PDF

Save this PDF as:
 WORD  PNG  TXT  JPG

Size: px
Start display at page:

Download "PDF"

Transcription

1 1 1

2 Fe C TEM C TEM Fe TEM

3 ,1 multiwall nanotube 1993 singlewall nanotube ( 1,) sp 7.4eV atom 1 1,3 c ( ) O A C h (chiral vector) O B T A B OBB A OB AB.4nm 1nm 1µm ( ) a1 a ( n m) C h na + ma, = (1.1) 1 = n m d θ n m t d t = 3a c c n + nm + m π (1.) θ = tan 1 3m n + m θ 6 π (1.3) 3

4 a (.14nm) c c n=m( = /6) (n,n) m=( =) (n,) ( 1, ) (armchair) (zigzag) n m (chiral) 1,5 T T (1.1) {( m + n) a ( n + m) a } 1 T d R = (1.4) dr (m+n) (n+m) T ( )l T 3l = (1.5) d R l = Ch = 3 ac c n + m + nm (1.6) (n,m) sp 3 1 1,6 (1.1) q C h k = πq (1.7) k (1.4) T 4

5 E k, k x y 5 ( ) k 1,7 K ( b ) 3 1 b (1.7) k K (1.7) (1.1) k= ( b ) 3 n m = 3q 1 b (1.8) n 3 ( 1,8) ( ) ( ) 1/3 / ( 1,9) 1 F + V = E + (1.9) F = p + h + s (1.1)

6 V ( 7s + 6h + 5 p) = (1.11) 3 E ( 7s + 6h + 5 p) = (1.1) (1.1),(1.11),(1.1) (1.9) s p + = h s + + p 1 + ( 7s + 6h + 5p) ( 7s + 6h + 5 p) 3 = 6 + (1.13) = ( 1,1) / cm 3 (1kV) 5V

7

8

9 (, ) 9

10

11 1-1,11 mm 1991 ( ) (Fe Co) ( / ) / Fe Ni Co Ni 1.11 Co (Ru Rh Pd Os Ir Pt ) (a ) (15A ) / 1 1.3nm 11

12 11 (SiC) 17 Si Si(A AB B) 1

13 13

14

15 - - (.1).1 z z= z= x E x iwt = A e sin kz (.1) x z= z= E = sin k = nπ ncπ k =, ω = (.) n n k= / (.) / n 15 x (.) sinkz n ( z ) z= z= ( ) f z (.) (.1) z= z= E ( ) <z< f z f ( ) z = n= A n πnz sin + B n π nz cos (.3) z= z ( z) f ( z ) f + = (.4) sinkz coskz z= (.3) k=n / (.)

16 sine cosine (.4) z= z= E E E = z z ( z = ) = E( z = ), ( z = ) = ( z ) (.5) x,y,z 3 τ τ a x,y,z 3 xˆ, yˆ, zˆ k ϖ ϖ k = k x xˆ + k yˆ + k y z zˆ A ϖ ρ ( i ω t ik r ) 16 c a (.6) exp (.7) r ρ A r ϖ = xxˆ + yyˆ + zzˆ x,y,z + k ϖ - k ϖ k ϖ n, n, n x= y= z= (.) k x π π π = nx, k y = ny, k z nz (.8) x y z

17 k = k + k + k x y z ( n + n n ) k = π x y + z (.9) n, n, n kc ω = ( n + n + n ) c ω = π x y z (.1) x, n, n, n x,y,z x y z R = n x + n y + n z ω = πc y z (.11) n, n, n 1/8 x y z π ω ω 3 = (.1) 3 πc 3π c +d ω π c 3 dω (.13) 3 +d ( ω ) dω dω π ω m = (.14) c = / +d 8πν c ( ν ) dν dν m 3 = (.15) 17

18 .1. n, n, n R x y z 18

19 - WU W WU W WU W ω = (.16) η (spontaneous emission) 1 A W( ) p ( U ) = A B W ( ω) (.17) U + U (induced emission stimulated emission) p ( U ) = B W ( ω ) (.18) U 1 B U = B U (.19) gu g (.19) g B = g B (.) U U U 1 (.16) (.17) A U B A B U 19

20 A B N P abs ( ω ) N = ηωbw (.1) N P emi { A BW( ω )} N U = η ω + (.) N U ηω = N kbt exp (.3) ( ) ( ) W ω W ( ) = ( ω ) ω W W ( ) th A th P abs = P emi (.) (.1) N U th ω = (.4) B N N U (.3) W th ( ) A 1 = ω kbt B e ω η (.5) 1 1 n ( U ) = ( n + )A P 1 (.6) ( U ) na P = (.7) m( ) +d dω

21 ( ω) m( ω) nηω W = (.8) (.6) (.7) A P ( U ) = + m ω ηω P ( U ) ( ) ( ω ) W ( ω ) A (.9) A = W ( ω ) (.3) m ηω (.17) (.18) A B = (.31) m ω η ( ) ω (.14) A B 3 ηω = m( ω) η ω = 3 (.3) π c (.5) W th ( ω ) ηω π c 1 3 = 3 ηω k T e B 1 (.33).3 1 d m( ) dω A = m ( ω) Bηω ηω (.17) (.18) W( ) ηω ( k B T ) exp ηω A= (.4) (.5) = A B π ν π A µ, 3 U Bν = µ 3ε hc 3ε h = U (.34) W th 1

22 B W( ) W th (.1) (.) B ( ω) = Bg( ω) (.35) B ( ω ) dω B B = (.36) g( ) B( ) NU N P ( N N ) ηωb( ω) c P = (.37) U z d P dz ( z) ( N N ) B( ω ) P( z) U ηω = (.38) c (amplitude absorption constant) ( ) d dz P ( z) α ( w) P( z) = (.39)

23 (.38) (.39) α ηω = U (.4) c ( ω ) ( N N ) B( ω ) (.35) (.34) A h = πη ν = ω π (.3) B = π ε η µ α ( ω) ( N N ) µ g( ω) 3 3 U πω = U U (.41) 6ε ηc (orentzian) Gaussian g ( ω) 1 = π ω g ( ω ω ) ( ) (.4) + ω ω ω = ± ω g ω g ω =1 π ω ( ) ( ) ω (half width at half maximum HWHM) ω ln 1 ω ω g G ( ω ) = exp ln (.43) ω ω ω ω ω = ln 1.47 g G ( ω ) = = (.44) π ω ω g ( ω ) π ln = g ( ω) g ( ω ).4 ω G (.19) ( ) NU N ( ω) = ( N N ) σ ( ω) α (.45) U (.45) (.41) (.4)

