橡試験直前配布.PDF

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1

2 d d/ /

3 P 0 d P 0 +d P 0 +d d P 0 +d=p 0 -d/ d/

4 P 0 P 0 +d=p 0 -d/ d/ Tayler d P 0 +dp 0 /dd dp 0 /dd= -P 0 d/ d/ /P 0 dp 0 /d= -/ / /P 0 dp 0 = -/ / d logp 0 =-/ /+cons. P 0 =e -/ / =0 0 0

5 +d f d d f d=p 0 d/ d/=e -/ / / d f =e -/ / / [ ] / / λ λ e / λd = e 0 = 0 = 0 λ / e d λ = λ 0

6 = y=e - =/ y=e -/ / y=e / / = y=e - = =/ y=e -/ y=e / / / =

7 [ ] λ λ λ λ λ / / 0 / 0 / / e e e d e = = = = = =/ / y y y e y log log / log / λ λ λ λ = = = = /λ e y =

8 y = e /λ

9 y = e /λ y = e / λ log y = / λ = λlog y = λlog y

10 F X U0 U< X=F - U 0

11 rnd 0 double ep_rndin { reurn *log/rnd;} a b ep_rnda ep_rndb

12

13 . 0 ep_rnda. ep_rndb a ep_rnda. 3b.

14 queue.c #include <sdio.h> #include <mah.h> 3 #include <sdlib.h> 4 #define NofClerk 3 5 enum even_ype {arivalfinish}; 6 sruc even_node { 7 long ime; 8 enum even_ype ype; 9 in clerk_id; 0 sruc even_node *ne; }; long mean_arival_inerval; 3 long mean_operaion_inerval; 4 long qui_ime; 5 in clerk_busy[nofclerk]; 6 in nof_person_in_queue; 7 long curren_ime; 8 sruc even_node *even_roo; 9 void even_addlong inervalenum even_ype ypein clerk_id; 0 long ep_rndlong mean_inerval; BSD

15 queue.c main in mainin argcchar **argv{ in i; 3 sruc even_node *rm_even; 4 ifargc!=4{ 5 prinf"usage: queue arival_inerval operaion_inerval qui_ime n"; 6 reurn ; 7 } 8 sscanfargv[]"%d"&mean_arival_inerval; 9 sscanfargv[]"%d"&mean_operaion_inerval; 30 sscanfargv[3]"%d"&qui_ime; 3 fori=0;i<nofclerk;i++ clerk_busy[i]=0; 3 nof_person_in_queue=; 33 curren_ime=0; 34 even_roo=null; 35 even_addep_rndmean_arival_inervalarival0;. 66 }

16 36 for;;{ 37 ifcurren_ime>qui_imereurn 0; 44 for;;{ 45 if!nof_person_in_queue break; 46 fori=0;i<nofclerk;i++{ 47 if!clerk_busy[i] break; 48 } 49 ifi==nofclerk break; 50 clerk_busy[i]++; 5 nof_person_in_queue--; 5 even_addep_rndmean_operaion_inervalfinishi; 53 } 54 rm_even=even_roo; 55 even_roo=rm_even->ne; 56 curren_ime=rm_even->ime; 57 ifrm_even->ype==arival{ 58 nof_person_in_queue++; 59 even_addep_rndmean_arival_inervalarival0; 60 } 6 else ifrm_even->ype==finish 6 clerk_busy[rm_even->clerk_id]=0; 63 else ; 64 freerm_even; 65 } queue.c main 38 /* */ 39 prinf"ime=%3d nof_p=%3d" curren_imenof_person_in_queue; 40 fori=0;i<nofclerk;i++ 4 prinf" busy[%d]=%d"iclerk_busy[i]; 4 prinf" n"; 43 /* */

17 67 void even_addlong inervalenum even_ype ypein clerk_id{ 68 sruc even_node *new_even; 69 sruc even_node *even; 70 new_even=sruc even_node *mallocsizeofsruc even_node; 7 new_even->ime=curren_ime+inerval; 7 new_even->ype=ype; 73 new_even->clerk_id=clerk_id; 74 ifeven_roo==null{ 75 new_even->ne=null; 76 even_roo=new_even; 77 reurn; 78 } 79 ifeven_roo->ime>new_even->ime{ 80 new_even->ne=even_roo; 8 even_roo=new_even; 8 reurn; 83 } 84 foreven=even_roo;;even=even->ne{ 85 ifeven->ne==null{ 86 new_even->ne=null; 87 even->ne=new_even; 88 reurn; 89 } 90 ifeven->ne->ime>new_even->ime{ 9 new_even->ne=even->ne; 9 even->ne=new_even; 93 reurn; 94 } 95 } 96 } queue.c even_add

