Vol. 32, Special Issue, S 1 S 17 (2011)

Size: px
Start display at page:

Download "Vol. 32, Special Issue, S 1 S 17 (2011)"

Transcription

1 Vol. 32, Special Issue, S 1 S 17 (2011) luke154@jcom.home.ne.jp

2 S Herman Nilsson-Ehle F 2 F E. M. East 1.3 Wilhelm Ludwig Johannsen , , gene genotype phenotype

3 S Ronald Aylmer Fisher The correlation between relatives on the supposition of Mendelian inheritance Biometrika 1918 epistasis population genetics A 3 A 1A 1, A 1A 2, A 2A 2 f 11, 2f 12, f 22 (f 11 +2f 12 + f 22 =1) g 11, g 12, g 22 A 1, A 2 2 A 1 : p = f 11 + f 12 A 2 : q = f 12 + f 22 (1) (p + q =1) ḡ ḡ = f 11g 11 +2f 12g 12 + f 22g 22 (2) ḡ y 11 = g 11 ḡ y 12 = g 12 ḡ

4 S4 y 22 = g 22 ḡ (3) y 11, y 12, y 22 A 1, A 2 θ 1, θ 2 A 1A 1, A 1A 2, A 2A 2 2θ 1, θ 1 + θ 2,2θ 2 dominance A 1A 1 y 11 2θ 1 2 Q = f 11(y 11 2θ 1) 2 +2f 12(y 12 θ 1 θ 2) 2 + f 22(y 22 2θ 2) 2 (4) Q θ 1, θ 2 θ 1, θ 2 A 1, A 2 average effect y 11, y 12, y 22 θ 1 + θ 1, θ 1 + θ 2, θ 2 + θ 2 A 1 1 Q θ 1, θ 2 (4) θ 1, θ θ 1, θ 2 g 11 = 100, g 12 = 90, g 22 =60 f 11 =0.25, f 12 =0.25, f 22 =0.25 ḡ = 85, θ 1 = 10, θ 2 = 10. f 11 =0.50, f 12 =0.25, f 22 =0.00 ḡ = 95, θ 1 =2.5, θ 2 = 7.5

5 Q = 4f 11(y 11 2θ 1) 4f 12(y 12 θ 1 θ 2) = 0 θ 1 Q = 4f 12(y 12 θ 1 θ 2) 4f 22(y 22 2θ 2)=0 θ 2 S5 (5a) (5b) pθ 1 + qθ 2 =0 (6) θ = θ 1 θ 2 (7) θ 1 = qθ θ 2 = pθ (8a) (8b) θ A 1 A 2 A 1 A 2 p = q a A 1A 1, A 1A 2, A 2A 2 2θ 1, θ 1 + θ 2,2θ 2 A 1 δ 11 = y 11 2θ 1 δ 12 = y 12 θ 1 θ 2 δ 22 = y 22 2θ 2 (9a) (9b) (9c) A 1A 1, A 1A 2, A 2A 2 population genetics A 1 A 2 p,q A 1A 1, A 1A 2, A 2A 2 p 2,2pq, q 2 HW HW HW

6 S6 V g V g = f 11y f 12y f 22y22 2 (10) V a = f 11(2θ 1) 2 +2f 12(θ 1 + θ 2) 2 + f 22(2θ 2) 2 = p 2 (2θ 1) 2 +2pq(θ 1 + θ 2) 2 + q 2 (2θ 2) 2 =2pqθ 2 (6) (11) The genetical interpretation of statistics of the third degree in the study of quantitative inheritance F. R. Immer Olof Tedin d,h, d d h F 2 F 3 F F 2 F d h F 2 2

7 S7 2 Kenneth Mather DNA g e p p = g + e (12) g e 0 σ 2 a i d i e 2 P 1 P 2 F 1,F 2,F 3 2 (12) A 2 A 1 A 2 3 A 1A 1 A 1A 2 A 2A 2 g 11, g 12, g 22 (g 11 g 22)/2 A a A A 1 A 2 A 1 A 2

8 S8 2.. a d g 11 = 100, g 12 = 90, g 22 =60. u = 80, a = 20, d =10 2 A 1 A 1 A 2 a i A 1 A 2 a i g 12 1 (g11 + g22) A 2 d A 0 d A =0 A d A < a A d A = a A d A > a A 2 P 1 P 2A, B 2 A, B a A, a B d A, d B F 1 A 1A 1B 1B 1 u + a A + a B (13a) A 1A 2B 1B 2 u + d A + d B (13b) A 2A 2B 2B 2 u a A a B (13c) u u

9 S9 u k (a)= (d)= (13a,b,c) kx i=1 kx i=1 a i d i (14a) (14b) A 1A 1B 1B 1 u +(a) (15a) A 1A 2B 1B 2 u +(d) (15b) A 2A 2B 2B 2 u (a) (15c) A B (k =2)F 2 9 A 1A 1B 1B 1, A 1A 1B 1B 2, A 1A 1B 2B 2, A 1A 2B 1B 1, A 1A 2B 1B 2, A 1A 2B 2B 2, A 2A 2B 1B 1, A 2A 2B 1B 2, A 2A 2B 2B 2 1:2:1:2:4:2:1:2:1 M g[f 2]=(1/16)A 1A 1B 1B 1 +(1/8)A 1A 1B 1B 2 + +(1/16)A 2A 2B 2B 2 =(1/16)(u + a A + a B)+(1/8)(u + a A + d A)+ +(1/16)(u a A a A) = u +(1/2)d A +(1/2)d B = u +(1/2)(d) (16) (a) (d) (12) V P = V G + E (17) V G E F 2 A (1/4)A 1A 1 :(1/2)A 1A 2 :(1/4)A 2A 2 V G[F 2]=(1/4)a 2 +(1/2)d 2 +(1/4)( a) 2 ((1/4)a +(1/2)d (1/4)a) 2 =(1/2)a 2 +(1/4)d 2 (18)

10 S10 i a i d i 2 A,D A = D = F 2 V P [F 2] kx i=1 kx i=1 a 2 i d 2 i (19a) (19b) V P [F 1 2]= 2 A D + E (20) E A D F 3 P 1 BC 1 P 2 BC 2 V P [F 3]=(3/4)A +(3/16)D + E (21) V P [BC 1]+V P [BC 2]=(1/2)A +(1/2)D +2E (22) F 2 F 3 F 2 F 3 F 2 P 1,P 2 F 1 V G =0, V P = E A,D E 3 A D V P A,D,E V P = c 1A + c 2D + E (23) c 1, c 2 F 2 c 1 =1/2, c 2 =1/4 h 2 B =(c 1A + c 2D)/(c 1A + c 2D + E) (24) h 2 N = c 1A/(c 1A + c 2D + E) (25) 2002