24 σ ηω ( ω) = µ g( ω) = B( ω) 3ε πω ηc U c (.46) NU N (.3) N U ηω kbt ( e ) N N = 1 (.47) ηω T N ηω k B N N U (.48) k T B ( ) ηω T k B N N N (.49) U ω x F dx dt dx F + γ + ω x = (.5) xt m ( ) t iω m -e E ω e (.5) d x + dt dx γ + ω dt e x = E m iωt ( ω) e (.51) x x iω t ( ω ) e = x (.5) (.51) ( ω) e E x ( ω ) = (.53) m ω iγω ω 4

25 x ( ω) e = mω E ω ω ( ω) iγ (.54) N N ( ) t iω P ω e P ( ) = ex( ω )( ) ω (.55) N N U χ ω = χ ω iχ ω ( ω ) ε χ ( ω ) E( ω ) P (complex susceptibility) ( ) ( ) ( ) = (.56) (.54) (.55) U χ ( ω) = ( N N ) ε U mω e ω 1 ω iγ (.57) ( ) ( ) ( ) ( ) ( ) χ ω χ ω χ ω = χ ω iχ ω χ χ ( ω ) ( ω ) = = ( N N ) U e ω ω ε mω γ ( N N ) ( ω ω ) + U e γ ε mω γ ( ω ω ) + (.58) (.59).5 ( ) χ ω ( ω) = ε { 1 χ( ω) } ε + (.6) µ = µ η η ( ω) ε η = η κ = = 1+ χ ε ( ω) i (.61) ( ) z exp iωt ikz η iκ 5

26 k ω ( η iκ ) c = (.6) ( iωt ikz ) = exp z exp iωt iη z κω c exp (.63) e αz ω α = κ (.64) c χ ( ω) κ χ ω c 1 (.59) α ( N N ) U e γ 4ε mc γ ( ω ω ) + (.65) e m ω 3 η (.41) g( ) (.4) 6 µ U χ χ µ U ω ω N N U (.66) 3ε η ( ω ω ) + γ ( ω) = ( ) ( ω ) = ( ) µ U γ 3ε γ N N U (.67) ( ω ω ) + f (.66) (.67) e f m ω µ 3η U = (.68) mω f µ 3e η U = (.69) f (oscillator Strength) NU N (.67) χ N N χ U

27 .3.4 g ω g ω ( ) G ( ).5 ( ) 7

28 -3 N U N N N U N N U (inverted population) N NU (pumping) -4 3 (three-level laser) 3 1,,3 W 1, W, W3 N 1, N, N3.6 W1 W W 3 N1 N N (relaxation) (radiative process) (non-radiativve Process) (relaxation rate) (relaxation constant) (fluorescence lifetime) 8

29 W W U γ U WU W γ N U U WU W γ = = U N γ U, NU N exp (.7) kbt γ γ U U WU W = exp kbt (.71) NU N 3 (rate equation) dn dt dn dt dn dt 1 ( Γ + γ 1 + γ 13 ) N1 + γ 1N + γ 31N3 = (.7) ( γ 1 + γ 3 ) N γ 3 3 γ N 1N1 + 3 = (.73) ( Γ + γ 13) N1γ 3N ( γ 31 + γ 3 ) N3 = (.74) N 1 + N + N 3 = const = N 3 (.7) (.74) k B T (.71) γ 1 γ 1, γ 13 γ 31, γ 3 γ 3 γ, γ 13 γ 3 (.7) (.74) 1 γ 1 ( γ 31 + γ 3 ) ( γ + γ ) + ( γ + γ ) N N 1 γ = (.75) N = γ 1 Γ ( γ + γ ) + ( γ + γ ) 31 γ Γ N (.76) 9

30 γ Γ > γ 3 γ (.77) N1 N (.77) γ γ 3 γ N = N N 1 (.75) (.76) N = γ 1 γ 3Γ γ 1( γ 31 + γ 3 ) ( γ + γ ) + ( γ + γ ) Γ N (.78).7 lim N Γ = γ γ 1 3 N + γ 3 = N γ 1+ γ 1 3 (.79) γ γ 1 3 NU N (.65) χ ( NU N ) χ e α z z ( ) - G z e α = e Gz z (gain) G (gain constant) G/ (amplification constant) N = N N 1 1 G ηω N B ω c ( ) = (.8) 3

31 G Nσ ( ω) = (.81) g 1, g g N g 1 N1 N g N = 1 ηω exp g k T 1 B (.8) g g 1 N N 1 N - N1 1 N 1, N N = N N 1 g N 1 N = (.83) g N g 1 g g 1 B B g = = (.84) B1 g1b1 1 (.8) B (.84) (.83) (.84) B (.8) (.83) (.35) (.34) B ν 3ε η U B = π µ 31

32 G g πω = N N1 µ 1 g( ω ) g (.85) 1 3 ε c η G g1 πω = N N1 µ 1 g( ω) g (.86) 3ε cη,1 1 P Q ( ) Q c ωw P = (.87) 1 dw κ = = W dt ω (.88) Q c (l= ) U P ωu = Q c (.89) N 3

33 P (.37) G P G Nηω B( ω)u = (.9) P P N G th 1 Q c = N th ( ) ηb ω (.91) R1 R /c ( 1 R )U R 1 c P ( 1 R1 R ) U = (.9) (.89) Q Q c = c ω ( 1 R R ) 1 (.93) (.9) (.93) ( R R ) c 1 1 ηωb( ω ) N th = (.94) z= +z E t( ωt kz) ( z t) = E e, (.95) k K G k k ε = ε { 1+ χ( ω )} G ω = k + i = 1 + χ c ( ω) ( ω ) k (.96) χ 33

34 k G ω 1 = 1 + χ ω c ( ) k (.97) ω = χ c ( ω ) G (.98) χ G (.95) (.96) z ( 1 ) ( t k ) ( t) E e G e i, E = (.99) Z, r 1, r (.99) z r -z z= r1 +z ( t k ) ( t) r r E e G e i ω, = E 1 (.1) (.95) z i t E e ω ik r r e G e 1 (.11) 1 = r1r r r R R e iθ 1 = 1 (.11) G R R e 1 (.1) 1 = n k = nπ +θ (.13) (.1) (.98) ω c 1 ( ) = ln R1 R χ ω (.14) ( ) R 1 R 1 ln R1R = R1R 1 Q (.93) (.14) 34

35 1 χ ( ω ) = (.15) Q c (.13) (.97) ω c { + χ ( ω )} = nπ + θ (.16) (.66) (.67) ( ω) = χ ( ω) ω ω (.17) χ γ (.15) χ ( ω) ω ω = γq c (.18) (.16) (.18) ω c ω ω + = π γ n Qc + θ (.19) ω (.16) χ = c ω = nπ π + c (.11) (.19) (.11) ω (.88) Q c c ω ω κ c ω + ω = γ (.111) ω κω + γω c = κ + γ (.11) ( 35

36 ) Q Q ω γ (.11) Qω + Qcω c ω = (.113) Q + Q c Q Q Q Q c > 1 (frequency pulling) 1 (.11) c / = Q

