橡Taro11-卒業論文.PDF

Size: px
Start display at page:

Download "橡Taro11-卒業論文.PDF"

Transcription

1 Recombination Generation Lifetime 13 9

2 Recombination Lifetime Si TEG 3 5. Recombination Lifetime Si TEG 6 6. Pulse Scanning C-V Generation Lifetime Appendix n p 3 31 Appendix 34 --

3 1. CPUHDD DRAM 1 Pulse Scanning C-V Generation Lifetime Recombination Lifeitime Recombination Generation Lifetime -3-

4 ..1. n p ( Efn Ei) n= n i exp kt ( Efp Ei) p= n i exp kt Appendix.1 Appendix. E fn Efp.1. np = n i.3 n p ni majority carrier minority carrier ( n) ( p) ( ).4 pn ni.4.3 GaAs Si Si -4-

5 E g E g a [K π/a] trap.1. Si n P E c G R E g E v p P, N.... G -5-

6 G = α N.5 α N n = G τ g.6 n τ g.. R dn dt dn n = R = dt τ r.7 τ r G R.3 pn ni R.3. R n.3. np p β R = β np.8 G R αn = βn p P P.9 n P, pp.. Na pp Na R = β n N P a.1-6-

7 n 1 [/Sec] n P n P E c G R E g E v p P, N.3. ( ) R= βn p = β n + n p P P P P.11 G G.1 n n n= n n P P.13 np np.13 n n P dn dt P n = R τ P r.14 n R = βnppp = τ P r.15-7-

8 τ r 1 β p P.16 τ r n G τ P g.17 np np G + n1 = R.18 n τ P i n τ p g r P.19 pp Na np ni τ τ r g ni N a. τ τ r g ni N d.1-8-

9 P E c N E fn E fp E v.4. P N

10 .7. P N W Ec P N E v E fp E fn E c

11 Diffusion potential built in potential q ϕ bi ϕ bi.9. ϕ bi q ϕ bi = Efn E fp. ϕ bi P N qϕ bi E i E fp qϕ E bi fp E fn E i E v E fn E i E c.9. ψ ρ = = + d ψ de s q * * dx dx εs ε εs ε ( N N p n) D A

12 * ρ Ω cm q c ε ε s s -3-3 F/cm ND NA cm p n cm.3 d ψ = dx.4 N N + p n= D A.5 NA n.9. Efn Ei qϕn ϕn.5 ND n p NA.3 ϕ n 1 kt N ( Ei Ef) = ln q q n x wn D i.6 ϕ p 1 kt N ( Ei Ef) = ln q q n x wp i A ϕ bi kt N ln DNA ϕbi = ϕn ϕp = q n i.8 Si wp wn -1 -

13 p n.3 d ψ dx q = A ε ε * s ( N N ) D.9 q(n D N A ) qn D w p w n x qn A W d ψ qn A wp x < = * dx ε ε s.3 d ψ < x wn dx qnd = ε ε * s

14 w p E w n x ϕ bi E max ψ (a) ϕ bi (b) W.11. a b x qn w = qn w A p D n.3 W W = w + w p n a.3.31 ( ) E x ( + p) dψ qna x w = = dx ε ε * s p w x <.34 ( ) E x ( ) qn x qn x w = E + = D D max * * εs ε εs ε n < x wn.35 Emax x= E qn w qn w = = D n A p max * * εs ε εs ε

15 ϕbi ϕ bi wn ( ) ( ) ( ) wn E x dx E x dx E x dx w p w p = = A p qndwn * * s s qn w = + = ε ε ε ε 1 E max W.37 ϕbi.11. a.3.37 W = * ε s ε N A + N D ϕbi q NAND.38 + NA ND wp wn wp W W w = n * ε s εϕ bi qn D.39 ( ) = Emax + * E x qn x ε s D ε.4 ND x W w n E qn W = D max * εs ε

16 ( ) E x ( ) qnd W + x x = = Emax 1 ε ε W * s.4 ψ x x x = Edx= Emax x C C + W.43 ( ) -16 -

17 3. Recombination Lifetime a b If Ir 3.1. P N P N Recombination E f p E v E f n Recombination Recombination E f p E v E c E f n Recombination E c (a) (b) 3.. a b

18 Function Generator FunctionGenerator DC

19 Recombination Lifetime 1 R 11 1kΩ R 1 1k Ω R3 1 1 Ω 3.6. TEG 3.6. Recombination Lifetime R 11 1kΩ R 1 1k Ω R3 1 1 Ω -19 -

20 I f I r t t τ r erf t If τ = I + I r f r I f I r t τ Appendix erf x r erf ( ) x = y dy π x exp 3. I f I r t

21 4. Si TEG 4.1. Si Si 3 4 V Si

22 E c E f E f E v 4.. E c E f E f E v

23 E c E f E f E v 4.4. E c E f E f E v TEG Metal SiO P N 4.6. TEG TEG 4.6. Metal -3 -

24 5. Recombination Lifetime 5.1. Si 4 Si 5 I f I r τ r ma τ r τ r.1µ Sec I f I r Recombination Lifetime τ r I f Recombination Lifetime R.L. 5.. I f I r τ r I I + I x τ r 5.3. I f I r τ r I f I r erf t τ r ( ) f f r -4 -

25 5.. I f Recombination Lifetime τ r 5.3. Recombination Lifetime τ r 1-5 -

26 5.. TEG TEG Recombination Lifetime τ r TEG TEG R.L. R.L. -6 -

27 6. Pulse Scanning C-V Generation Lifetime MOS Generation Lifetime G.L. Pulse Scanning C-V Metal SiO N-Si (a) c d V b (b) C a V V a b c t (c) c d b a t 6.1. MOS a b Pulse Scanning C-V c 6.1. a MOS 6.1. c 6.1. b C V t V - n cm qn = Cox V 6.1 q - n t cm /Sec n = t Cox V q

28 cm Sec [ ] G.L. Sec τ r τ g τ r τ g.1..1 τ τ r g ni N D 6.3 ND n i TEG ND 1. 1 cm n i cm τ r τ g τ r 9 µ sec τ g sec