11 S11 Anderson and Kempthorne Biometrical Genetics 2 17 polygenic system 1

12 S Jay L. Lush Animal Breeding Plans 1937 Oscar Kempthorne Introduction to Genetic Statistics 1957Douglas Scott Falconer Introduction to Quantitative Genetics1961 Hayman (1954a,b) Griffing (1956) Finlay Wilkinson (1963) DNA QTL 4.1 2

13 S AABB aabb F 1 AB ab Ab ab A B 2 DNA DNA QTL 1980 RFLPRAPD AFLP SSR DNA DNA DNA DNA DNA DNA 1989 Lander Botstein Interval Mapping Quantitative Trait Locus QTL QTL QTL QTL DNA QTL QTL QTL QTL

14 S14 QTL QTL 4.4 QTL QTL F 2 QTL QTL 1 Q 2 A, B A, Q, B 3 AAQQBB, aaqqbb F 1 AQB/aqb / AQB aqb A Q Q B r 1, r 2 A B r 1+2 r 1 r 2 r 1 F 2 AABB, AABb, AAbb, AaBB, AaBb, Aabb, aabb, aabb, aabb Q QQ, Qq, qq 1 3 F 2 i Q j p ij 1 r 1, r 2, r 1+2 Q a,d QQ,Qq,qq 1. 2 i QTL Q 1 Q 1, Q 1 Q 2, Q 2 Q 2 p ij (F 2 ) i: Q 1 Q 1 (p i1 ) Q 1 Q 2 (p i2 ) Q 2 Q 2 (p i3 ) 1: A 1 A 1 B 1 B 1 q1 2 2 q 1 q 2 q2 2 2: A 1 A 1 B 1 B 2 q 1 q 3 q 1 q 4 + q 2 q 3 q 2 q 4 3: A 1 A 1 B 2 B 2 q3 2 2 q 3 q 4 q4 2 4: A 1 A 2 B 1 B 1 q 1 q 4 q 1 q 3 + q 2 q 4 q 2 q 3 5: A 1 A 2 B 1 B 2 z 1 q 1 q 2 + z 2 q 3 q 4 z 1 (q1 2 + q2 2 )+z 2(q3 2 + q2 4 ) z 1 q 1 q 2 + z 2 q 3 q 4 6: A 1 A 2 B 2 B 2 q 2 q 3 q 1 q 3 + q 2 q 4 q 1 q 4 7: A 2 A 2 B 1 B 1 q4 2 2 q 3 q 4 q3 2 8: A 2 A 2 B 1 B 2 q 2 q 4 q 1 q 4 + q 2 q 3 q 1 q 3 9: A 2 A 2 B 2 B 2 q2 2 2 q 1 q 2 q1 2 q 1 =(1 r 1 r 2 + r 12 )/(1 r 1+2 ) q 2 = r 12 /(1 r 1+2 ) q 3 =(r 2 r 12 )/r 1+2 (r 12 =2r 1+2 r 1 r 2 ) q 4 =(r 1 r 12 )/r 1+2 z 1 =(1 r 1+2 ) 2 /{(1 r 1+ ) 2 + r 2 1+2} z 2 =1 z 1 p i1 + p i2 + p i3 =1 (i =1, 2,...,9)

15 S15 u + a, u + d, u a u e e 0 σ 2 QQ,Qq,qq y QQ: φ 1 = 1 e (y u a)2 2σ 2 (26a) 2π Qq : φ 2 = 1 e (y u d)2 2σ 2 2π qq: φ 3 = 1 e (y u+a)2 2σ 2 2π (26b) (26c) i Q 1 QQ y p i1ϕ 1 i y Q QQ,Qq,qq z 1,z 2,z 3 z 1 + z 2 + z 3 =1 QQ : z 1 = p i1ϕ 1/(p i1ϕ 1 + p i2ϕ 2 + p i3ϕ 3) Qq : z 2 = p i2ϕ 2/(p i1ϕ 1 + p i2ϕ 2 + p i3ϕ 3) qq : z 3 = p i3ϕ 3/(p i1ϕ 1 + p i2ϕ 2 + p i3ϕ 3) (27a) (27b) (27c) z 1,z 2,z 3 n 9Y Y i L (p i1φ ij1) z ij1 (p i2φ ij2) z ij2 (p i3φ ij3) z ij3 (28) i=1 j=1 z ij1 i j j =1,...,n iq QQ p i1φ ij1,p i2φ ij2,p i3φ ij3 i j QTL Q 1Q 1, Q 1Q 2, Q 2Q 2 (28) Q 3 n 9Y Y i L (p i1φ ij1 + p i2φ ij2 + p i3φ ij3) (29) i=1 j=1 QTL u a d σ 2 4 u QTL 1 QTL QTL QTL L û,â, ˆd, ˆσ 2 log L 1 H 0 :û = u 0,â =0, ˆd =0, ˆσ 2 = σ0 2 log L 0

16 S16 3. QTL LOD 68cM 17 A Q LOD 33cM LOD =log 10 L log 10 L 0 (30) EM QTL 1 cm LOD LOD QTL 3 QTL QTL QTL DNA QTL 5. DNA Anderson, V.L. and Kempthorne, O. (1954). A model for the study of quantitative inheritance. Genetics, 39: Falconer, D.S. (1961). Introduction to Quantitative Genetics. Oliver and Boyd, Edinburgh.

17 S17 Finlay, K.W. and Wilkinson, G.N. (1963). The analysis of adaptation in a plant-breeding programme. Australian Journal of Agricultural Research, 14: Fisher, R.A. (1918). The correlation between relatives on the supposition of Mendelian inheritance. Transactions of the Royal Society of Edinburgh: Earth Sciences, 52: Fisher, R.A, Immer, F.R. and Tedin, O. (1932). The genetical interpretation of statistics of the third degree in the study of quantitative inheritance. Genetics, 17: Griffing, B. (1956). Concept of general and specific combining ability in relation to diallel crossing systems. Australian Journal of Biological Sciences, 9: Hayman, B.I. (1954a). The analysis of variance of diallel tables. Biometrics, 10: Hayman, B.I. (1954b). The theory and analysis of diallel crosses. Genetics, 39: Kempthorne, O. (1957). Introduction to Genetic Statistics. Iowa State Univ. Press. Iowa. (1960)... Lander, E.S. and Botstein, D. (1989). Mapping Mendelian factors underlying quantitative traits using RFLP linkage maps. Genetics, 121: Lush, J.L. (1937). (1 st ), (1943) (2 nd ). Animal Breeding Plans. Iowa State Univ. Press. Ames, Iowa. (1972). 2., 22: (2000)... (2002)...