37 3-1 3,1 (Nd) 53 m 1Hz Q Q Q 1 ( ) 53nm mJ 5. 5 Torr

38 3.1 38

39 3- ( ) mm ( ) mm ( ) mm 5. mm 1 1.mm 3. Fe 3 1 Fe Fe 7 Fe Fe A A B TEM 39

40 3-3 SEM( ) TEM( ) SEM TEM TEM TEM ( ) SEM TEM 4

41 4 4-1 SEM 4,1 4,( ) 4,3( ) Cu.3 m 5nm 4,1 41

42 4, 4,3 4

43 4- Fe C TEM TEM 4.4 a B 5 c 1 4,4c 3 A B.71 C ( ) ( ) ( ) 43

44 44

45 45

46 4-3 C TEM TEM 4,5 1 A H A B C ( ) 46

47 47

48 4-4 Fe TEM TEM 4,6 1 (a) 5 (b) 4,6a ( ) 48

49 49

50 4,6c 3nm.g cm g cm 4.7 6% 3 ( ) 4.7 5

51 51

52 4-5 C %

53 5 ( 1983) ( ) Carbon Nanotubes and Related Structures edited by Peter J.F.Harris (Cambridge University Press 1999 The Science and Technology of Carbon Nanotubes edited by K.Tanaka, T.Yamabe and K.Fukui Elsevier (Elsevier Science 1999) 53

54 6 TEM SEM TEM 54

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

Z: Q: R: C: 3. Green Cauchy

Z: Q: R: C: 3. Green Cauchy 7 Z: Q: R: C: 3. Green.............................. 3.............................. 5.3................................. 6.4 Cauchy..................... 6.5 Taylor..........................6...............................

More information

( ) 2002 1 1 1 1.1....................................... 1 1.1.1................................. 1 1.1.2................................. 1 1.1.3................... 3 1.1.4......................................

More information

untitled

untitled (a) (b) (c) (d) Wunderlich 2.5.1 = = =90 2 1 (hkl) {hkl} [hkl] L tan 2θ = r L nλ = 2dsinθ dhkl ( ) = 1 2 2 2 h k l + + a b c c l=2 l=1 l=0 Polanyi nλ = I sinφ I: B A a 110 B c 110 b b 110 µ a 110

More information

= hυ = h c λ υ λ (ev) = 1240 λ W=NE = Nhc λ W= N 2 10-16 λ / / Φe = dqe dt J/s Φ = km Φe(λ)v(λ)dλ THBV3_0101JA Qe = Φedt (W s) Q = Φdt lm s Ee = dφe ds E = dφ ds Φ Φ THBV3_0102JA Me = dφe ds M = dφ ds

More information

kawa (Spin-Orbit Tomography: Kawahara and Fujii 21,Kawahara and Fujii 211,Fujii & Kawahara submitted) 2 van Cittert-Zernike Appendix A V 2

kawa (Spin-Orbit Tomography: Kawahara and Fujii 21,Kawahara and Fujii 211,Fujii & Kawahara submitted) 2 van Cittert-Zernike Appendix A V 2 Hanbury-Brown Twiss (ver. 1.) 24 2 1 1 1 2 2 2.1 van Cittert - Zernike..................................... 2 2.2 mutual coherence................................. 3 3 Hanbury-Brown Twiss ( ) 4 3.1............................................

More information

lim lim lim lim 0 0 d lim 5. d 0 d d d d d d 0 0 lim lim 0 d

lim lim lim lim 0 0 d lim 5. d 0 d d d d d d 0 0 lim lim 0 d lim 5. 0 A B 5-5- A B lim 0 A B A 5. 5- 0 5-5- 0 0 lim lim 0 0 0 lim lim 0 0 d lim 5. d 0 d d d d d d 0 0 lim lim 0 d 0 0 5- 5-3 0 5-3 5-3b 5-3c lim lim d 0 0 5-3b 5-3c lim lim lim d 0 0 0 3 3 3 3 3 3

More information

1

1 016 017 6 16 1 1 5 1.1............................................... 5 1................................................... 5 1.3................................................ 5 1.4...............................................

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

量子力学A

量子力学A c 1 1 1.1....................................... 1 1............................................ 4 1.3.............................. 6 10.1.................................. 10......................................

More information

1 variation 1.1 imension unit L m M kg T s Q C QT 1 A = C s 1 MKSA F = ma N N = kg m s 1.1 J E = 1 mv W = F x J = kg m s 1 = N m 1.

1 variation 1.1 imension unit L m M kg T s Q C QT 1 A = C s 1 MKSA F = ma N N = kg m s 1.1 J E = 1 mv W = F x J = kg m s 1 = N m 1. 1.1 1. 1.3.1..3.4 3.1 3. 3.3 4.1 4. 4.3 5.1 5. 5.3 6.1 6. 6.3 7.1 7. 7.3 1 1 variation 1.1 imension unit L m M kg T s Q C QT 1 A = C s 1 MKSA F = ma N N = kg m s 1.1 J E = 1 mv W = F x J = kg m s 1 = N

More information

gr09.dvi

gr09.dvi .1, θ, ϕ d = A, t dt + B, t dtd + C, t d + D, t dθ +in θdϕ.1.1 t { = f1,t t = f,t { D, t = B, t =.1. t A, tdt e φ,t dt, C, td e λ,t d.1.3,t, t d = e φ,t dt + e λ,t d + dθ +in θdϕ.1.4 { = f1,t t = f,t {

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

統計学のポイント整理

統計学のポイント整理 .. September 17, 2012 1 / 55 n! = n (n 1) (n 2) 1 0! = 1 10! = 10 9 8 1 = 3628800 n k np k np k = n! (n k)! (1) 5 3 5 P 3 = 5! = 5 4 3 = 60 (5 3)! n k n C k nc k = npk k! = n! k!(n k)! (2) 5 3 5C 3 = 5!