29

30 1 S.Kawazu, T.Matsukawa and H.Nakata:"Pulse Scanning C-V Technique for The Analysis of Carrier Generation in Silicon", Electro-chamical Society Spring Meeting Extended Abstract pp6-633 R.H.Kingston, Associate member, IRE:"Switching Time in Junction Diodes and Junction Transistors" 3 W.shockley:"The Theory of p-n Junction in Semiconductors and p-n Junction Transistors" 4 S.M. :" " :" " :" " :" " :" " :" " A.S.Grove :" " :" " :" " B.G.Streetman :" " :" 3 " :" "

31 . Appendix. n p N f E ( E) = N f.1 N f n E f p E 1 f n ( E) = E E 1 exp kt fn f p ( E) = 1 = E Efp E Efp 1+ exp 1+ exp kt kt.3. E E fn 3kT E E E E fn ( ) fn f n E exp kt.4 E E E E fn ( ) fp f n E 1 exp kt.5 E fp n p -31 -

32 Ec ( E) n= N f de n E E = N exp Ec kt fn de E E fn E Efn = N exp exp kt kt E Efn = N ktexp kt Ec Efn Ec Efn = N ktexp ktexp kt kt Ec Efn = NkTexp kt Ec.6 Ev ( E) p = N f de p E Efp = N exp de E v kt E E fp E E fp = N exp exp kt kt E Efp = N ktexp kt Efp Ev Efp = N ktexp ktexp kt kt Ev Efp Efp Ev = NkTexp = NkTexp kt kt Ev Ev.7 n i E i -3 -

33 Ec Efn n= NkTexp kt E E c Ei fn Ei = NkTexp exp kt kt Efn Ei = ni exp kt.8 Efp Ev p = NkTexp kt Ei Efp Ei Efp = NkTexp exp kt kt Ei Efp = ni exp kt.9 E fn E fp pn ni Efn Ei Ei Efp n p = ni exp niexp kt kt Efn Efp = ni exp kt.1 E fn E fp n p= n i

34 Appendix. erf x t dt π ( ) = x exp.1 x x x 1 3 erf ( x) = xf 1 1 ; ; x π. d y dy + ( ) = x c x ay dx dx.3 ( ) = 1 1(, ; ) = (, ; ) ( ) y x F ac x M a c x ax a a+ 1 x = , c, 1,, c1! c( c+ 1)!.4 x 1 x 3 erf( x) exp x F 1; ; x π = x 3 exp x 1F1 1; ; x a π = n= n

35 a x exp = x π x an = a 1 n + n = 1,, n x.5 erf x x 5. erf x x 1 x sec x erfcx erf erfc ( x) = 1 erfc( x) x t dt x π ( ) = exp.8 erfc x F,1;, x ( ) exp x 1 1 π x x.9.9 x x erfc ( x) ( ) ( ) exp x = π x x x x x.1 1.E 9 x 16 ( ) exp x erf( x) = π x x x

36 x.7 x sn = an, v= n+, mk = 8 k a exp x = π yes x? no a s n n x exp = x π = a 1 v = ; = n n 1 n ( n ) x an = an 1, ( n = n ) v + 1 s = s + a n = n v = v+ 1 ( ) m k = = 8 z = x m 8 zk = x+ = x+ k = z x 1 mk = mk 1 ( ) yes a > 1.E 1? n m >? no yes no erf ( x) = s n a erf ( x) = 1 z k.1. erf x BASIC -36 -

37 .1. BASIC x erf x erf1 erfx x erf 1!********************************************! ERROR FUNCTION PROGRAM 3! erf x :erf1 4!******************************************** 5 DIM A1 6 DIM S1 7 DIM M1 8 DIM Z1 9 PRINT "X=" 1 INPUT X 11 PRINT X 1 IF XTHEN GOTO 4 13 A = *X/SQR PI *EXP -X^ 14!PRINT "A =",A 15 N= 16 N=N+1 17 AN = X^/ N+ 1/ *A N-1 18!PRINT "N=",N,"AN =",A N 19 S =A x A = exp x π A S n x = A 1 n + = A n 1 SN =A N +SN-1 1!PRINT "SN =",S N IF AN 1.E-1 THEN GOTO 37 A n 1.E 1 3 IF AN 1.E-1 THEN GOTO 16 4 M =8 S = A + S n n n 1 x M =

38 5 Z =X 6 K= 7 K=K+1 8 ZK =X+ MK-1 /Z K-1 9 MK =M K-1-1/ 3!PRINT "K=",K,"MK =",M K,"ZK =",Z K 31 IF MK = THEN GOTO 33 M k 3 IF MK THEN GOTO 7 33 E=1-EXP -X^ /SQR PI /Z K 34!PRINT "E=",E 35 PRINT "erfx =",E 36 GOTO PRINT "erfx =",S N-1 38 END Z Z k M = x k M = x+ Z Mk 1 k 1 k 1 = 1 exp x 1 π E = Z k.. erf x 1!*******************************************! ERROR FUNCTION PROGRAM 3! Y=erf X :erf 4!******************************************* 5 DIM X1 6 DIM A1 7 DIM S1 8 DIM M1 9 DIM Z1 1 PRINT "******** Y =1 ********" 11 PRINT "Y=" 1 INPUT Y 13 PRINT Y -38 -

39 14 X1= X = 16 B= 17 Q= 18 Q=Q+1 b 1 19 XQ =X1* -1^ B * 1/^ Q-1 +X Q-1 Xq = X ( 1) X q 1 q + IF XQ THEN GOTO 9 X q X q 1 A = *X Q /SQR PI *EXP - X Q ^ A= exp X π N= 3 N=N+1 4 AN = X Q ^/ N+ 1/ *AN-1 5 S =A 6 SN =A N +SN-1 7 IF AN 1.E-1 THEN GOTO 4 A n 1.E 1 8 IF AN 1.E-1 THEN GOTO 3 9 M =8 3 Z =X Q 31 K= 3 K=K+1 33 ZK =X Q + M K-1 /Z K-1 34 MK =M K-1-1/ X q 35 IF MK= THEN GOTO 37 M k 36 IF MK THEN GOTO 3 37 F=1-EXP - X Q ^ /SQR PI /ZK 38 E=F 39 GOTO 41 A n 1 1 X q = A 1 n + M = 8 Z Z = X q k M M = Xq + Z k = Mk 1 n 1 k 1 k 1 1 q exp X 1 π F = Z k q -39 -