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

EPSON VP-1200 取扱説明書

EPSON VP-1200 取扱説明書 4020178-01 w p s 2 p 3 4 5 6 7 8 p s s s p 9 p A B p C 10 D p E 11 F G H H 12 p G I s 13 p s A D p B 14 C D E 15 F s p G 16 A B p 17 18 s p s 19 p 20 21 22 A B 23 A B C 24 A B 25 26 p s p s 27 28 p s p

More information

15 実 験 物 動7(1),1958 近交係数計算の1 を知 るた め に,利 用 す る こ とが で き る 更 に 育 種 の 上 般 式 か ら,劣 性遺 伝 子 を明 るみ に 出す た め,選 技 淘汰 が容 易 とな り,好 ま しい遺 伝 子 頻 度 を高 め る こ とが で き る で あ る 但 し,Fx:Xの 近 交 係数 n:父 近 交 系 を め ぐ る2-3の 及び

More information

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 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.

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

untitled

untitled 17 5 13 1 2 1.1... 2 1.2... 2 1.3... 3 2 3 2.1... 3 2.2... 5 3 6 3.1... 6 3.2... 7 3.3 t... 7 3.4 BC a... 9 3.5... 10 4 11 1 1 θ n ˆθ. ˆθ, ˆθ, ˆθ.,, ˆθ.,.,,,. 1.1 ˆθ σ 2 = E(ˆθ E ˆθ) 2 b = E(ˆθ θ). Y 1,,Y

More information

ohpmain.dvi

ohpmain.dvi fujisawa@ism.ac.jp 1 Contents 1. 2. 3. 4. γ- 2 1. 3 10 5.6, 5.7, 5.4, 5.5, 5.8, 5.5, 5.3, 5.6, 5.4, 5.2. 5.5 5.6 +5.7 +5.4 +5.5 +5.8 +5.5 +5.3 +5.6 +5.4 +5.2 =5.5. 10 outlier 5 5.6, 5.7, 5.4, 5.5, 5.8,

More information

EPSON LP-S7000 セットアップガイド

EPSON LP-S7000 セットアップガイド h h h h h h h h h h h h h h h abc ade o n A A B o C F D G E o H B G n K I L M I K J o o C A D B E F G h h h h h h h abc ade B ade A C D F E G A C h ade A C D B o ade E G H F G I F J M K N L O A B n C P

More information

A (1) = 4 A( 1, 4) 1 A 4 () = tan A(0, 0) π A π

A (1) = 4 A( 1, 4) 1 A 4 () = tan A(0, 0) π A π 4 4.1 4.1.1 A = f() = f() = a f (a) = f() (a, f(a)) = f() (a, f(a)) f(a) = f 0 (a)( a) 4.1 (4, ) = f() = f () = 1 = f (4) = 1 4 4 (4, ) = 1 ( 4) 4 = 1 4 + 1 17 18 4 4.1 A (1) = 4 A( 1, 4) 1 A 4 () = tan

More information

新たな基礎年金制度の構築に向けて

新たな基礎年金制度の構築に向けて [ ] 1 1 4 60 1 ( 1 ) 1 1 1 4 1 1 1 1 1 4 1 2 1 1 1 ( ) 2 1 1 1 1 1 1 1996 1 3 4.3(2) 1997 1 65 1 1 2 1/3 ( )2/3 1 1/3 ( ) 1 1 2 3 2 4 6 2.1 1 2 1 ( ) 13 1 1 1 1 2 2 ( ) ( ) 1 ( ) 60 1 1 2.2 (1) (3) ( 9

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

48 * *2

48 * *2 374-1- 17 2 1 1 B A C A C 48 *2 49-2- 2 176 176 *2 -3- B A A B B C A B A C 1 B C B C 2 B C 94 2 B C 3 1 6 2 8 1 177 C B C C C A D A A B A 7 B C C A 3 C A 187 187 C B 10 AC 187-4- 10 C C B B B B A B 2 BC

More information

さくらの個別指導 ( さくら教育研究所 ) A 2 2 Q ABC 2 1 BC AB, AC AB, BC AC 1 B BC AB = QR PQ = 1 2 AC AB = PR 3 PQ = 2 BC AC = QR PR = 1

さくらの個別指導 ( さくら教育研究所 ) A 2 2 Q ABC 2 1 BC AB, AC AB, BC AC 1 B BC AB = QR PQ = 1 2 AC AB = PR 3 PQ = 2 BC AC = QR PR = 1 ... 0 60 Q,, = QR PQ = = PR PQ = = QR PR = P 0 0 R 5 6 θ r xy r y y r, x r, y x θ x θ θ (sine) (cosine) (tangent) sin θ, cos θ, tan θ. θ sin θ = = 5 cos θ = = 4 5 tan θ = = 4 θ 5 4 sin θ = y r cos θ =

More information

EPSON LP-8900ユーザーズガイド

EPSON LP-8900ユーザーズガイド 3 4 5 6 7 8 abc ade w p s 9 10 s s 11 p 12 p 13 14 p s 15 p s A B 16 w 17 C p 18 D E F 19 p w G H 20 A B 21 C s p D 22 E s p w 23 w w s 24 p w s 25 w 26 p p 27 w p s 28 w p 29 w p s 30 p s 31 A s B 32

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

140 120 100 80 60 40 20 0 115 107 102 99 95 97 95 97 98 100 64 72 37 60 50 53 50 36 32 18 H18 H19 H20 H21 H22 H23 H24 H25 H26 H27 1 100 () 80 60 40 20 0 1 19 16 10 11 6 8 9 5 10 35 76 83 73 68 46 44 H11

More information

1. 4cm 16 cm 4cm 20cm 18 cm L λ(x)=ax [kg/m] A x 4cm A 4cm 12 cm h h Y 0 a G 0.38h a b x r(x) x y = 1 h 0.38h G b h X x r(x) 1 S(x) = πr(x) 2 a,b, h,π

1. 4cm 16 cm 4cm 20cm 18 cm L λ(x)=ax [kg/m] A x 4cm A 4cm 12 cm h h Y 0 a G 0.38h a b x r(x) x y = 1 h 0.38h G b h X x r(x) 1 S(x) = πr(x) 2 a,b, h,π . 4cm 6 cm 4cm cm 8 cm λ()=a [kg/m] A 4cm A 4cm cm h h Y a G.38h a b () y = h.38h G b h X () S() = π() a,b, h,π V = ρ M = ρv G = M h S() 3 d a,b, h 4 G = 5 h a b a b = 6 ω() s v m θ() m v () θ() ω() dθ()

More information

Jacobson Prime Avoidance

Jacobson Prime Avoidance 2016 2017 2 22 1 1 3 2 4 2.1 Jacobson................. 4 2.2.................... 5 3 6 3.1 Prime Avoidance....................... 7 3.2............................. 8 3.3..............................