18 queue.c ep_rnd 97 long ep_rndlong mean_inerval{ 98 double r; 99 r=doublemean_inerval*logdoublerand_max/doublerandom; 00 reurn longr; 0 } random0 RAND_MAX

19 v e v e3 e e5 e4 e6 e7 v3 e8 v4

20 G= =V E V V V V V v e v e3 V ={v v 3 } V ={v v 4 } e v3 e5 e4 e8 e6 v4 e7 E ={e e 4 e 5 e 8 } CE =V V

21

22 G =V E G =V E E E G G G G G G

23 G= =VE G G

24

25

26

27 A B readera wrier readerb

28 sae machine

29 marked graph

30 NG OK OK NG

31 free choice ne

32 fork join selec

33 simple Peri ne

34

35 Peri Peri

36

37 TOP Daa Flow Diagram

38 DFD

39

40 DFD

41 TOP MiniSpec

42 Mealey

43 A B C D A=BCD E=F+G+H J=K* E F o G o H o J K*

44 * o o

45 decision ree 5g 90 50g60 5g0 50g90 5g30 50g30

46 decision able decision able 3

47

48 BDD 3 90 no yes 5g no yes no no yes yes

49 GFq q m p p { 0 L p } p mod p

50 i + F F F GF p GF p m GF p m

51 m F GF m p F α m GF p α m 0 p α = α α L α m p α p m = m GF p

52 α m F F α = 0 α m Gα m α m = Gα m m GF p i α α m i m α = a0 + aα + L + am α a 0 a m a L 0 a m a a L m GF p

53 GF / GF m α + α = + α = 0 α = α

54 b b F = f 0 + f + L + fb + b α GF b α α

55 a0 a L a b GF b a = a 0 + aα + L + a b α b α α

56 3 3 b a b a a a α α α α = L b α 0 0 = = b b f b f f F α α α α L = b b b f f f α α α L = b b b b b b f a a f a a f a a α α α L a α b b b b b f a a f a a f a L

57 a α b b b b b f a a f a a f a L b b f f f f a a a L L L L L L L L L L a 0 a b a a L

58 f f a 0 a a b- f 0 f f f b- M

59 ++ 4 M ++ 4 = a 0 a a a 3 a 0 a a a 3

60 Mersenne Twiser GF = 3... ^9937- ^ ^

61 M - M

62 0 d p = md m = nt n p00= p0=0 0 p+t=/p-d+/p+d

63 d d d p p d p d p T d T p T p + = + d p p p d p p T p + = +

64 d d d p p d p d p T d T p T p + = + T d 0 d T p p T d p = 0 p δ =

65 d d d p p d p d p T d T p T p + = + p md = nt = T d p T d p = 0 p δ =

66 p T d p = p D p = D > 0 0 p δ = D e D p 4 4 = π

67 µ σ N µ σ µ σ f = e πσ p = e 4D 4πD D = σ

68 T d / n + n - nt md pmd nt + n n = + n n + n = m p md nt n n + n n! p md nt = nc + n = + + n! n n! n

69 n! p md nt n! n n! n n = nc + n = + + n + + n = n n + n = m p md nt = n + n!! n! n = n n! + m n! m! n

70 3 3 n n n ne n n π! log log! log π + + n n n n n m e n nt md p = π

71 D e D p 4 4 = π n m e n nt md p = π md = nt = T d D = n m n T d d m e nd e nt T d nt md p 4 4 = = π π

72 m p md nt = e n πn d m p md nt = e n πnd

73 3 m p md nt = e n πnd p n m md d md d

74 -l n l n v h l / l l τc = v h

75 -l A B l A 0 l n d n τc B n d l 0

76 3 -l A B l n τ c 0 n d l 0 l n d

77 4 n -l A n B l 0 n d l 0 l n d / dn d l

78 5 A B dn d l τ c -l l l dn τ c d l τ c D

79 6 + n D n D + n D n n n = D +

80 7 7 + = + n n D n n D n n D n = = +

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

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

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

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