More information

『共形場理論』

『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

More information

untitled

untitled V. 8 9 9 8.. SI 5 6 7 8 9. - - SI 6 6 6 6 6 6 6 SI -- l -- 6 -- -- 6 6 u 6cod5 6 h5 -oo ch 79 79 85 875 99 79 58 886 9 89 9 959 966 - - NM /6 Nucl Ml SI NM/6/685 85co /./ /h / /6/.6 / /.6 /h o NM o.85

More information

2. 2 P M A 2 F = mmg AP AP 2 AP (G > : ) AP/ AP A P P j M j F = n j=1 mm j G AP j AP j 2 AP j 3 P ψ(p) j ψ(p j ) j (P j j ) A F = n j=1 mgψ(p j ) j AP

2. 2 P M A 2 F = mmg AP AP 2 AP (G > : ) AP/ AP A P P j M j F = n j=1 mm j G AP j AP j 2 AP j 3 P ψ(p) j ψ(p j ) j (P j j ) A F = n j=1 mgψ(p j ) j AP 1. 1 213 1 6 1 3 1: ( ) 2: 3: SF 1 2 3 1: 3 2 A m 2. 2 P M A 2 F = mmg AP AP 2 AP (G > : ) AP/ AP A P P j M j F = n j=1 mm j G AP j AP j 2 AP j 3 P ψ(p) j ψ(p j ) j (P j j ) A F = n j=1 mgψ(p j ) j AP

More information

<4D F736F F D B B83578B6594BB2D834A836F815B82D082C88C60202E646F63>

<4D F736F F D B B83578B6594BB2D834A836F815B82D082C88C60202E646F63> 通信方式第 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/072662 このサンプルページの内容は, 第 2 版発行当時のものです. i 2 2 2 2012 5 ii,.,,,,,,.,.,,,,,.,,.,,..,,,,.,,.,.,,.,,.. 1990 5 iii 1 1

More information

No2 4 y =sinx (5) y = p sin(2x +3) (6) y = 1 tan(3x 2) (7) y =cos 2 (4x +5) (8) y = cos x 1+sinx 5 (1) y =sinx cos x 6 f(x) = sin(sin x) f 0 (π) (2) y

No2 4 y =sinx (5) y = p sin(2x +3) (6) y = 1 tan(3x 2) (7) y =cos 2 (4x +5) (8) y = cos x 1+sinx 5 (1) y =sinx cos x 6 f(x) = sin(sin x) f 0 (π) (2) y No1 1 (1) 2 f(x) =1+x + x 2 + + x n, g(x) = 1 (n +1)xn + nx n+1 (1 x) 2 x 6= 1 f 0 (x) =g(x) y = f(x)g(x) y 0 = f 0 (x)g(x)+f(x)g 0 (x) 3 (1) y = x2 x +1 x (2) y = 1 g(x) y0 = g0 (x) {g(x)} 2 (2) y = µ

More information

2 FIG. 1: : n FIG. 2: : n (Ch h ) N T B Ch h n(z) = (sin ϵ cos ω(z), sin ϵ sin ω(z), cos ϵ), (1) 1968 Meyer [5] 50 N T B Ch h [4] N T B 10 nm Ch h 1 µ

2 FIG. 1: : n FIG. 2: : n (Ch h ) N T B Ch h n(z) = (sin ϵ cos ω(z), sin ϵ sin ω(z), cos ϵ), (1) 1968 Meyer [5] 50 N T B Ch h [4] N T B 10 nm Ch h 1 µ : (Dated: February 5, 2016), (Ch), (Oblique Helicoidal) (Ch H ), Twist-bend (N T B ) I. (chiral: ) (achiral) (n) (Ch) (N ) 1996 [1] [2] 2013 (N T B ) [3] 2014 [4] (oblique helicoid) 2016 1 29 Electronic

More information

untitled

untitled . 96. 99. ( 000 SIC SIC N88 SIC for Windows95 6 6 3 0 . amano No.008 6. 6.. z σ v σ v γ z (6. σ 0 (a (b 6. (b 0 0 0 6. σ σ v σ σ 0 / v σ v γ z σ σ 0 σ v 0γ z σ / σ ν /( ν, ν ( 0 0.5 0.0 0 v sinφ, φ 0 (6.

More information

I No. sin cos sine, cosine : trigonometric function π : π =.4 : n =, ±, ±, sin + nπ = sin cos + nπ = cos sin = sin : cos = cos :. sin. sin. sin + π si

I No. sin cos sine, cosine : trigonometric function π : π =.4 : n =, ±, ±, sin + nπ = sin cos + nπ = cos sin = sin : cos = cos :. sin. sin. sin + π si I 8 No. : No. : No. : No.4 : No.5 : No.6 : No.7 : No.8 : No.9 : No. : I No. sin cos sine, cosine : trigonometric function π : π =.4 : n =, ±, ±, sin + nπ = sin cos + nπ = cos sin = sin : cos = cos :. sin.

More information

I-2 (100 ) (1) y(x) y dy dx y d2 y dx 2 (a) y + 2y 3y = 9e 2x (b) x 2 y 6y = 5x 4 (2) Bernoulli B n (n = 0, 1, 2,...) x e x 1 = n=0 B 0 B 1 B 2 (3) co

I-2 (100 ) (1) y(x) y dy dx y d2 y dx 2 (a) y + 2y 3y = 9e 2x (b) x 2 y 6y = 5x 4 (2) Bernoulli B n (n = 0, 1, 2,...) x e x 1 = n=0 B 0 B 1 B 2 (3) co 16 I ( ) (1) I-1 I-2 I-3 (2) I-1 ( ) (100 ) 2l x x = 0 y t y(x, t) y(±l, t) = 0 m T g y(x, t) l y(x, t) c = 2 y(x, t) c 2 2 y(x, t) = g (A) t 2 x 2 T/m (1) y 0 (x) y 0 (x) = g c 2 (l2 x 2 ) (B) (2) (1)

More information

1990 IMO 1990/1/15 1:00-4:00 1 N N N 1, N 1 N 2, N 2 N 3 N 3 2 x x + 52 = 3 x x , A, B, C 3,, A B, C 2,,,, 7, A, B, C

1990 IMO 1990/1/15 1:00-4:00 1 N N N 1, N 1 N 2, N 2 N 3 N 3 2 x x + 52 = 3 x x , A, B, C 3,, A B, C 2,,,, 7, A, B, C 0 9 (1990 1999 ) 10 (2000 ) 1900 1994 1995 1999 2 SAT ACT 1 1990 IMO 1990/1/15 1:00-4:00 1 N 1990 9 N N 1, N 1 N 2, N 2 N 3 N 3 2 x 2 + 25x + 52 = 3 x 2 + 25x + 80 3 2, 3 0 4 A, B, C 3,, A B, C 2,,,, 7,

More information

4.6: 3 sin 5 sin θ θ t θ 2t θ 4t : sin ωt ω sin θ θ ωt sin ωt 1 ω ω [rad/sec] 1 [sec] ω[rad] [rad/sec] 5.3 ω [rad/sec] 5.7: 2t 4t sin 2t sin 4t

4.6: 3 sin 5 sin θ θ t θ 2t θ 4t : sin ωt ω sin θ θ ωt sin ωt 1 ω ω [rad/sec] 1 [sec] ω[rad] [rad/sec] 5.3 ω [rad/sec] 5.7: 2t 4t sin 2t sin 4t 1 1.1 sin 2π [rad] 3 ft 3 sin 2t π 4 3.1 2 1.1: sin θ 2.2 sin θ ft t t [sec] t sin 2t π 4 [rad] sin 3.1 3 sin θ θ t θ 2t π 4 3.2 3.1 3.4 3.4: 2.2: sin θ θ θ [rad] 2.3 0 [rad] 4 sin θ sin 2t π 4 sin 1 1