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 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

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) (2) (1) (2) 2 3 {a n } a 2 + a 4 + a a n S n S n = n = S n

(1) (2) (1) (2) 2 3 {a n } a 2 + a 4 + a a n S n S n = n = S n . 99 () 0 0 0 () 0 00 0 350 300 () 5 0 () 3 {a n } a + a 4 + a 6 + + a 40 30 53 47 77 95 30 83 4 n S n S n = n = S n 303 9 k d 9 45 k =, d = 99 a d n a n d n a n = a + (n )d a n a n S n S n = n(a + a n

More information

R R 16 ( 3 )

R R 16   ( 3 ) (017 ) 9 4 7 ( ) ( 3 ) ( 010 ) 1 (P3) 1 11 (P4) 1 1 (P4) 1 (P15) 1 (P16) (P0) 3 (P18) 3 4 (P3) 4 3 4 31 1 5 3 5 4 6 5 9 51 9 5 9 6 9 61 9 6 α β 9 63 û 11 64 R 1 65 13 66 14 7 14 71 15 7 R R 16 http://wwwecoosaka-uacjp/~tazak/class/017

More information

ii 3.,. 4. F. ( ), ,,. 8.,. 1. (75% ) (25% ) =7 24, =7 25, =7 26 (. ). 1.,, ( ). 3.,...,.,.,.,.,. ( ) (1 2 )., ( ), 0., 1., 0,.

ii 3.,. 4. F. ( ), ,,. 8.,. 1. (75% ) (25% ) =7 24, =7 25, =7 26 (. ). 1.,, ( ). 3.,...,.,.,.,.,. ( ) (1 2 )., ( ), 0., 1., 0,. (1 C205) 4 10 (2 C206) 4 11 (2 B202) 4 12 25(2013) http://www.math.is.tohoku.ac.jp/~obata,.,,,..,,. 1. 2. 3. 4. 5. 6. 7. 8. 1., 2007 ( ).,. 2. P. G., 1995. 3. J. C., 1988. 1... 2.,,. ii 3.,. 4. F. ( ),..

More information

直交座標系の回転

直交座標系の回転 b T.Koama x l x, Lx i ij j j xi i i i, x L T L L, L ± x L T xax axx, ( a a ) i, j ij i j ij ji λ λ + λ + + λ i i i x L T T T x ( L) L T xax T ( T L T ) A( L) T ( LAL T ) T ( L AL) λ ii L AL Λ λi i axx

More information

第84回日本遺伝学会-抄録集.indd

第84回日本遺伝学会-抄録集.indd A S1 9 24 14 00 17 00 Epigenomic regulation of cell fate determination and homeostasis Organizers: (National Institute of GeneticsKyushu University 14 00 S1-1 1 RIKEN BioResource Center 2 Graduate School

More information

PSCHG000.PS

PSCHG000.PS a b c a ac bc ab bc a b c a c a b bc a b c a ac bc ab bc a b c a ac bc ab bc a b c a ac bc ab bc de df d d d d df d d d d d d d a a b c a b b a b c a b c b a a a a b a b a

More information

waseda2010a-jukaiki1-main.dvi

waseda2010a-jukaiki1-main.dvi November, 2 Contents 6 2 8 3 3 3 32 32 33 5 34 34 6 35 35 7 4 R 2 7 4 4 9 42 42 2 43 44 2 5 : 2 5 5 23 52 52 23 53 53 23 54 24 6 24 6 6 26 62 62 26 63 t 27 7 27 7 7 28 72 72 28 73 36) 29 8 29 8 29 82 3

More information

DVIOUT-ar

DVIOUT-ar 1 4 μ=0, σ=1 5 μ=2, σ=1 5 μ=0, σ=2 3 2 1 0-1 -2-3 0 10 20 30 40 50 60 70 80 90 4 3 2 1 0-1 0 10 20 30 40 50 60 70 80 90 4 3 2 1 0-1 -2-3 -4-5 0 10 20 30 40 50 60 70 80 90 8 μ=2, σ=2 5 μ=1, θ 1 =0.5, σ=1

More information

Stepwise Chow Test * Chow Test Chow Test Stepwise Chow Test Stepwise Chow Test Stepwise Chow Test Riddell Riddell first step second step sub-step Step

Stepwise Chow Test * Chow Test Chow Test Stepwise Chow Test Stepwise Chow Test Stepwise Chow Test Riddell Riddell first step second step sub-step Step Stepwise Chow Test * Chow Test Chow Test Stepwise Chow Test Stepwise Chow Test Stepwise Chow Test Riddell Riddell first step second step sub-step Stepwise Chow Test a Stepwise Chow Test Takeuchi 1991Nomura

More information

さくらの個別指導 ( さくら教育研究所 ) 1 φ = φ 1 : φ [ ] a [ ] 1 a : b a b b(a + b) b a 2 a 2 = b(a + b). b 2 ( a b ) 2 = a b a/b X 2 X 1 = 0 a/b > 0 2 a

さくらの個別指導 ( さくら教育研究所 ) 1 φ = φ 1 : φ [ ] a [ ] 1 a : b a b b(a + b) b a 2 a 2 = b(a + b). b 2 ( a b ) 2 = a b a/b X 2 X 1 = 0 a/b > 0 2 a φ + 5 2 φ : φ [ ] a [ ] a : b a b b(a + b) b a 2 a 2 b(a + b). b 2 ( a b ) 2 a b + a/b X 2 X 0 a/b > 0 2 a b + 5 2 φ φ : 2 5 5 [ ] [ ] x x x : x : x x : x x : x x 2 x 2 x 0 x ± 5 2 x x φ : φ 2 : φ ( )

More information

研究シリーズ第40号

研究シリーズ第40号 165 PEN WPI CPI WAGE IIP Feige and Pearce 166 167 168 169 Vector Autoregression n (z) z z p p p zt = φ1zt 1 + φ2zt 2 + + φ pzt p + t Cov( 0 ε t, ε t j )= Σ for for j 0 j = 0 Cov( ε t, zt j ) = 0 j = >

More information

ρ /( ρ) + ( q, v ) : ( q, v ), L < q < q < q < L 0 0 ( t) ( q ( t), v ( t)) dq ( t) v ( t) lmr + 0 Φ( r) dt lmr + 0 Φ ( r) dv ( t) Φ ( q ( t) q ( t)) + Φ ( q+ ( t) q ( t)) dt ( ) < 0 ( q (0), v (0)) (

More information

23_02.dvi

23_02.dvi Vol. 2 No. 2 10 21 (Mar. 2009) 1 1 1 Effect of Overconfidencial Investor to Stock Market Behaviour Ryota Inaishi, 1 Fei Zhai 1 and Eisuke Kita 1 Recently, the behavioral finance theory has been interested

More information

note4.dvi

note4.dvi 10 016 6 0 4 (quantum wire) 4.1 4.1.1.6.1, 4.1(a) V Q N dep ( ) 4.1(b) w σ E z (d) E z (d) = σ [ ( ) ( )] x w/ x+w/ π+arctan arctan πǫǫ 0 d d (4.1) à ƒq [ƒg w ó R w d V( x) QŽŸŒ³ džq x (a) (b) 4.1 (a)