40 4 E=S N IF 1/^Q-1 ^ -1 THEN GOTO IF Y-ETHEN GOTO IF Y-E1.E-11 THEN GOTO 5 Y E 1.E IF E-Y1.E-11 THEN GOTO 5 45 IF YETHEN GOTO IF YETHEN B= 47 GOTO B=1 49 GOTO 18 5 PRINT "X=",XQ 51 END > 1 q.3. erf x x erf x.4. erf x -4 -

MOSFET HiSIM HiSIM2 1

MOSFET HiSIM HiSIM2 1 MOSFET 2007 11 19 HiSIM HiSIM2 1 p/n Junction Shockley - - on-quasi-static - - - Y- HiSIM2 2 Wilson E f E c E g E v Bandgap: E g Fermi Level: E f HiSIM2 3 a Si 1s 2s 2p 3s 3p HiSIM2 4 Fermi-Dirac Distribution

More information

jse2000.dvi

jse2000.dvi pn 1 2 1 1947 1 (800MHz) (12GHz) (CPUDSP ) 1: MOS (MOSFET) CCD MOSFET MES (MESFET) (HBT) (HEMT) GTO MOSFET (IGBT) (SIT) pn { 3 3 3 pn 2 pn pn 1 2 sirafuji@dj.kit.ac.jp yoshimot@dj.kit.ac.jp 1 3 3.1 III

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

24.15章.微分方程式

24.15章.微分方程式 m d y dt = F m d y = mg dt V y = dy dt d y dt = d dy dt dt = dv y dt dv y dt = g dv y dt = g dt dt dv y = g dt V y ( t) = gt + C V y ( ) = V y ( ) = C = V y t ( ) = gt V y ( t) = dy dt = gt dy = g t dt

More information

,..,,.,,.,.,..,,.,,..,,,. 2

,..,,.,,.,.,..,,.,,..,,,. 2 A.A. (1906) (1907). 2008.7.4 1.,.,.,,.,,,.,..,,,.,,.,, R.J.,.,.,,,..,.,. 1 ,..,,.,,.,.,..,,.,,..,,,. 2 1, 2, 2., 1,,,.,, 2, n, n 2 (, n 2 0 ).,,.,, n ( 2, ), 2 n.,,,,.,,,,..,,. 3 x 1, x 2,..., x n,...,,

More information

untitled

untitled MOSFET 17 1 MOSFET.1 MOS.1.1 MOS.1. MOS.1.3 MOS 4.1.4 8.1.5 9. MOSFET..1 1.. 13..3 18..4 18..5 0..6 1.3 MOSFET.3.1.3. Poon & Yau 3.3.3 LDD MOSFET 5 3.1 3.1.1 6 3.1. 6 3. p MOSFET 3..1 8 3.. 31 3..3 36

More information

13 2 9

13 2 9 13 9 1 1.1 MOS ASIC 1.1..3.4.5.6.7 3 p 3.1 p 3. 4 MOS 4.1 MOS 4. p MOS 4.3 5 CMOS NAND NOR 5.1 5. CMOS 5.3 CMOS NAND 5.4 CMOS NOR 5.5 .1.1 伝導帯 E C 禁制帯 E g E g E v 価電子帯 図.1 半導体のエネルギー帯. 5 4 伝導帯 E C 伝導電子

More information

330

330 330 331 332 333 334 t t P 335 t R t t i R +(P P ) P =i t P = R + P 1+i t 336 uc R=uc P 337 338 339 340 341 342 343 π π β τ τ (1+π ) (1 βτ )(1 τ ) (1+π ) (1 βτ ) (1 τ ) (1+π ) (1 τ ) (1 τ ) 344 (1 βτ )(1

More information

3 - { } / f ( ) e nπ + f( ) = Cne n= nπ / Eucld r e (= N) j = j e e = δj, δj = 0 j r e ( =, < N) r r r { } ε ε = r r r = Ce = r r r e ε = = C = r C r e + CC e j e j e = = ε = r ( r e ) + r e C C 0 r e =

More information

0.,,., m Euclid m m. 2.., M., M R 2 ψ. ψ,, R 2 M.,, (x 1 (),, x m ()) R m. 2 M, R f. M (x 1,, x m ), f (x 1,, x m ) f(x 1,, x m ). f ( ). x i : M R.,,

0.,,., m Euclid m m. 2.., M., M R 2 ψ. ψ,, R 2 M.,, (x 1 (),, x m ()) R m. 2 M, R f. M (x 1,, x m ), f (x 1,, x m ) f(x 1,, x m ). f ( ). x i : M R.,, 2012 10 13 1,,,.,,.,.,,. 2?.,,. 1,, 1. (θ, φ), θ, φ (0, π),, (0, 2π). 1 0.,,., m Euclid m m. 2.., M., M R 2 ψ. ψ,, R 2 M.,, (x 1 (),, x m ()) R m. 2 M, R f. M (x 1,, x m ), f (x 1,, x m ) f(x 1,, x m ).

More information

N88 BASIC 0.3 C: My Documents 0.6: 0.3: (R) (G) : enterreturn : (F) BA- SIC.bas 0.8: (V) 0.9: 0.5:

N88 BASIC 0.3 C: My Documents 0.6: 0.3: (R) (G) : enterreturn : (F) BA- SIC.bas 0.8: (V) 0.9: 0.5: BASIC 20 4 10 0 N88 Basic 1 0.0 N88 Basic..................................... 1 0.1............................................... 3 1 4 2 5 3 6 4 7 5 10 6 13 7 14 0 N88 Basic 0.0 N88 Basic 0.1: N88Basic

More information

3 3.3. I 3.3.2. [ ] N(µ, σ 2 ) σ 2 (X 1,..., X n ) X := 1 n (X 1 + + X n ): µ X N(µ, σ 2 /n) 1.8.4 Z = X µ σ/ n N(, 1) 1.8.2 < α < 1/2 Φ(z) =.5 α z α