More information

(2 X Poisso P (λ ϕ X (t = E[e itx ] = k= itk λk e k! e λ = (e it λ k e λ = e eitλ e λ = e λ(eit 1. k! k= 6.7 X N(, 1 ϕ X (t = e 1 2 t2 : Cauchy ϕ X (t

(2 X Poisso P (λ ϕ X (t = E[e itx ] = k= itk λk e k! e λ = (e it λ k e λ = e eitλ e λ = e λ(eit 1. k! k= 6.7 X N(, 1 ϕ X (t = e 1 2 t2 : Cauchy ϕ X (t 6 6.1 6.1 (1 Z ( X = e Z, Y = Im Z ( Z = X + iy, i = 1 (2 Z E[ e Z ] < E[ Im Z ] < Z E[Z] = E[e Z] + ie[im Z] 6.2 Z E[Z] E[ Z ] : E[ Z ] < e Z Z, Im Z Z E[Z] α = E[Z], Z = Z Z 1 {Z } E[Z] = α = α [ α ]

More information

1 1.1 / Fik Γ= D n x / Newton Γ= µ vx y / Fouie Q = κ T x 1. fx, tdx t x x + dx f t = D f x 1 fx, t = 1 exp x 4πDt 4Dt lim fx, t =δx 3 t + dxfx, t = 1

1 1.1 / Fik Γ= D n x / Newton Γ= µ vx y / Fouie Q = κ T x 1. fx, tdx t x x + dx f t = D f x 1 fx, t = 1 exp x 4πDt 4Dt lim fx, t =δx 3 t + dxfx, t = 1 1 1.1......... 1............. 1.3... 1.4......... 1.5.............. 1.6................ Bownian Motion.1.......... Einstein.............. 3.3 Einstein........ 3.4..... 3.5 Langevin Eq.... 3.6................

More information

5 36 5................................................... 36 5................................................... 36 5.3..............................

5 36 5................................................... 36 5................................................... 36 5.3.............................. 9 8 3............................................. 3.......................................... 4.3............................................ 4 5 3 6 3..................................................

More information

2 σ γ l σ ο 4..5 cos 5 D c D u U b { } l + b σ l r l + r { r m+ m } b + l + + l l + 4..0 D b0 + r l r m + m + r 4..7 4..0 998 ble4.. ble4.. 8 0Z Fig.4.. 0Z 0Z Fig.4.. ble4.. 00Z 4 00 0Z Fig.4.. MO S 999

More information

第86回日本感染症学会総会学術集会後抄録(I)

第86回日本感染症学会総会学術集会後抄録(I) κ κ κ κ κ κ μ μ β β β γ α α β β γ α β α α α γ α β β γ μ β β μ μ α ββ β β β β β β β β β β β β β β β β β β γ β μ μ μ μμ μ μ μ μ β β μ μ μ μ μ μ μ μ μ μ μ μ μ μ β

More information

* 1 2014 7 8 *1 iii 1. Newton 1 1.1 Newton........................... 1 1.2............................. 4 1.3................................. 5 2. 9 2.1......................... 9 2.2........................

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

42 3 u = (37) MeV/c 2 (3.4) [1] u amu m p m n [1] m H [2] m p = (4) MeV/c 2 = (13) u m n = (4) MeV/c 2 =

42 3 u = (37) MeV/c 2 (3.4) [1] u amu m p m n [1] m H [2] m p = (4) MeV/c 2 = (13) u m n = (4) MeV/c 2 = 3 3.1 3.1.1 kg m s J = kg m 2 s 2 MeV MeV [1] 1MeV=1 6 ev = 1.62 176 462 (63) 1 13 J (3.1) [1] 1MeV/c 2 =1.782 661 731 (7) 1 3 kg (3.2) c =1 MeV (atomic mass unit) 12 C u = 1 12 M(12 C) (3.3) 41 42 3 u

More information

1 1 H Li Be Na M g B A l C S i N P O S F He N Cl A e K Ca S c T i V C Mn Fe Co Ni Cu Zn Ga Ge As Se B K Rb S Y Z Nb Mo Tc Ru Rh Pd Ag Cd In Sn Sb T e

1 1 H Li Be Na M g B A l C S i N P O S F He N Cl A e K Ca S c T i V C Mn Fe Co Ni Cu Zn Ga Ge As Se B K Rb S Y Z Nb Mo Tc Ru Rh Pd Ag Cd In Sn Sb T e No. 1 1 1 H Li Be Na M g B A l C S i N P O S F He N Cl A e K Ca S c T i V C Mn Fe Co Ni Cu Zn Ga Ge As Se B K Rb S Y Z Nb Mo Tc Ru Rh Pd Ag Cd In Sn Sb T e I X e Cs Ba F Ra Hf Ta W Re Os I Rf Db Sg Bh

More information

F8302D_1目次_160527.doc

F8302D_1目次_160527.doc N D F 830D.. 3. 4. 4. 4.. 4.. 4..3 4..4 4..5 4..6 3 4..7 3 4..8 3 4..9 3 4..0 3 4. 3 4.. 3 4.. 3 4.3 3 4.4 3 5. 3 5. 3 5. 3 5.3 3 5.4 3 5.5 4 6. 4 7. 4 7. 4 7. 4 8. 4 3. 3. 3. 3. 4.3 7.4 0 3. 3 3. 3 3.

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

nsg02-13/ky045059301600033210

nsg02-13/ky045059301600033210 φ φ φ φ κ κ α α μ μ α α μ χ et al Neurosci. Res. Trpv J Physiol μ μ α α α β in vivo β β β β β β β β in vitro β γ μ δ μδ δ δ α θ α θ α In Biomechanics at Micro- and Nanoscale Levels, Volume I W W v W

More information

10:30 12:00 P.G. vs vs vs 2

10:30 12:00 P.G. vs vs vs 2 1 10:30 12:00 P.G. vs vs vs 2 LOGIT PROBIT TOBIT mean median mode CV 3 4 5 0.5 1000 6 45 7 P(A B) = P(A) + P(B) - P(A B) P(B A)=P(A B)/P(A) P(A B)=P(B A) P(A) P(A B) P(A) P(B A) P(B) P(A B) P(A) P(B) P(B

More information

34 2 2 h = h/2π 3 V (x) E 4 2 1 ψ = sin kxk = 2π/λ λ = h/p p = h/λ = kh/2π = k h 5 2 ψ = e ax2 ガウス 型 関 数 1.2 1 関 数 値 0.8 0.6 0.4 0.2 0 15 10 5 0 5 10