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

学習の手順

学習の手順 NAVI 2 MAP 3 m 17 13 19 12 17 24 1 20 18 23 18 12 1 12 17 11 14 16 19 22 m 12 16 A 16 20 B 20 24 24 28 C 20 AC 40 cm AD A 0.20 12 0.300 B 0.200 0.12 12 C D 40 1.000 20 2 2 0 20 30 cm 14 1 1 160 160 16

More information

(2) Fisher α (α) α Fisher α ( α) 0 Levi Civita (1) ( 1) e m (e) (m) ([1], [2], [13]) Poincaré e m Poincaré e m Kähler-like 2 Kähler-like

(2) Fisher α (α) α Fisher α ( α) 0 Levi Civita (1) ( 1) e m (e) (m) ([1], [2], [13]) Poincaré e m Poincaré e m Kähler-like 2 Kähler-like () 10 9 30 1 Fisher α (α) α Fisher α ( α) 0 Levi Civita (1) ( 1) e m (e) (m) ([1], [], [13]) Poincaré e m Poincaré e m Kähler-like Kähler-like Kähler M g M X, Y, Z (.1) Xg(Y, Z) = g( X Y, Z) + g(y, XZ)

More information

(Junjiro Ogawa),,,,, 1 IT (Internet Technology) (Big-Data) IoT (Internet of Things) ECO-FORUM 2018 ( ) ( ) ( ) ( ) 1

(Junjiro Ogawa),,,,, 1 IT (Internet Technology) (Big-Data) IoT (Internet of Things) ECO-FORUM 2018 ( ) ( ) ( ) ( ) 1 SDS-6 失われた 50 年 : ビッグデータ時代における統計科学の人材育成の課題 国友直人 November 2017 Statistics & Data Science Series back numbers: http://www.mims.meiji.ac.jp/publications/datascience.html 50 2017 10 50 (Junjiro Ogawa),,,,,

More information

φ 4 Minimal subtraction scheme 2-loop ε 2008 (University of Tokyo) (Atsuo Kuniba) version 21/Apr/ Formulas Γ( n + ɛ) = ( 1)n (1 n! ɛ + ψ(n + 1)

φ 4 Minimal subtraction scheme 2-loop ε 2008 (University of Tokyo) (Atsuo Kuniba) version 21/Apr/ Formulas Γ( n + ɛ) = ( 1)n (1 n! ɛ + ψ(n + 1) φ 4 Minimal subtraction scheme 2-loop ε 28 University of Tokyo Atsuo Kuniba version 2/Apr/28 Formulas Γ n + ɛ = n n! ɛ + ψn + + Oɛ n =,, 2, ψn + = + 2 + + γ, 2 n ψ = γ =.5772... Euler const, log + ax x

More information

2 (2016 3Q N) c = o (11) Ax = b A x = c A n I n n n 2n (A I n ) (I n X) A A X A n A A A (1) (2) c 0 c (3) c A A i j n 1 ( 1) i+j A (i, j) A (i, j) ã i

2 (2016 3Q N) c = o (11) Ax = b A x = c A n I n n n 2n (A I n ) (I n X) A A X A n A A A (1) (2) c 0 c (3) c A A i j n 1 ( 1) i+j A (i, j) A (i, j) ã i [ ] (2016 3Q N) a 11 a 1n m n A A = a m1 a mn A a 1 A A = a n (1) A (a i a j, i j ) (2) A (a i ca i, c 0, i ) (3) A (a i a i + ca j, j i, i ) A 1 A 11 0 A 12 0 0 A 1k 0 1 A 22 0 0 A 2k 0 1 0 A 3k 1 A rk

More information

shuron.dvi

shuron.dvi 01M3065 1 4 1.1........................... 4 1.2........................ 5 1.3........................ 6 2 8 2.1.......................... 8 2.2....................... 9 3 13 3.1.............................

More information

.5 z = a + b + c n.6 = a sin t y = b cos t dy d a e e b e + e c e e e + e 3 s36 3 a + y = a, b > b 3 s363.7 y = + 3 y = + 3 s364.8 cos a 3 s365.9 y =,

.5 z = a + b + c n.6 = a sin t y = b cos t dy d a e e b e + e c e e e + e 3 s36 3 a + y = a, b > b 3 s363.7 y = + 3 y = + 3 s364.8 cos a 3 s365.9 y =, [ ] IC. r, θ r, θ π, y y = 3 3 = r cos θ r sin θ D D = {, y ; y }, y D r, θ ep y yddy D D 9 s96. d y dt + 3dy + y = cos t dt t = y = e π + e π +. t = π y =.9 s6.3 d y d + dy d + y = y =, dy d = 3 a, b

More information

Microsoft Word - 11問題表紙(選択).docx

Microsoft Word - 11問題表紙(選択).docx A B A.70g/cm 3 B.74g/cm 3 B C 70at% %A C B at% 80at% %B 350 C γ δ y=00 x-y ρ l S ρ C p k C p ρ C p T ρ l t l S S ξ S t = ( k T ) ξ ( ) S = ( k T) ( ) t y ξ S ξ / t S v T T / t = v T / y 00 x v S dy dx

More information

) a + b = i + 6 b c = 6i j ) a = 0 b = c = 0 ) â = i + j 0 ˆb = 4) a b = b c = j + ) cos α = cos β = 6) a ˆb = b ĉ = 0 7) a b = 6i j b c = i + 6j + 8)

) a + b = i + 6 b c = 6i j ) a = 0 b = c = 0 ) â = i + j 0 ˆb = 4) a b = b c = j + ) cos α = cos β = 6) a ˆb = b ĉ = 0 7) a b = 6i j b c = i + 6j + 8) 4 4 ) a + b = i + 6 b c = 6i j ) a = 0 b = c = 0 ) â = i + j 0 ˆb = 4) a b = b c = j + ) cos α = cos β = 6) a ˆb = b ĉ = 0 7) a b = 6i j b c = i + 6j + 8) a b a b = 6i j 4 b c b c 9) a b = 4 a b) c = 7

More information

chap10.dvi

chap10.dvi . q {y j } I( ( L y j =Δy j = u j = C l ε j l = C(L ε j, {ε j } i.i.d.(,i q ( l= y O p ( {u j } q {C l } A l C l

More information

クローニングのための遺伝学

クローニングのための遺伝学 7. 量的形質の解析 クローニングのための遺伝学 ( 後編 Akifumi Shimiu 7. 量的形質とは量的形質 (quantitative character とは 表現型の値が数値で表される形質のことです 例えば長さや重さなどの形質の場合 F 世代での分離は左下図のように連続的になり易いです そのため 量的形質は質的形質と違い 表現型から遺伝子型を推測することが困難なため 一般的にマッピングが容易ではありません