3 3.3. I 3.3.2. [ ] N(µ, σ 2 ) σ 2 (X 1,..., X n ) X := 1 n (X 1 + + X n ): µ X N(µ, σ 2 /n) 1.8.4 Z = X µ σ/ n N(, 1) 1.8.2 < α < 1/2 Φ(z) =.5 α z α 2 2.1. : : 2 : ( ): : ( ): : : : ( ) ( ) ( ) : ( pp.53 6 2.3 2.4 ) : 2.2. ( ). i X i (i = 1, 2,..., n) X 1, X 2,..., X n X i (X 1, X 2,..., X n ) ( ) n (x 1, x 2,..., x n ) (X 1, X 2,..., X n ) : X 1,

More information

S = k B (N A n c A + N B n c B ) (83) [ ] B A (N A N B ) G = N B µ 0 B (T,P)+N Aψ(T,P)+N A k B T n N A en B (84) 2 A N A 3 (83) N A N B µ B = µ 0 B(T,

S = k B (N A n c A + N B n c B ) (83) [ ] B A (N A N B ) G = N B µ 0 B (T,P)+N Aψ(T,P)+N A k B T n N A en B (84) 2 A N A 3 (83) N A N B µ B = µ 0 B(T, 8.5 [ ] 2 A B Z(T,V,N) = d 3N A p N A!N B!(2π h) 3N A d 3N A q A d 3N B p B d 3N B q B e β(h A(p A,q A ;V )+H B (p B,q B ;V )) = Z A (T,V,N A )Z B (T,V,N B ) (74) F (T,V,N)=F A (T,V,N A )+F B (T,V,N

More information

サイバネットニュース No.121

サイバネットニュース No.121 2007 Spring No.121 01 02 03 04 05 06 07 08 09 10 12 13 14 18 01 02 03 04 05 06 07 L R L R L R I x C G C G C G x 08 09 σ () t σ () t = Sx() t Q σ=0 P y O S x= y y & T S= 1 1 x& () t = Ax() t + Bu() t +

More information

devicemondai

devicemondai c 2019 i 3 (1) q V I T ε 0 k h c n p (2) T 300 K (3) A ii c 2019 i 1 1 2 13 3 30 4 53 5 78 6 89 7 101 8 112 9 116 A 131 B 132 c 2019 1 1 300 K 1.1 1.5 V 1.1 qv = 1.60 10 19 C 1.5 V = 2.4 10 19 J (1.1)

More information

●70974_100_AC009160_KAPヘ<3099>ーシス自動車約款(11.10).indb

●70974_100_AC009160_KAPヘ<3099>ーシス自動車約款(11.10).indb " # $ % & ' ( ) * +, -. / 0 1 2 3 4 5 6 7 8 9 : ; < = >? @ A B C D E F G H I J K L M N O P Q R S T U V W X Y " # $ % & ' ( ) * + , -. / 0 1 2 3 4 5 6 7 8 9 : ; < = > ? @ A 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

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

Acrobat Distiller, Job 2

Acrobat Distiller, Job 2 2 3 4 5 Eg φm s M f 2 qv ( q qφ ) = qφ qχ + + qφ 0 0 = 6 p p ( Ei E f ) kt = n e i Q SC = qn W A n p ( E f Ei ) kt = n e i 7 8 2 d φ( x) qn = A 2 dx ε ε 0 s φ qn s 2ε ε A ( x) = ( x W ) 2 0 E s A 2 EOX

More information

1 913 10301200 A B C D E F G H J K L M 1A1030 10 : 45 1A1045 11 : 00 1A1100 11 : 15 1A1115 11 : 30 1A1130 11 : 45 1A1145 12 : 00 1B1030 1B1045 1C1030

1 913 10301200 A B C D E F G H J K L M 1A1030 10 : 45 1A1045 11 : 00 1A1100 11 : 15 1A1115 11 : 30 1A1130 11 : 45 1A1145 12 : 00 1B1030 1B1045 1C1030 1 913 9001030 A B C D E F G H J K L M 9:00 1A0900 9:15 1A0915 9:30 1A0930 9:45 1A0945 10 : 00 1A1000 10 : 15 1B0900 1B0915 1B0930 1B0945 1B1000 1C0900 1C0915 1D0915 1C0930 1C0945 1C1000 1D0930 1D0945 1D1000

More information

46 Y 5.1.1 Y Y Y 3.1 R Y Figures 5-1 5-3 3.2mm Nylon Glass Y (X > X ) X Y X Figure 5-1 X min Y Y d Figure 5-3 X =X min Y X =10 Y Y Y 5.1.2 Y Figure 5-

46 Y 5.1.1 Y Y Y 3.1 R Y Figures 5-1 5-3 3.2mm Nylon Glass Y (X > X ) X Y X Figure 5-1 X min Y Y d Figure 5-3 X =X min Y X =10 Y Y Y 5.1.2 Y Figure 5- 45 5 5.1 Y 3.2 Eq. (3) 1 R [s -1 ] ideal [s -1 ] Y [-] Y [-] ideal * [-] S [-] 3 R * ( ω S ) = ω Y = ω 3-1a ideal ideal X X R X R (X > X ) ideal * X S Eq. (3-1a) ( X X ) = Y ( X ) R > > θ ω ideal X θ =

More information

untitled

untitled Y = Y () x i c C = i + c = ( x ) x π (x) π ( x ) = Y ( ){1 + ( x )}( 1 x ) Y ( )(1 + C ) ( 1 x) x π ( x) = 0 = ( x ) R R R R Y = (Y ) CS () CS ( ) = Y ( ) 0 ( Y ) dy Y ( ) A() * S( π ), S( CS) S( π ) =

More information

高齢化の経済分析.pdf

高齢化の経済分析.pdf ( 2 65 1995 14.8 2050 33.4 1 2 3 1 7 3 2 1980 3 79 4 ( (1992 1 ( 6069 8 7079 5 80 3 80 1 (1 (Sample selection bias 1 (1 1* 80 1 1 ( (1 0.628897 150.5 0.565148 17.9 0.280527 70.9 0.600129 31.5 0.339812

More information

( )/2 hara/lectures/lectures-j.html 2, {H} {T } S = {H, T } {(H, H), (H, T )} {(H, T ), (T, T )} {(H, H), (T, T )} {1

