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
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22 G =V E G =V E E E G G G G G G
23 G= =VE G G
24
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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
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37 TOP Daa Flow Diagram
38 DFD
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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 = = +
橡CompSimmAllcpct.PDF
3 1 M dx 1 dx/ 1/ x P 0 (x) x dx x P 0 (x) x+dx P 0 (x+dx) x dx P 0 (x+dx)=p 0 (x)(1-dx/ dx/) x P 0 (x) P 0 (x+dx)=p 0 (x)(1-dx/ dx/) Tayler (dx) P 0 (x)+(dp 0 /dx)dx (dp 0 (x)/dx)dx= -P 0 (x) dx/
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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
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Super perfect numbers and Mersenne perefect numbers /2/22 1 m, , 31 8 P = , P =
Super perfect numbers and Mersenne perefect numbers 3 2019/2/22 1 m, 2 2 5 3 5 4 18 5 20 6 25 7, 31 8 P = 5 35 9, 38 10 P = 5 39 1 1 m, 1: m = 28 m = 28 m = 10 height48 2 4 3 A 40 2 3 5 A 2002 2 7 11 13
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18 I ( ) (1) I-1,I-2,I-3 (2) (3) I-1 ( ) (100 ) θ ϕ θ ϕ m m l l θ ϕ θ ϕ 2 g (1) (2) 0 (3) θ ϕ (4) (3) θ(t) = A 1 cos(ω 1 t + α 1 ) + A 2 cos(ω 2 t + α
18 I ( ) (1) I-1,I-2,I-3 (2) (3) I-1 ( ) (100 ) θ ϕ θ ϕ m m l l θ ϕ θ ϕ 2 g (1) (2) 0 (3) θ ϕ (4) (3) θ(t) = A 1 cos(ω 1 t + α 1 ) + A 2 cos(ω 2 t + α 2 ), ϕ(t) = B 1 cos(ω 1 t + α 1 ) + B 2 cos(ω 2 t
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1. A0 A B A0 A : A1,...,A5 B : B1,...,B12 2. 3. 4. 5. A0 A B f : A B 4 (i) f (ii) f (iii) C 2 g, h: C A f g = f h g = h (iv) C 2 g, h: B C g f = h f g = h 4 (1) (i) (iii) (2) (iii) (i) (3) (ii) (iv) (4)
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t χ 2 F Q t χ 2 F 1 2 µ, σ 2 N(µ, σ 2 ) f(x µ, σ 2 ) = 1 ( exp (x ) µ)2 2πσ 2 2σ 2 0, N(0, 1) (100 α) z(α) t χ 2 *1 2.1 t (i)x N(µ, σ 2 ) x µ σ N(0, 1
t χ F Q t χ F µ, σ N(µ, σ ) f(x µ, σ ) = ( exp (x ) µ) πσ σ 0, N(0, ) (00 α) z(α) t χ *. t (i)x N(µ, σ ) x µ σ N(0, ) (ii)x,, x N(µ, σ ) x = x+ +x N(µ, σ ) (iii) (i),(ii) z = x µ N(0, ) σ N(0, ) ( 9 97.
(τ τ ) τ, σ ( ) w = τ iσ, w = τ + iσ (w ) w, w ( ) τ, σ τ = (w + w), σ = i (w w) w, w w = τ w τ + σ w σ = τ + i σ w = τ w τ + σ w σ = τ i σ g ab w, w
S = 4π dτ dσ gg ij i X µ j X ν η µν η µν g ij g ij = g ij = ( 0 0 ) τ, σ (+, +) τ τ = iτ ds ds = dτ + dσ ds = dτ + dσ δ ij ( ) a =, a = τ b = σ g ij δ ab g g ( +, +,... ) S = 4π S = 4π ( i) = i 4π dτ dσ
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平成20年5月 協会創立50年の歩み 海の安全と環境保全を目指して 友國八郎 海上保安庁 長官 岩崎貞二 日本船主協会 会長 前川弘幸 JF全国漁業協同組合連合会 代表理事会長 服部郁弘 日本船長協会 会長 森本靖之 日本船舶機関士協会 会長 大内博文 航海訓練所 練習船船長 竹本孝弘 第二管区海上保安本部長 梅田宜弘
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145 13 13.1 13.1.1 0 m mg S 13.1 F 13.1 F /m S F F 13.1 F mg S F F mg 13.1: m d2 r 2 = F + F = 0 (13.1) 146 13 F = F (13.2) S S S S S P r S P r r = r 0 + r (13.3) r 0 S S m d2 r 2 = F (13.4) (13.3) d 2
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1 1.1 (population) (sample) (event) (trial) Ω () 1 1 Ω 1.2 P 1. A A P (A) 0 1 0 P (A) 1 (1) 2. P 1 P 0 1 6 1 1 6 0 3. A B P (A B) = P (A) + P (B) (2) A B A B A 1 B 2 A B 1 2 1 2 1 1 2 2 3 1.3 A B P (A
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
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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)
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(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
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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
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