More information

1 A A.1 G = A,B,C, A,B, (1) A,B AB (2) (AB)C = A(BC) (3) 1 A 1A = A1 = A (4) A A 1 A 1 A = AA 1 = 1 AB = BA ( ) AB BA ( ) 3 SU(N),N 2 (Lie) A(θ 1,θ 2,

1 A A.1 G = A,B,C, A,B, (1) A,B AB (2) (AB)C = A(BC) (3) 1 A 1A = A1 = A (4) A A 1 A 1 A = AA 1 = 1 AB = BA ( ) AB BA ( ) 3 SU(N),N 2 (Lie) A(θ 1,θ 2, 1 A A.1 G = A,B,C, A,B, (1) A,B AB (2) (AB)C = A(BC) (3) 1 A 1A = A1 = A (4) A A 1 A 1 A = AA 1 = 1 AB = BA ( ) AB BA ( ) 3 SU(N),N 2 (Lie) A(θ 1,θ 2,θ n ) = exp(i n i=1 θ i F i ) (A.1) F i 2 0 θ 2π 1

More information

D v D F v/d F v D F η v D (3.2) (a) F=0 (b) v=const. D F v Newtonian fluid σ ė σ = ηė (2.2) ė kl σ ij = D ijkl ė kl D ijkl (2.14) ė ij (3.3) µ η visco

D v D F v/d F v D F η v D (3.2) (a) F=0 (b) v=const. D F v Newtonian fluid σ ė σ = ηė (2.2) ė kl σ ij = D ijkl ė kl D ijkl (2.14) ė ij (3.3) µ η visco post glacial rebound 3.1 Viscosity and Newtonian fluid f i = kx i σ ij e kl ideal fluid (1.9) irreversible process e ij u k strain rate tensor (3.1) v i u i / t e ij v F 23 D v D F v/d F v D F η v D (3.2)

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

行列代数2010A

行列代数2010A a ij i j 1) i +j i, j) ij ij 1 j a i1 a ij a i a 1 a j a ij 1) i +j 1,j 1,j +1 a i1,1 a i1,j 1 a i1,j +1 a i1, a i +1,1 a i +1.j 1 a i +1,j +1 a i +1, a 1 a,j 1 a,j +1 a, ij i j 1,j 1,j +1 ij 1) i +j a

More information

untitled

untitled 3-1 ( sit ) (stead state vibratio) (trasiet vibratio) sit(a)w s ( W s ) W / g C (b) sit ( + s ) ( + s ) c + W + sit W s si t + s + c + si t (3.1) si t (3.1) a C W b sit(respose) () 3- acost+ bsit a sit+

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

zz + 3i(z z) + 5 = 0 + i z + i = z 2i z z z y zz + 3i (z z) + 5 = 0 (z 3i) (z + 3i) = 9 5 = 4 z 3i = 2 (3i) zz i (z z) + 1 = a 2 {

zz + 3i(z z) + 5 = 0 + i z + i = z 2i z z z y zz + 3i (z z) + 5 = 0 (z 3i) (z + 3i) = 9 5 = 4 z 3i = 2 (3i) zz i (z z) + 1 = a 2 { 04 zz + iz z) + 5 = 0 + i z + i = z i z z z 970 0 y zz + i z z) + 5 = 0 z i) z + i) = 9 5 = 4 z i = i) zz i z z) + = a {zz + i z z) + 4} a ) zz + a + ) z z) + 4a = 0 4a a = 5 a = x i) i) : c Darumafactory

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

t.dvi

t.dvi T-1 http://adapt.cs.tsukuba.ac.jp/moodle263/course/view.php?id=7 (Keisuke.Kameyama@cs.tsukuba.ac.jp) 29 10 11 1 ( ) (a) (b) (c) (d) SVD Tikhonov 3 (e) 1: ( ) 1 Objective Output s Known system p(s) b =

More information

(, Goo Ishikawa, Go-o Ishikawa) ( ) 1

(, Goo Ishikawa, Go-o Ishikawa) ( ) 1 (, Goo Ishikawa, Go-o Ishikawa) ( ) 1 ( ) ( ) ( ) G7( ) ( ) ( ) () ( ) BD = 1 DC CE EA AF FB 0 0 BD DC CE EA AF FB =1 ( ) 2 (geometry) ( ) ( ) 3 (?) (Topology) ( ) DNA ( ) 4 ( ) ( ) 5 ( ) H. 1 : 1+ 5 2

More information

: : : : ) ) 1. d ij f i e i x i v j m a ij m f ij n x i =

: : : : ) ) 1. d ij f i e i x i v j m a ij m f ij n x i = 1 1980 1) 1 2 3 19721960 1965 2) 1999 1 69 1980 1972: 55 1999: 179 2041999: 210 211 1999: 211 3 2003 1987 92 97 3) 1960 1965 1970 1985 1990 1995 4) 1. d ij f i e i x i v j m a ij m f ij n x i = n d ij

More information

20 4 20 i 1 1 1.1............................ 1 1.2............................ 4 2 11 2.1................... 11 2.2......................... 11 2.3....................... 19 3 25 3.1.............................

More information

85 4

85 4 85 4 86 Copright c 005 Kumanekosha 4.1 ( ) ( t ) t, t 4.1.1 t Step! (Step 1) (, 0) (Step ) ±V t (, t) I Check! P P V t π 54 t = 0 + V (, t) π θ : = θ : π ) θ = π ± sin ± cos t = 0 (, 0) = sin π V + t +V

More information

e a b a b b a a a 1 a a 1 = a 1 a = e G G G : x ( x =, 8, 1 ) x 1,, 60 θ, ϕ ψ θ G G H H G x. n n 1 n 1 n σ = (σ 1, σ,..., σ N ) i σ i i n S n n = 1,,

e a b a b b a a a 1 a a 1 = a 1 a = e G G G : x ( x =, 8, 1 ) x 1,, 60 θ, ϕ ψ θ G G H H G x. n n 1 n 1 n σ = (σ 1, σ,..., σ N ) i σ i i n S n n = 1,, 01 10 18 ( ) 1 6 6 1 8 8 1 6 1 0 0 0 0 1 Table 1: 10 0 8 180 1 1 1. ( : 60 60 ) : 1. 1 e a b a b b a a a 1 a a 1 = a 1 a = e G G G : x ( x =, 8, 1 ) x 1,, 60 θ, ϕ ψ θ G G H H G x. n n 1 n 1 n σ = (σ 1,

More information

10_11p01(Ł\”ƒ)

10_11p01(Ł\”ƒ) q q q q q q q q q q q q q q q q q q q q q q q q q qq q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q