34 2 2 h = h/2π 3 V (x) E 4 2 1 ψ = sin kxk = 2π/λ λ = h/p p = h/λ = kh/2π = k h 5 2 ψ = e ax2 ガウス 型 関 数 1.2 1 関 数 値 0.8 0.6 0.4 0.2 0 15 10 5 0 5 10 33 2 2.1 2.1.1 x 1 T x T 0 F = ma T ψ) 1 x ψ(x) 2.1.2 1 1 h2 d 2 ψ(x) + V (x)ψ(x) = Eψ(x) (2.1) 2m dx 2 1 34 2 2 h = h/2π 3 V (x) E 4 2 1 ψ = sin kxk = 2π/λ λ = h/p p = h/λ = kh/2π = k h 5 2 ψ = e ax2

More information

現代物理化学 1-1(4)16.ppt

現代物理化学 1-1(4)16.ppt (pdf) pdf pdf http://www1.doshisha.ac.jp/~bukka/lecture/index.html http://www.doshisha.ac.jp/ Duet -1-1-1 2-a. 1-1-2 EU E = K E + P E + U ΔE K E = 0P E ΔE = ΔU U U = εn ΔU ΔU = Q + W, du = d 'Q + d 'W

More information

C p (.2 C p [[T ]] Bernoull B n,χ C p p q p 2 q = p p = 2 q = 4 ω Techmüller a Z p ω(a a ( mod q φ(q ω(a Z p a pz p ω(a = 0 Z p φ Euler Techmüller ω Q

C p (.2 C p [[T ]] Bernoull B n,χ C p p q p 2 q = p p = 2 q = 4 ω Techmüller a Z p ω(a a ( mod q φ(q ω(a Z p a pz p ω(a = 0 Z p φ Euler Techmüller ω Q p- L- [Iwa] [Iwa2] -Leopoldt [KL] p- L-. Kummer Remann ζ(s Bernoull B n (. ζ( n = B n n, ( n Z p a = Kummer [Kum] ( Kummer p m n 0 ( mod p m n a m n ( mod (p p a ( p m B m m ( pn B n n ( mod pa Z p Kummer

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

,

, 2002 9710178 15 2 6 , 1 1 15 2 6 Mopac2000lite, Gaussian Moapc2000lite Gaussian98 2 1 1 1.1... 1 1.2... 2 1.3... 2 1.3.1... 2 1.3.2... 4 1.3.3... 5 1.4... 6 1.4.1 Mopac (5,5)... 6 1.4.2 Gaussian (3,3)...

More information

CKY CKY CKY 4 Kerr CKY

CKY CKY CKY 4 Kerr CKY ( ) 1. (I) Hidden Symmetry and Exact Solutions in Einstein Gravity Houri-Y.Y: Progress Supplement (2011) (II) Generalized Hidden Symmetries and Kerr-Sen Black Hole Houri-Kubiznak-Warnick-Y.Y: JHEP (2010)

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

学習内容と日常生活との関連性の研究-第2部-第6章

学習内容と日常生活との関連性の研究-第2部-第6章 378 379 10% 10%10% 10% 100% 380 381 2000 BSE CJD 5700 18 1996 2001 100 CJD 1 310-7 10-12 10-6 CJD 100 1 10 100 100 1 1 100 1 10-6 1 1 10-6 382 2002 14 5 1014 10 10.4 1014 100 110-6 1 383 384 385 2002 4

More information

Hz

Hz ( ) 2006 1 3 3 3 4 10 Hz 1 1 1.1.................................... 1 1.2.................................... 1 2 2 2.1.................................... 2 2.2.................................... 3

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

4 3 1 Introduction 3 2 7 2.1.................................. 7 2.1.1..................... 8 2.1.2............................. 8 2.1.3.......................... 10 2.2...............................

More information

n Y 1 (x),..., Y n (x) 1 W (Y 1 (x),..., Y n (x)) 0 W (Y 1 (x),..., Y n (x)) = Y 1 (x)... Y n (x) Y 1(x)... Y n(x) (x)... Y n (n 1) (x) Y (n 1)

n Y 1 (x),..., Y n (x) 1 W (Y 1 (x),..., Y n (x)) 0 W (Y 1 (x),..., Y n (x)) = Y 1 (x)... Y n (x) Y 1(x)... Y n(x) (x)... Y n (n 1) (x) Y (n 1) D d dx 1 1.1 n d n y a 0 dx n + a d n 1 y 1 dx n 1 +... + a dy n 1 dx + a ny = f(x)...(1) dk y dx k = y (k) a 0 y (n) + a 1 y (n 1) +... + a n 1 y + a n y = f(x)...(2) (2) (2) f(x) 0 a 0 y (n) + a 1 y

More information

[ ] = L [δ (D ) (x )] = L D [g ] = L D [E ] = L Table : ħh = m = D D, V (x ) = g δ (D ) (x ) E g D E (Table )D = Schrödinger (.3)D = (regularization)

[ ] = L [δ (D ) (x )] = L D [g ] = L D [E ] = L Table : ħh = m = D D, V (x ) = g δ (D ) (x ) E g D E (Table )D = Schrödinger (.3)D = (regularization) . D............................................... : E = κ ............................................ 3.................................................

More information

CVMに基づくNi-Al合金の

CVMに基づくNi-Al合金の CV N-A (-' by T.Koyama ennard-jones fcc α, β, γ, δ β α γ δ = or α, β. γ, δ α β γ ( αβγ w = = k k k ( αβγ w = ( αβγ ( αβγ w = w = ( αβγ w = ( αβγ w = ( αβγ w = ( αβγ w = ( αβγ w = ( βγδ w = = k k k ( αγδ

More information

2 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 information

2005 17 1 19 ( 18:00 20:30 (4 ( ( ( ( 21 30 1. ( 2. 3. ( 4. ( 5. ( 6. ( 7. ( 8. ( ( ( 17 2 ; 17 2 16 (18 20 30 ; ( 2 5F(AB ; ( 21 ( ; 1 (H17.2.16( 2 3 (H17.2.16( 4 16 5 ( 5 ( 6 17 ( ( 1. ( 6,000V 4

More information

5.. z = f(x, y) y y = b f x x g(x) f(x, b) g x ( ) A = lim h g(a + h) g(a) h g(x) a A = g (a) = f x (a, b)............................................

5.. z = f(x, y) y y = b f x x g(x) f(x, b) g x ( ) A = lim h g(a + h) g(a) h g(x) a A = g (a) = f x (a, b)............................................ 5 partial differentiation (total) differentiation 5. z = f(x, y) (a, b) A = lim h f(a + h, b) f(a, b) h........................................................... ( ) f(x, y) (a, b) x A (a, b) x (a, b)

More information

text_0821.dvi

text_0821.dvi Team DIANA 2007 8 21 2 ( ) ( ) Team DIANA 1 2 1 1 1 1 1 1 1 1 2 1 1 1 1 1 Janosfalvi Zsuzsa 1 1 3 1 5 1.1.................................. 5 1.2................................. 5 1.3.....................................

