23 a, b R a 2 4b < 0 λ 2 + aλ + b = 0 λ =

More information

II A A441 : October 02, 2014 Version : Kawahira, Tomoki TA (Kondo, Hirotaka )

II A A441 : October 02, 2014 Version : Kawahira, Tomoki TA (Kondo, Hirotaka ) II 214-1 : October 2, 214 Version : 1.1 Kawahira, Tomoki TA (Kondo, Hirotaka ) http://www.math.nagoya-u.ac.jp/~kawahira/courses/14w-biseki.html pdf 1 2 1 9 1 16 1 23 1 3 11 6 11 13 11 2 11 27 12 4 12 11

More information

ALM

ALM ALM 4 60025480 1 1.1 1.1.1 1.1.2 1.2 ALM 2. 2.11 2.1.1 2.1.2 2.2 2.3 3. 3.1 3.1.1 3.1.2 3.1.3 3.1.4 3.2 3.2.1 3.2.2 4. 4.1 4.1.1 4.1.2 4.1.3 4.2 4.2.1 4.2.2 4.2.3 5. 5.1 5.1.1 5.1.2 5.2 2 6. 6.1 6.2 6.1.1

More information

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

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

More information

. ev=,604k m 3 Debye ɛ 0 kt e λ D = n e n e Ze 4 ln Λ ν ei = 5.6π / ɛ 0 m/ e kt e /3 ν ei v e H + +e H ev Saha x x = 3/ πme kt g i g e n

. ev=,604k m 3 Debye ɛ 0 kt e λ D = n e n e Ze 4 ln Λ ν ei = 5.6π / ɛ 0 m/ e kt e /3 ν ei v e H + +e H ev Saha x x = 3/ πme kt g i g e n 003...............................3 Debye................. 3.4................ 3 3 3 3. Larmor Cyclotron... 3 3................ 4 3.3.......... 4 3.3............ 4 3.3...... 4 3.3.3............ 5 3.4.........

More information

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

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

More information

untitled

untitled C L C L 4.5m 3.0m 10% 25% 50% 90% 75% 50% N N N 90% 90% 10% 10% 100 100 10 10 10% 10% :49kN :17 :17kN CBR CBR CBR 5 3,000 / 3,000 /mm /mm 1.2mm 89dB 190dB 3,000 3,000 /mm 20% 20%

More information

S I. dy fx x fx y fx + C 3 C vt dy fx 4 x, y dy yt gt + Ct + C dt v e kt xt v e kt + C k x v k + C C xt v k 3 r r + dr e kt S Sr πr dt d v } dt k e kt

S I. dy fx x fx y fx + C 3 C vt dy fx 4 x, y dy yt gt + Ct + C dt v e kt xt v e kt + C k x v k + C C xt v k 3 r r + dr e kt S Sr πr dt d v } dt k e kt S I. x yx y y, y,. F x, y, y, y,, y n http://ayapin.film.s.dendai.ac.jp/~matuda n /TeX/lecture.html PDF PS yx.................................... 3.3.................... 9.4................5..............

More information

newmain.dvi

newmain.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 information

Microsoft Word - CTCWEB講座(4章照査)0419.doc

Microsoft Word - CTCWEB講座(4章照査)0419.doc 1912 1914 3 58 16 1 58 2 16 3 4 62 61 4 16 1 16 1914 ( 3) 1955 (30) 1961 (36) 1965 (40) 1970 (45) 1983 (58) 1992 ( 4) 1999 (11) 2004 (16) 2 1 2 3 4 5 6 7 8 9 1 10 2 11 12 13 14 15 16 17 18 19 20 21 22

More information

untitled

untitled .. 3. 3 3. 3 4 3. 5 6 3 7 3.3 9 4. 9 0 6 3 7 0705 φ c d φ d., φ cd, φd. ) O x s + b l cos s s c l / q taφ / q taφ / c l / X + X E + C l w q B s E q q ul q q ul w w q q E E + E E + ul X X + (a) (b) (c)

More information

Microsoft Word - 章末問題

Microsoft Word - 章末問題 1906 R n m 1 = =1 1 R R= 8h ICP s p s HeNeArXe 1 ns 1 1 1 1 1 17 NaCl 1.3 nm 10nm 3s CuAuAg NaCl CaF - - HeNeAr 1.7(b) 2 2 2d = a + a = 2a d = 2a 2 1 1 N = 8 + 6 = 4 8 2 4 4 2a 3 4 π N πr 3 3 4 ρ = = =

More information

t, x (4) 3 u(t, x) + 6u(t, x) u(t, x) + u(t, x) = 0 t x x3 ( u x = u x (4) u t + 6uu x + u xxx = 0 ) ( ): ( ) (2) Riccati ( ) ( ) ( ) 2 (1) : f

t, x (4) 3 u(t, x) + 6u(t, x) u(t, x) + u(t, x) = 0 t x x3 ( u x = u x (4) u t + 6uu x + u xxx = 0 ) ( ): ( ) (2) Riccati ( ) ( ) ( ) 2 (1) : f : ( ) 2008 5 31 1 f(t) t (1) d 2 f(t) + f(t) = 0 dt2 f(t) = sin t f(t) = cos t (1) 1 (2) d dt f(t) + f(t)2 = 0 (1) (2) t (c ) (3) 2 2 u(t, x) c2 u(t, x) = 0 t2 x2 1 (1) (1) 1 t, x (4) 3 u(t, x) + 6u(t,

More information

4 Mindlin -Reissner 4 δ T T T εσdω= δ ubdω+ δ utd Γ Ω Ω Γ T εσ (1.1) ε σ u b t 3 σ ε. u T T T = = = { σx σ y σ z τxy τ yz τzx} { εx εy εz γ xy γ yz γ

4 Mindlin -Reissner 4 δ T T T εσdω= δ ubdω+ δ utd Γ Ω Ω Γ T εσ (1.1) ε σ u b t 3 σ ε. u T T T = = = { σx σ y σ z τxy τ yz τzx} { εx εy εz γ xy γ yz γ Mindlin -Rissnr δ εσd δ ubd+ δ utd Γ Γ εσ (.) ε σ u b t σ ε. u { σ σ σ z τ τ z τz} { ε ε εz γ γ z γ z} { u u uz} { b b bz} b t { t t tz}. ε u u u u z u u u z u u z ε + + + (.) z z z (.) u u NU (.) N U

More information