More information

レイアウト 1

レイアウト 1 1 1 3 5 25 41 51 57 109 2 4 Q1 A. 93% 62% 41% 6 7 8 Q1-(1) Q2 A. 24% 13% 52% Q3 Q3 A. 68% 64 Q3-(2) Q3-(1) 9 10 A. Q3-(1) 11 A. Q3-(2) 12 A. 64% Q4 A. 47% 47% Q5 QQ A. Q Q A. 13 QQ A. 14 Q5-(1) A. Q6

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

5 H Boltzmann Einstein Brown 5.1 Onsager [ ] Tr Tr Tr = dγ (5.1) A(p, q) Â 0 = Tr Âe βĥ0 Tr e βĥ0 = dγ e βh 0(p,q) A(p, q) dγ e βh 0(p,q) (5.2) e βĥ0

5 H Boltzmann Einstein Brown 5.1 Onsager [ ] Tr Tr Tr = dγ (5.1) A(p, q) Â 0 = Tr Âe βĥ0 Tr e βĥ0 = dγ e βh 0(p,q) A(p, q) dγ e βh 0(p,q) (5.2) e βĥ0 5 H Boltzmann Einstein Brown 5.1 Onsager [ ] Tr Tr Tr = dγ (5.1) A(p, q) Â = Tr Âe βĥ Tr e βĥ = dγ e βh (p,q) A(p, q) dγ e βh (p,q) (5.2) e βĥ A(p, q) p q Â(t) = Tr Â(t)e βĥ Tr e βĥ = dγ() e βĥ(p(),q())

More information

) 9 81

) 9 81 4 4.0 2000 ) 9 81 10 4.1 natural numbers 1, 2, 3, 4, 4.2, 3, 2, 1, 0, 1, 2, 3, integral numbers integers 1, 2, 3,, 3, 2, 1 1 4.3 4.3.1 ( ) m, n m 0 n m 82 rational numbers m 1 ( ) 3 = 3 1 4.3.2 3 5 = 2

More information

untitled

untitled 1 ( 12 11 44 7 20 10 10 1 1 ( ( 2 10 46 11 10 10 5 8 3 2 6 9 47 2 3 48 4 2 2 ( 97 12 ) 97 12 -Spencer modulus moduli (modulus of elasticity) modulus (le) module modulus module 4 b θ a q φ p 1: 3 (le) module

More information

N cos s s cos ψ e e e e 3 3 e e 3 e 3 e

N cos s s cos ψ e e e e 3 3 e e 3 e 3 e 3 3 5 5 5 3 3 7 5 33 5 33 9 5 8 > e > f U f U u u > u ue u e u ue u ue u e u e u u e u u e u N cos s s cos ψ e e e e 3 3 e e 3 e 3 e 3 > A A > A E A f A A f A [ ] f A A e > > A e[ ] > f A E A < < f ; >

More information

Mantel-Haenszelの方法

Mantel-Haenszelの方法 Mantel-Haenszel 2008 6 12 ) 2008 6 12 1 / 39 Mantel & Haenzel 1959) Mantel N, Haenszel W. Statistical aspects of the analysis of data from retrospective studies of disease. J. Nat. Cancer Inst. 1959; 224):

More information

dvi

dvi 2017 65 2 185 200 2017 1 2 2016 12 28 2017 5 17 5 24 PITCHf/x PITCHf/x PITCHf/x MLB 2014 PITCHf/x 1. 1 223 8522 3 14 1 2 223 8522 3 14 1 186 65 2 2017 PITCHf/x 1.1 PITCHf/x PITCHf/x SPORTVISION MLB 30

More information

ADM-Hamiltonian Cheeger-Gromov 3. Penrose

ADM-Hamiltonian Cheeger-Gromov 3. Penrose ADM-Hamiltonian 1. 2. Cheeger-Gromov 3. Penrose 0. ADM-Hamiltonian (M 4, h) Einstein-Hilbert M 4 R h hdx L h = R h h δl h = 0 (Ric h ) αβ 1 2 R hg αβ = 0 (Σ 3, g ij ) (M 4, h ij ) g ij, k ij Σ π ij = g(k

More information

.3. (x, x = (, u = = 4 (, x x = 4 x, x 0 x = 0 x = 4 x.4. ( z + z = 8 z, z 0 (z, z = (0, 8, (,, (8, 0 3 (0, 8, (,, (8, 0 z = z 4 z (g f(x = g(

.3. (x, x = (, u = = 4 (, x x = 4 x, x 0 x = 0 x = 4 x.4. ( z + z = 8 z, z 0 (z, z = (0, 8, (,, (8, 0 3 (0, 8, (,, (8, 0 z = z 4 z (g f(x = g( 06 5.. ( y = x x y 5 y 5 = (x y = x + ( y = x + y = x y.. ( Y = C + I = 50 + 0.5Y + 50 r r = 00 0.5Y ( L = M Y r = 00 r = 0.5Y 50 (3 00 0.5Y = 0.5Y 50 Y = 50, r = 5 .3. (x, x = (, u = = 4 (, x x = 4 x,

More information

さくらの個別指導 ( さくら教育研究所 ) A 2 P Q 3 R S T R S T P Q ( ) ( ) m n m n m n n n

さくらの個別指導 ( さくら教育研究所 ) A 2 P Q 3 R S T R S T P Q ( ) ( ) m n m n m n n n 1 1.1 1.1.1 A 2 P Q 3 R S T R S T P 80 50 60 Q 90 40 70 80 50 60 90 40 70 8 5 6 1 1 2 9 4 7 2 1 2 3 1 2 m n m n m n n n n 1.1 8 5 6 9 4 7 2 6 0 8 2 3 2 2 2 1 2 1 1.1 2 4 7 1 1 3 7 5 2 3 5 0 3 4 1 6 9 1

More information

SO(2)

SO(2) TOP URL http://amonphys.web.fc2.com/ 1 12 3 12.1.................................. 3 12.2.......................... 4 12.3............................. 5 12.4 SO(2).................................. 6

More information

2 (1) a = ( 2, 2), b = (1, 2), c = (4, 4) c = l a + k b l, k (2) a = (3, 5) (1) (4, 4) = l( 2, 2) + k(1, 2), (4, 4) = ( 2l + k, 2l 2k) 2l + k = 4, 2l

2 (1) a = ( 2, 2), b = (1, 2), c = (4, 4) c = l a + k b l, k (2) a = (3, 5) (1) (4, 4) = l( 2, 2) + k(1, 2), (4, 4) = ( 2l + k, 2l 2k) 2l + k = 4, 2l ABCDEF a = AB, b = a b (1) AC (3) CD (2) AD (4) CE AF B C a A D b F E (1) AC = AB + BC = AB + AO = AB + ( AB + AF) = a + ( a + b) = 2 a + b (2) AD = 2 AO = 2( AB + AF) = 2( a + b) (3) CD = AF = b (4) CE

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

( )

( ) 18 10 01 ( ) 1 2018 4 1.1 2018............................... 4 1.2 2018......................... 5 2 2017 7 2.1 2017............................... 7 2.2 2017......................... 8 3 2016 9 3.1 2016...............................