More information

閨75, 縺5 [ ィ チ573, 縺 ィ ィ

閨75, 縺5 [ ィ チ573, 縺 ィ ィ 39ィ 8 998 3. 753 68, 7 86 タ7 9 9989769 438 縺48 縺55 3783645 タ5 縺473 タ7996495 ィ 59754 8554473 9 8984473 3553 7. 95457357, 4.3. 639745 5883597547 6755887 67996499 ィ 597545 4953473 9 857473 3553, 536583, 89573,

More information

3章 問題・略解

3章 問題・略解 S S W R S O( l) O( ) c Jg g J Jg S R J 7. K.9 JK S W S R S JK S S R J 7. K.9JK 4 (a) -Tice 7.K T ice T N 77 K S R.9 JK 4. JK T T ice N.6JK S W S R S JK S S.6JK R (b) S R JK S.6 JK T T ice N 6 O( c) O(

More information

z z x = y = /x lim y = + x + lim y = x (x a ) a (x a+) lim z z f(z) = A, lim z z g(z) = B () lim z z {f(z) ± g(z)} = A ± B (2) lim {f(z) g(z)} = AB z

z z x = y = /x lim y = + x + lim y = x (x a ) a (x a+) lim z z f(z) = A, lim z z g(z) = B () lim z z {f(z) ± g(z)} = A ± B (2) lim {f(z) g(z)} = AB z Tips KENZOU 28 6 29 sin 2 x + cos 2 x = cos 2 z + sin 2 z = OK... z < z z < R w = f(z) z z w w f(z) w lim z z f(z) = w x x 2 2 f(x) x = a lim f(x) = lim f(x) x a+ x a z z x = y = /x lim y = + x + lim y

More information

body.dvi

body.dvi ..1 f(x) n = 1 b n = 1 f f(x) cos nx dx, n =, 1,,... f(x) sin nx dx, n =1,, 3,... f(x) = + ( n cos nx + b n sin nx) n=1 1 1 5 1.1........................... 5 1.......................... 14 1.3...........................

More information

Fig. Division of unbounded domain into closed interior domain and its eterior domain. Zienkiewicz [5, 6] Burnett [7, 8] [3] The conjugated Ast

Fig. Division of unbounded domain into closed interior domain and its eterior domain. Zienkiewicz [5, 6] Burnett [7, 8] [3] The conjugated Ast 7 6 pp. 635 643 635 43..Rz; 43.4.Rj * 3 3 Unbounded problems, Finite element method, Infinite element, Hybrid variational principle, Fourier series. Boundary Element Method: BEM BEM Finite Element Method:

More information

縺 縺8 縺, [ 縺 チ : () () () 4 チ93799; () "64": ィャ 9997ィ

縺 縺8 縺, [ 縺 チ : () () () 4 チ93799; () 64: ィャ 9997ィ 34978 998 3. 73 68, 86 タ7 9 9989769 438 縺48 縺 378364 タ 縺473 399-4 8 637744739 683 6744939 3.9. 378,.. 68 ィ 349 889 3349947 89893 683447 4 334999897447 (9489) 67449, 6377447 683, 74984 7849799 34789 83747

More information

nsg04-28/ky208684356100043077

nsg04-28/ky208684356100043077 δ!!! μ μ μ γ UBE3A Ube3a Ube3a δ !!!! α α α α α α α α α α μ μ α β α β β !!!!!!!! μ! Suncus murinus μ Ω! π μ Ω in vivo! μ μ μ!!! ! in situ! in vivo δ δ !!!!!!!!!! ! in vivo Orexin-Arch Orexin-Arch !!

More information

(Basic of Proability Theory). (Probability Spacees ad Radom Variables , (Expectatios, Meas) (Weak Law

(Basic of Proability Theory). (Probability Spacees ad Radom Variables , (Expectatios, Meas) (Weak Law I (Radom Walks ad Percolatios) 3 4 7 ( -2 ) (Preface),.,,,...,,.,,,,.,.,,.,,. (,.) (Basic of Proability Theory). (Probability Spacees ad Radom Variables...............2, (Expectatios, Meas).............................

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

7 9 7..................................... 9 7................................ 3 7.3...................................... 3 A A. ω ν = ω/π E = hω. E

7 9 7..................................... 9 7................................ 3 7.3...................................... 3 A A. ω ν = ω/π E = hω. E B 8.9.4, : : MIT I,II A.P. E.F.,, 993 I,,, 999, 7 I,II, 95 A A........................... A........................... 3.3 A.............................. 4.4....................................... 5 6..............................

More information

1320M/161320M

1320M/161320M " # $ %! θθ v m g y v θ O v α x! O x y x α x y y " v # v sinα $ & v cosα ' v cosα v sinα ( v cosα % v sinα " g # gsinθ $ g sinθ ' g ( gsinθ ) g sinθ % gcosθ & g cosθ * gcosθ! g cosθ xy y L v g x xy L α

More information

122 6 A 0 (p 0 q 0 ). ( p 0 = p cos ; q sin + p 0 (6.1) q 0 = p sin + q cos + q 0,, 2 Ox, O 1 x 1., q ;q ( p 0 = p cos + q sin + p 0 (6.2) q 0 = p sin

122 6 A 0 (p 0 q 0 ). ( p 0 = p cos ; q sin + p 0 (6.1) q 0 = p sin + q cos + q 0,, 2 Ox, O 1 x 1., q ;q ( p 0 = p cos + q sin + p 0 (6.2) q 0 = p sin 121 6,.,,,,,,. 2, 1. 6.1,.., M, A(2 R).,. 49.. Oxy ( ' ' ), f Oxy, O 1 x 1 y 1 ( ' ' ). A (p q), A 0 (p q). y q A q q 0 y 1 q A O 1 p x 1 O p p 0 p x 6.1: ( ), 6.1, 122 6 A 0 (p 0 q 0 ). ( p 0 = p cos

More information

Big Bang Planck Big Bang 1 43 Planck Planck quantum gravity Planck Grand Unified Theories: GUTs X X W X 1 15 ev 197 Glashow Georgi 1 14 GeV 1 2

Big Bang Planck Big Bang 1 43 Planck Planck quantum gravity Planck Grand Unified Theories: GUTs X X W X 1 15 ev 197 Glashow Georgi 1 14 GeV 1 2 12 Big Bang 12.1 Big Bang Big Bang 12.1 1-5 1 32 K 1 19 GeV 1-4 time after the Big Bang [ s ] 1-3 1-2 1-1 1 1 1 1 2 inflationary epoch gravity strong electromagnetic weak 1 27 K 1 14 GeV 1 15 K 1 2 GeV

More information

1: *2 W, L 2 1 (WWL) 4 5 (WWL) W (WWL) L W (WWL) L L 1 2, 1 4, , 1 4 (cf. [4]) 2: 2 3 * , , = , 1

1: *2 W, L 2 1 (WWL) 4 5 (WWL) W (WWL) L W (WWL) L L 1 2, 1 4, , 1 4 (cf. [4]) 2: 2 3 * , , = , 1 I, A 25 8 24 1 1.1 ( 3 ) 3 9 10 3 9 : (1,2,6), (1,3,5), (1,4,4), (2,2,5), (2,3,4), (3,3,3) 10 : (1,3,6), (1,4,5), (2,2,6), (2,3,5), (2,4,4), (3,3,4) 6 3 9 10 3 9 : 6 3 + 3 2 + 1 = 25 25 10 : 6 3 + 3 3

More information

...............y.\....07..