( )/2   hara/lectures/lectures-j.html 2, {H} {T } S = {H, T } {(H, H), (H, T )} {(H, T ), (T, T )} {(H, H), (T, T )} {1 ( )/2 http://www2.math.kyushu-u.ac.jp/ hara/lectures/lectures-j.html 1 2011 ( )/2 2 2011 4 1 2 1.1 1 2 1 2 3 4 5 1.1.1 sample space S S = {H, T } H T T H S = {(H, H), (H, T ), (T, H), (T, T )} (T, H) S

More information

x, y x 3 y xy 3 x 2 y + xy 2 x 3 + y 3 = x 3 y xy 3 x 2 y + xy 2 x 3 + y 3 = 15 xy (x y) (x + y) xy (x y) (x y) ( x 2 + xy + y 2) = 15 (x y)

x, y x 3 y xy 3 x 2 y + xy 2 x 3 + y 3 = x 3 y xy 3 x 2 y + xy 2 x 3 + y 3 = 15 xy (x y) (x + y) xy (x y) (x y) ( x 2 + xy + y 2) = 15 (x y) x, y x 3 y xy 3 x 2 y + xy 2 x 3 + y 3 = 15 1 1977 x 3 y xy 3 x 2 y + xy 2 x 3 + y 3 = 15 xy (x y) (x + y) xy (x y) (x y) ( x 2 + xy + y 2) = 15 (x y) ( x 2 y + xy 2 x 2 2xy y 2) = 15 (x y) (x + y) (xy

More 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

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

1 P2 P P3P4 P5P8 P9P10 P11 P12

1 P2 P P3P4 P5P8 P9P10 P11 P12 1 P2 P14 2 3 4 5 1 P3P4 P5P8 P9P10 P11 P12 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 & 11 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 1! 3 2 3! 4 4 3 5 6 I 7 8 P7 P7I P5 9 P5! 10 4!! 11 5 03-5220-8520

More information

kou05.dvi

kou05.dvi 2 C () 25 1 3 1.1........................................ 3 1.2..................................... 4 1.3..................................... 7 1.3.1................................ 7 1.3.2.................................

More information

untitled

untitled /Si FET /Si FET Improvement of tunnel FET performance using narrow bandgap semiconductor silicide Improvement /Si hetero-structure of tunnel FET performance source electrode using narrow bandgap semiconductor

More information

卒論 提出用ファイル.doc

卒論 提出用ファイル.doc 11 13 1LT99097W (i) (ii) 0. 0....1 1....3 1.1....3 1.2....4 2....7 2.1....7 2.2....8 2.2.1....8 2.2.2....9 2.2.3.... 10 2.3.... 12 3.... 15 Appendix... 17 1.... 17 2.... 19 3.... 20... 22 (1) a. b. c.

More information

f (x) f (x) f (x) f (x) f (x) 2 f (x) f (x) f (x) f (x) 2 n f (x) n f (n) (x) dn f f (x) dx n dn dx n D n f (x) n C n C f (x) x = a 1 f (x) x = a x >

f (x) f (x) f (x) f (x) f (x) 2 f (x) f (x) f (x) f (x) 2 n f (x) n f (n) (x) dn f f (x) dx n dn dx n D n f (x) n C n C f (x) x = a 1 f (x) x = a x > 5.1 1. x = a f (x) a x h f (a + h) f (a) h (5.1) h 0 f (x) x = a f +(a) f (a + h) f (a) = lim h +0 h (5.2) x h h 0 f (a) f (a + h) f (a) f (a h) f (a) = lim = lim h 0 h h 0 h (5.3) f (x) x = a f (a) =

More information

+ + + + n S (n) = + + + + n S (n) S (n) S 0 (n) S (n) 6 4 S (n) S (n) 7 S (n) S 4 (n) 8 6 S k (n) 0 7 (k + )S k (n) 8 S 6 (n), S 7 (n), S 8 (n), S 9 (

+ + + + n S (n) = + + + + n S (n) S (n) S 0 (n) S (n) 6 4 S (n) S (n) 7 S (n) S 4 (n) 8 6 S k (n) 0 7 (k + )S k (n) 8 S 6 (n), S 7 (n), S 8 (n), S 9 ( k k + k + k + + n k 006.7. + + + + n S (n) = + + + + n S (n) S (n) S 0 (n) S (n) 6 4 S (n) S (n) 7 S (n) S 4 (n) 8 6 S k (n) 0 7 (k + )S k (n) 8 S 6 (n), S 7 (n), S 8 (n), S 9 (n), S 0 (n) 9 S (n) S 4

More information

Appendix A BASIC BASIC Beginner s All-purpose Symbolic Instruction Code FORTRAN COBOL C JAVA PASCAL (NEC N88-BASIC Windows BASIC (1) (2) ( ) BASIC BAS

Appendix A BASIC BASIC Beginner s All-purpose Symbolic Instruction Code FORTRAN COBOL C JAVA PASCAL (NEC N88-BASIC Windows BASIC (1) (2) ( ) BASIC BAS Appendix A BASIC BASIC Beginner s All-purpose Symbolic Instruction Code FORTRAN COBOL C JAVA PASCAL (NEC N88-BASIC Windows BASIC (1 (2 ( BASIC BASIC download TUTORIAL.PDF http://hp.vector.co.jp/authors/va008683/

More information

診療ガイドライン外来編2014(A4)/FUJGG2014‐01(大扉)

診療ガイドライン外来編2014(A4)/FUJGG2014‐01(大扉) !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

More information

Part. 4. () 4.. () 4.. 3 5. 5 5.. 5 5.. 6 5.3. 7 Part 3. 8 6. 8 6.. 8 6.. 8 7. 8 7.. 8 7.. 3 8. 3 9., 34 9.. 34 9.. 37 9.3. 39. 4.. 4.. 43. 46.. 46..