...............y.\....07.. 150 11.512.0 11.812.0 12.013.0 12.514.0 1 a c d e 1 3 a 1m b 6 20 30cm day a b a b 6 6 151 6 S 5m 11.511.8 G 515m 11.812.0 SG 10m 11.812.0 10m 11.511.8 1020m 11.812.0 SF 5m 11.511.8 510m 11.812.0 V 5m

More information

観測量と物理量の関係.pptx

観測量と物理量の関係.pptx (I! F! ( (! "! (#, $ #, $!! di! d"! =!I! + B! (T ex T ex : "! n 2 / g 2 = exp(! h! n 1 / g 1 kt ex " I! ("! = I! (0e "! +! e ("! " #! B! [T ex ("! ]d " d! " = # " ds = h" 4$ %("(n dsb h" 1 12 [1! exp(!

More information

‚åŁÎ“·„´Šš‡ðŠp‡¢‡½‹âfi`fiI…A…‰…S…−…Y…•‡ÌMarkovŸA“½fiI›ð’Í

‚åŁÎ“·„´Šš‡ðŠp‡¢‡½‹âfi`fiI…A…‰…S…−…Y…•‡ÌMarkovŸA“½fiI›ð’Í Markov 2009 10 2 Markov 2009 10 2 1 / 25 1 (GA) 2 GA 3 4 Markov 2009 10 2 2 / 25 (GA) (GA) L ( 1) I := {0, 1} L f : I (0, ) M( 2) S := I M GA (GA) f (i) i I Markov 2009 10 2 3 / 25 (GA) ρ(i, j), i, j I

More information

13 0 1 1 4 11 4 12 5 13 6 2 10 21 10 22 14 3 20 31 20 32 25 33 28 4 31 41 32 42 34 43 38 5 41 51 41 52 43 53 54 6 57 61 57 62 60 70 0 Gauss a, b, c x, y f(x, y) = ax 2 + bxy + cy 2 = x y a b/2 b/2 c x

More information

p.2/76

p.2/76 kino@info.kanagawa-u.ac.jp p.1/76 p.2/76 ( ) (2001). (2006). (2002). p.3/76 N n, n {1, 2,...N} 0 K k, k {1, 2,...,K} M M, m {1, 2,...,M} p.4/76 R =(r ij ), r ij = i j ( ): k s r(k, s) r(k, 1),r(k, 2),...,r(k,

More information

Unidirectional Measurement Current-Shunt Monitor with Dual Comparators (Rev. B

Unidirectional Measurement Current-Shunt Monitor with Dual Comparators (Rev. B www.tij.co.jp INA206 INA207 INA208 INA206-INA208 INA206-INA208 V S 1 14 V IN+ V S 1 10 V IN+ OUT CMP1 IN /0.6V REF 2 3 1.2V REF 13 12 V IN 1.2V REF OUT OUT CMP1 IN+ 2 3 9 8 V IN CMP1 OUT CMP1 IN+ 4 11

More information

2

2 1 12123456789012345678901234 12123456789012345678901234 12123456789012345678901234 12123456789012345678901234 12123456789012345678901234 12123456789012345678901234 12123456789012345678901234 12123456789012345678901234

More information

E F = q b E (2) E q a r q a q b N/C q a (electric flux line) q a E r r r E 4πr 2 E 4πr 2 = k q a r 2 4πr2 = 4πkq a (3) 4πkq a 1835 4πk 1 ɛ 0 ɛ 0 (perm

E F = q b E (2) E q a r q a q b N/C q a (electric flux line) q a E r r r E 4πr 2 E 4πr 2 = k q a r 2 4πr2 = 4πkq a (3) 4πkq a 1835 4πk 1 ɛ 0 ɛ 0 (perm 1 1.1 18 (static electricity) 20 (electric charge) A,B q a, q b r F F = k q aq b r 2 (1) k q b F F q a r?? 18 (Coulomb) 1 N C r 1m 9 10 9 N 1C k 9 10 9 Nm 2 /C 2 1 k q a r 2 (Electric Field) 1 E F = q

More information

LHC ALICE (QGP) QGP QGP QGP QGP ω ϕ J/ψ ALICE s = ev + J/ψ

LHC ALICE (QGP) QGP QGP QGP QGP ω ϕ J/ψ ALICE s = ev + J/ψ 8 + J/ψ ALICE B597 : : : 9 LHC ALICE (QGP) QGP QGP QGP QGP ω ϕ J/ψ ALICE s = ev + J/ψ 6..................................... 6. (QGP)..................... 6.................................... 6.4..............................

More information

0 1-4. 1-5. (1) + b = b +, (2) b = b, (3) + 0 =, (4) 1 =, (5) ( + b) + c = + (b + c), (6) ( b) c = (b c), (7) (b + c) = b + c, (8) ( + b)c = c + bc (9

0 1-4. 1-5. (1) + b = b +, (2) b = b, (3) + 0 =, (4) 1 =, (5) ( + b) + c = + (b + c), (6) ( b) c = (b c), (7) (b + c) = b + c, (8) ( + b)c = c + bc (9 1-1. 1, 2, 3, 4, 5, 6, 7,, 100,, 1000, n, m m m n n 0 n, m m n 1-2. 0 m n m n 0 2 = 1.41421356 π = 3.141516 1-3. 1 0 1-4. 1-5. (1) + b = b +, (2) b = b, (3) + 0 =, (4) 1 =, (5) ( + b) + c = + (b + c),

More information

卒業論文.PDF

卒業論文.PDF SPM 1010197 SPM 1 3 2.1 3 2.2 ESCA 4 2.3 4 2.4 5 2.5 6 2.6 6 8 3.1 8 3.2 SPM 10 3.3 AFM 11 3.3.1 AFM 11 3.3.2 AFM 12 3.4 LFM 13 3.4.1 LFM 13 3.4.2 LFM 13 3.5 14 3.5.1 14 3.5.2 SiN 15 3.6 16 3.6.1 16 3.6.2

More information

ver 0.3 Chapter 0 0.1 () 0( ) 0.2 3 4 CHAPTER 0. http://www.jaist.ac.jp/~t-yama/k116 0.3 50% ( Wikipedia ) ( ) 0.4! 2006 0.4. 5 MIT OCW ( ) MIT Open Courseware MIT (Massachusetts Institute of Technology)

More information