Part. 4. () 4.. () 4.. 3 5. 5 5.. 5 5.. 6 5.3. 7 Part 3. 8 6. 8 6.. 8 6.. 8 7. 8 7.. 8 7.. 3 8. 3 9., 34 9.. 34 9.. 37 9.3. 39. 4.. 4.. 43. 46.. 46.. Cotets 6 6 : 6 6 6 6 6 6 7 7 7 Part. 8. 8.. 8.. 9..... 3. 3 3.. 3 3.. 7 3.3. 8 Part. 4. () 4.. () 4.. 3 5. 5 5.. 5 5.. 6 5.3. 7 Part 3. 8 6. 8 6.. 8 6.. 8 7. 8 7.. 8 7.. 3 8. 3 9., 34 9.. 34 9.. 37 9.3.

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

1. ( ) 1.1 t + t [m]{ü(t + t)} + [c]{ u(t + t)} + [k]{u(t + t)} = {f(t + t)} (1) m ü f c u k u 1.2 Newmark β (1) (2) ( [m] + t ) 2 [c] + β( t)2

1. ( ) 1.1 t + t [m]{ü(t + t)} + [c]{ u(t + t)} + [k]{u(t + t)} = {f(t + t)} (1) m ü f c u k u 1.2 Newmark β (1) (2) ( [m] + t ) 2 [c] + β( t)2 212 1 6 1. (212.8.14) 1 1.1............................................. 1 1.2 Newmark β....................... 1 1.3.................................... 2 1.4 (212.8.19)..................................

More information

[ ] 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

[ ] 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 [ ]. 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 =

More information

8.1 Fubini 8.2 Fubini 9 (0%) 10 (50%) 10.1 10.2 Carathéodory 10.3 Fubini 1 Introduction [1],, [2],, [3],, [4],, [5],, [6],, [7],, [8],, [1, 2, 3] 1980

8.1 Fubini 8.2 Fubini 9 (0%) 10 (50%) 10.1 10.2 Carathéodory 10.3 Fubini 1 Introduction [1],, [2],, [3],, [4],, [5],, [6],, [7],, [8],, [1, 2, 3] 1980 % 100% 1 Introduction 2 (100%) 2.1 2.2 2.3 3 (100%) 3.1 3.2 σ- 4 (100%) 4.1 4.2 5 (100%) 5.1 5.2 5.3 6 (100%) 7 (40%) 8 Fubini (90%) 2006.11.20 1 8.1 Fubini 8.2 Fubini 9 (0%) 10 (50%) 10.1 10.2 Carathéodory

More information

2002 7 i 1 1 2 3 2.1............................. 3 2.1.1....................... 5 2.2............................ 5 2.2.1........................ 6 2.2.2.................... 6 2.3...........................

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

<4D F736F F D B B BB2D834A836F815B82D082C88C602E646F63>

<4D F736F F D B B BB2D834A836F815B82D082C88C602E646F63> 入門モーター工学 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/074351 このサンプルページの内容は, 初版 1 刷発行当時のものです. 10 kw 21 20 50 2 20 IGBT IGBT IGBT 21 (1) 1 2 (2) (3) ii 20 2013 2 iii iv...

More information

30

30 3 ............................................2 2...........................................2....................................2.2...................................2.3..............................

More information

WECPNL = LA +10log10 N 27 N = N 2 + 3N3 + 10( N1 + N 4) L A N N N N N 1 2 3 4 Lden Lden Lden Lden LAE L pa pa 2 a /10 LpA = 20 log 10 ( pa = p 10 ) n na p0 p na n an n p0 2 Lp p L p

More information

3

3 00D8103005L 004 3 3 1... 1....1.......4..1...4.....5 3... 7 3.1...7 3....8 3.3...9 3.3.1...9 3.3.... 11 3.4...13 3.4.1...13 3.4....17 4... 4.1 NEEDS Financial QUEST... 4....5 4.3...30 4.4...31 4.5...34

More information

untitled

untitled 10 log 10 W W 10 L W = 10 log 10 W 10 12 10 log 10 I I 0 I 0 =10 12 I = P2 ρc = ρcv2 L p = 10 log 10 p 2 p 0 2 = 20 log 10 p p = 20 log p 10 0 2 10 5 L 3 = 10 log 10 10 L 1 /10 +10 L 2 ( /10 ) L 1 =10

More information

example2_time.eps

example2_time.eps Google (20/08/2 ) ( ) Random Walk & Google Page Rank Agora on Aug. 20 / 67 Introduction ( ) Random Walk & Google Page Rank Agora on Aug. 20 2 / 67 Introduction Google ( ) Random Walk & Google Page Rank

More information

1 1 ( ) ( 1.1 1.1.1 60% mm 100 100 60 60% 1.1.2 A B A B A 1

1 1 ( ) ( 1.1 1.1.1 60% mm 100 100 60 60% 1.1.2 A B A B A 1 1 21 10 5 1 E-mail: qliu@res.otaru-uc.ac.jp 1 1 ( ) ( 1.1 1.1.1 60% mm 100 100 60 60% 1.1.2 A B A B A 1 B 1.1.3 boy W ID 1 2 3 DI DII DIII OL OL 1.1.4 2 1.1.5 1.1.6 1.1.7 1.1.8 1.2 1.2.1 1. 2. 3 1.2.2

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

1 2 3 6 10 < > 13 16 16 4 17 13 00 15 30 5

1 2 3 6 10 < > 13 16 16 4 17 13 00 15 30 5 2004 16 3 23 q 4 21 r 1 2 3 6 10 < > 13 16 16 4 17 13 00 15 30 5 13 2 2 16 4 4 17 3 16 3 1 16 3 2 905 1438 1201 1205 1210 70 1812 25 1635 1654 3 44 47 10 10 911.18-R 1193 34 1652 4 911.107-H 1159 1685

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

5 5.1 E 1, E 2 N 1, N 2 E tot N tot E tot = E 1 + E 2, N tot = N 1 + N 2 S 1 (E 1, N 1 ), S 2 (E 2, N 2 ) E 1, E 2 S tot = S 1 + S 2 2 S 1 E 1 = S 2 E

5 5.1 E 1, E 2 N 1, N 2 E tot N tot E tot = E 1 + E 2, N tot = N 1 + N 2 S 1 (E 1, N 1 ), S 2 (E 2, N 2 ) E 1, E 2 S tot = S 1 + S 2 2 S 1 E 1 = S 2 E 5 5.1 E 1, E 2 N 1, N 2 E tot N tot E tot = E 1 + E 2, N tot = N 1 + N 2 S 1 (E 1, N 1 ), S 2 (E 2, N 2 ) E 1, E 2 S tot = S 1 + S 2 2 S 1 E 1 = S 2 E 2, S 1 N 1 = S 2 N 2 2 (chemical potential) µ S N

More information

1 9 v.0.1 c (2016/10/07) Minoru Suzuki T µ 1 (7.108) f(e ) = 1 e β(e µ) 1 E 1 f(e ) (Bose-Einstein distribution function) *1 (8.1) (9.1)

1 9 v.0.1 c (2016/10/07) Minoru Suzuki T µ 1 (7.108) f(e ) = 1 e β(e µ) 1 E 1 f(e ) (Bose-Einstein distribution function) *1 (8.1) (9.1) 1 9 v..1 c (216/1/7) Minoru Suzuki 1 1 9.1 9.1.1 T µ 1 (7.18) f(e ) = 1 e β(e µ) 1 E 1 f(e ) (Bose-Einstein distribution function) *1 (8.1) (9.1) E E µ = E f(e ) E µ (9.1) µ (9.2) µ 1 e β(e µ) 1 f(e )

More information

untitled

untitled Tylor 006 5 ..........5. -...... 5....5 5 - E. G. BASIC Tylor.. E./G. b δ BASIC.. b) b b b b δ b δ ) δ δ δ δ b b, b ) b δ v, b v v v v) ) v v )., 0 OPTION ARITHMETIC DECIMAL_HIGH INPUT FOR t TO 9 LET /*/)

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

平成18年度弁理士試験本試験問題とその傾向

平成18年度弁理士試験本試験問題とその傾向 CBA CBA CBA CBA CBA CBA Vol. No. CBA CBA CBA CBA a b a bm m swkmsms kgm NmPa WWmK σ x σ y τ xy θ σ θ τ θ m b t p A-A' σ τ A-A' θ B-B' σ τ B-B' A-A' B-B' B-B' pσ σ B-B' pτ τ l x x I E Vol. No. w x xl/ 3

More information

5 n P j j (P i,, P k, j 1) 1 n n ) φ(n) = n (1 1Pj [ ] φ φ P j j P j j = = = = = n = φ(p j j ) (P j j P j 1 j ) P j j ( 1 1 P j ) P j j ) (1 1Pj (1 1P

5 n P j j (P i,, P k, j 1) 1 n n ) φ(n) = n (1 1Pj [ ] φ φ P j j P j j = = = = = n = φ(p j j ) (P j j P j 1 j ) P j j ( 1 1 P j ) P j j ) (1 1Pj (1 1P p P 1 n n n 1 φ(n) φ φ(1) = 1 1 n φ(n), n φ(n) = φ()φ(n) [ ] n 1 n 1 1 n 1 φ(n) φ() φ(n) 1 3 4 5 6 7 8 9 1 3 4 5 6 7 8 9 1 4 5 7 8 1 4 5 7 8 10 11 1 13 14 15 16 17 18 19 0 1 3 4 5 6 7 19 0 1 3 4 5 6 7

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

2001 Miller-Rabin Rabin-Solovay-Strassen self-contained RSA RSA RSA ( ) Shor RSA RSA 1 Solovay-Strassen Miller-Rabin [3, pp

2001 Miller-Rabin Rabin-Solovay-Strassen self-contained RSA RSA RSA ( ) Shor RSA RSA 1 Solovay-Strassen Miller-Rabin [3, pp 200 Miller-Rabin 2002 3 Rabin-Solovay-Strassen self-contained RSA RSA RSA ( ) Shor 996 2 RSA RSA Solovay-Strassen Miller-Rabin [3, pp. 8 84] Rabin-Solovay-Strassen 2 Miller-Rabin 3 4 Miller-Rabin 5 Miller-Rabin

More information

II 2014 2 (1) log(1 + r/100) n = log 2 n log(1 + r/100) = log 2 n = log 2 log(1 + r/100) (2) y = f(x) = log(1 + x) x = 0 1 f (x) = 1/(1 + x) f (0) = 1

II 2014 2 (1) log(1 + r/100) n = log 2 n log(1 + r/100) = log 2 n = log 2 log(1 + r/100) (2) y = f(x) = log(1 + x) x = 0 1 f (x) = 1/(1 + x) f (0) = 1 II 2014 1 1 I 1.1 72 r 2 72 8 72/8 = 9 9 2 a 0 1 a 1 a 1 = a 0 (1+r/100) 2 a 2 a 2 = a 1 (1 + r/100) = a 0 (1 + r/100) 2 n a n = a 0 (1 + r/100) n a n a 0 2 n a 0 (1 + r/100) n = 2a 0 (1 + r/100) n = 2

More information

. (.8.). t + t m ü(t + t) + c u(t + t) + k u(t + t) = f(t + t) () m ü f. () c u k u t + t u Taylor t 3 u(t + t) = u(t) + t! u(t) + ( t)! = u(t) + t u(

. (.8.). t + t m ü(t + t) + c u(t + t) + k u(t + t) = f(t + t) () m ü f. () c u k u t + t u Taylor t 3 u(t + t) = u(t) + t! u(t) + ( t)! = u(t) + t u( 3 8. (.8.)............................................................................................3.............................................4 Nermark β..........................................

More information

http://www2.math.kyushu-u.ac.jp/~hara/lectures/lectures-j.html 2 N(ε 1 ) N(ε 2 ) ε 1 ε 2 α ε ε 2 1 n N(ɛ) N ɛ ɛ- (1.1.3) n > N(ɛ) a n α < ɛ n N(ɛ) a n

http://www2.math.kyushu-u.ac.jp/~hara/lectures/lectures-j.html 2 N(ε 1 ) N(ε 2 ) ε 1 ε 2 α ε ε 2 1 n N(ɛ) N ɛ ɛ- (1.1.3) n > N(ɛ) a n α < ɛ n N(ɛ) a n http://www2.math.kyushu-u.ac.jp/~hara/lectures/lectures-j.html 1 1 1.1 ɛ-n 1 ɛ-n lim n a n = α n a n α 2 lim a n = 1 n a k n n k=1 1.1.7 ɛ-n 1.1.1 a n α a n n α lim n a n = α ɛ N(ɛ) n > N(ɛ) a n α < ɛ

More information

" " " " "!!

    !! ""!!!!! "! "! " " " " " " " "!! !!!!!!!!! ! !!!!! "β!"β"! " " "!! "! "!!! "!! !!! "! "!!!! "! !!!!! !!! " "!! "!!! " " "!!! ! "!! !!!!!!! " " " " "!! α!!!!! ! "! " " !!!!!!! "! ! ""!!!! !!!!!! " "! "!

More information

note2.dvi

note2.dvi 8 216614 2.4 Joh Bardee, William Shockley, Walter Brattai. 1948 Bell William Shockley BrattaiBardee Shockley 1947 (12/16 23)Shockley BrattaiBardee (Trasistor, TrasferResistor ) Shockley 1/23 1 [2] 2.4.1

More information

untitled

untitled 0. =. =. (999). 3(983). (980). (985). (966). 3. := :=. A A. A A. := := 4 5 A B A B A B. A = B A B A B B A. A B A B, A B, B. AP { A, P } = { : A, P } = { A P }. A = {0, }, A, {0, }, {0}, {}, A {0}, {}.

More information

橡Taro9-生徒の活動.PDF

橡Taro9-生徒の活動.PDF 3 1 4 1 20 30 2 2 3-1- 1 2-2- -3- 18 1200 1 4-4- -5- 15 5 25 5-6- 1 4 2 1 10 20 2 3-7- 1 2 3 150 431 338-8- 2 3 100 4 5 6 7 1-9- 1291-10 - -11 - 10 1 35 2 3 1866 68 4 1871 1873 5 6-12 - 1 2 3 4 1 4-13

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

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

A B 5 C 9 3.4 7 mm, 89 mm 7/89 = 3.4. π 3 6 π 6 6 = 6 π > 6, π > 3 : π > 3

A B 5 C 9 3.4 7 mm, 89 mm 7/89 = 3.4. π 3 6 π 6 6 = 6 π > 6, π > 3 : π > 3 π 9 3 7 4. π 3................................................. 3.3........................ 3.4 π.................... 4.5..................... 4 7...................... 7..................... 9 3 3. p

More information

i 0 1 0.1 I................................................ 1 0.2.................................................. 2 0.2.1...........................

i 0 1 0.1 I................................................ 1 0.2.................................................. 2 0.2.1........................... 2008 II 21 1 31 i 0 1 0.1 I................................................ 1 0.2.................................................. 2 0.2.1............................................. 2 0.2.2.............................................

More information

1/68 A. 電気所 ( 発電所, 変電所, 配電塔 ) における変圧器の空き容量一覧 平成 31 年 3 月 6 日現在 < 留意事項 > (1) 空容量は目安であり 系統接続の前には 接続検討のお申込みによる詳細検討が必要となります その結果 空容量が変更となる場合があります (2) 特に記載

1/68 A. 電気所 ( 発電所, 変電所, 配電塔 ) における変圧器の空き容量一覧 平成 31 年 3 月 6 日現在 < 留意事項 > (1) 空容量は目安であり 系統接続の前には 接続検討のお申込みによる詳細検討が必要となります その結果 空容量が変更となる場合があります (2) 特に記載 1/68 A. 電気所 ( 発電所, 変電所, 配電塔 ) における変圧器の空き容量一覧 平成 31 年 3 月 6 日現在 < 留意事項 > (1) 空容量は目安であり 系統接続の前には 接続検討のお申込みによる詳細検討が必要となります その結果 空容量が変更となる場合があります (2) 特に記載のない限り 熱容量を考慮した空き容量を記載しております その他の要因 ( 電圧や系統安定度など ) で連系制約が発生する場合があります

More information

1 180m g 10m/s 2 2 6 1 3 v 0 (t=0) z max t max t z = z max 1 2 g(t t max) 2 (6) 1.3 2 3 3 r = (x, y, z) e x, e y, e z r = xe x + ye y + ze z. (7) v =

1 180m g 10m/s 2 2 6 1 3 v 0 (t=0) z max t max t z = z max 1 2 g(t t max) 2 (6) 1.3 2 3 3 r = (x, y, z) e x, e y, e z r = xe x + ye y + ze z. (7) v = 1. 2. 3 3. 4. 5. 6. 7. 8. 9. I http://risu.lowtem.hokudai.ac.jp/ hidekazu/class.html 1 1.1 1 a = g, (1) v = g t + v 0, (2) z = 1 2 g t2 + v 0 t + z 0. (3) 1.2 v-t. z-t. z 1 z 0 = dz = v, t1 dv v(t), v

More information

IA

IA IA 31 4 11 1 1 4 1.1 Planck.............................. 4 1. Bohr.................................... 5 1.3..................................... 6 8.1................................... 8....................................

More information

QMI_10.dvi

QMI_10.dvi ... black body radiation black body black body radiation Gustav Kirchhoff 859 895 W. Wien O.R. Lummer cavity radiation ν ν +dν f T (ν) f T (ν)dν = 8πν2 c 3 kt dν (Rayleigh Jeans) (.) f T (ν) spectral energy

More information

講義ノート 物性研究 電子版 Vol.3 No.1, (2013 年 T c µ T c Kammerlingh Onnes 77K ρ 5.8µΩcm 4.2K ρ 10 4 µωcm σ 77K ρ 4.2K σ σ = ne 2 τ/m τ 77K

講義ノート 物性研究 電子版 Vol.3 No.1, (2013 年 T c µ T c Kammerlingh Onnes 77K ρ 5.8µΩcm 4.2K ρ 10 4 µωcm σ 77K ρ 4.2K σ σ = ne 2 τ/m τ 77K 2 2 T c µ T c 1 1.1 1911 Kammerlingh Onnes 77K ρ 5.8µΩcm 4.2K ρ 1 4 µωcm σ 77K ρ 4.2K σ σ = ne 2 τ/m τ 77K τ 4.2K σ 58 213 email:takada@issp.u-tokyo.ac.jp 1933 Meissner Ochsenfeld λ = 1 5 cm B = χ B =

More information