More information

Taro10-名張1審無罪判決.PDF

Taro10-名張1審無罪判決.PDF -------------------------------------------------------------------------------- -------------------------------------------------------------------------------- -1- 39 12 23 36 4 11 36 47 15 5 13 14318-2-

More information

1 (1) () (3) I 0 3 I I d θ = L () dt θ L L θ I d θ = L = κθ (3) dt κ T I T = π κ (4) T I κ κ κ L l a θ L r δr δl L θ ϕ ϕ = rθ (5) l

1 (1) () (3) I 0 3 I I d θ = L () dt θ L L θ I d θ = L = κθ (3) dt κ T I T = π κ (4) T I κ κ κ L l a θ L r δr δl L θ ϕ ϕ = rθ (5) l 1 1 ϕ ϕ ϕ S F F = ϕ (1) S 1: F 1 1 (1) () (3) I 0 3 I I d θ = L () dt θ L L θ I d θ = L = κθ (3) dt κ T I T = π κ (4) T I κ κ κ L l a θ L r δr δl L θ ϕ ϕ = rθ (5) l : l r δr θ πrδr δf (1) (5) δf = ϕ πrδr

More information

x T = (x 1,, x M ) x T x M K C 1,, C K 22 x w y 1: 2 2

x T = (x 1,, x M ) x T x M K C 1,, C K 22 x w y 1: 2 2 Takio Kurita Neurosceince Research Institute, National Institute of Advanced Indastrial Science and Technology takio-kurita@aistgojp (Support Vector Machine, SVM) 1 (Support Vector Machine, SVM) ( ) 2

More information

,, 2. Matlab Simulink 2018 PC Matlab Scilab 2

,, 2. Matlab Simulink 2018 PC Matlab Scilab 2 (2018 ) ( -1) TA Email : ohki@i.kyoto-u.ac.jp, ske.ta@bode.amp.i.kyoto-u.ac.jp : 411 : 10 308 1 1 2 2 2.1............................................ 2 2.2..................................................

More information

linearal1.dvi

linearal1.dvi 19 4 30 I 1 1 11 1 12 2 13 3 131 3 132 4 133 5 134 6 14 7 2 9 21 9 211 9 212 10 213 13 214 14 22 15 221 15 222 16 223 17 224 20 3 21 31 21 32 21 33 22 34 23 341 23 342 24 343 27 344 29 35 31 351 31 352

More information

I A A441 : April 15, 2013 Version : 1.1 I Kawahira, Tomoki TA (Shigehiro, Yoshida )

I A A441 : April 15, 2013 Version : 1.1 I   Kawahira, Tomoki TA (Shigehiro, Yoshida ) I013 00-1 : April 15, 013 Version : 1.1 I Kawahira, Tomoki TA (Shigehiro, Yoshida) http://www.math.nagoya-u.ac.jp/~kawahira/courses/13s-tenbou.html pdf * 4 15 4 5 13 e πi = 1 5 0 5 7 3 4 6 3 6 10 6 17

More information

n ( (

n ( ( 1 2 27 6 1 1 m-mat@mathscihiroshima-uacjp 2 http://wwwmathscihiroshima-uacjp/~m-mat/teach/teachhtml 2 1 3 11 3 111 3 112 4 113 n 4 114 5 115 5 12 7 121 7 122 9 123 11 124 11 125 12 126 2 2 13 127 15 128

More information

1 Abstract 2 3 n a ax 2 + bx + c = 0 (a 0) (1) ( x + b ) 2 = b2 4ac 2a 4a 2 D = b 2 4ac > 0 (1) 2 D = 0 D < 0 x + b 2a = ± b2 4ac 2a b ± b 2

1 Abstract 2 3 n a ax 2 + bx + c = 0 (a 0) (1) ( x + b ) 2 = b2 4ac 2a 4a 2 D = b 2 4ac > 0 (1) 2 D = 0 D < 0 x + b 2a = ± b2 4ac 2a b ± b 2 1 Abstract n 1 1.1 a ax + bx + c = 0 (a 0) (1) ( x + b ) = b 4ac a 4a D = b 4ac > 0 (1) D = 0 D < 0 x + b a = ± b 4ac a b ± b 4ac a b a b ± 4ac b i a D (1) ax + bx + c D 0 () () (015 8 1 ) 1. D = b 4ac

More information

G H J(g, τ G g G J(g, τ τ J(g 1 g, τ = J(g 1, g τj(g, τ J J(1, τ = 1 k g = ( a b c d J(g, τ = (cτ + dk G = SL (R SL (R G G α, β C α = α iθ (θ R

G H J(g, τ G g G J(g, τ τ J(g 1 g, τ = J(g 1, g τj(g, τ J J(1, τ = 1 k g = ( a b c d J(g, τ = (cτ + dk G = SL (R SL (R G G α, β C α = α iθ (θ R 1 1.1 SL (R 1.1.1 SL (R H SL (R SL (R H H H = {z = x + iy C; x, y R, y > 0}, SL (R = {g M (R; dt(g = 1}, gτ = aτ + b a b g = SL (R cτ + d c d 1.1. Γ H H SL (R f(τ f(gτ G SL (R G H J(g, τ τ g G Hol f(τ

More information

2019 1 5 0 3 1 4 1.1.................... 4 1.1.1......................... 4 1.1.2........................ 5 1.1.3................... 5 1.1.4........................ 6 1.1.5......................... 6 1.2..........................

More information

EPSON LP-8900スタートアップガイド

EPSON LP-8900スタートアップガイド 1 2 3 4 5 6 7 8 4020009-01 F04 abc ade abc 1 abc ade 2 ade ade 3 4 w s A B C D E s s s s s s s s s 5 6 s 7 8 s s 9 10 w 700mm 200mm 400mm 878mm 200mm *1 720mm 200mm 1354mm w 11 abc w B A C w 12 D w s

More information

() [REQ] 0m 0 m/s () [REQ] (3) [POS] 4.3(3) ()() () ) m/s 4. ) 4. AMEDAS

() [REQ] 0m 0 m/s () [REQ] (3) [POS] 4.3(3) ()() () ) m/s 4. ) 4. AMEDAS () [REQ] 4. 4. () [REQ] 0m 0 m/s () [REQ] (3) [POS] 4.3(3) ()() () 0 0 4. 5050 0 ) 00 4 30354045m/s 4. ) 4. AMEDAS ) 4. 0 3 ) 4. 0 4. 4 4.3(3) () [REQ] () [REQ] (3) [POS] () ()() 4.3 P = ρ d AnC DG ()

More information

21 2 26 i 1 1 1.1............................ 1 1.2............................ 3 2 9 2.1................... 9 2.2.......... 9 2.3................... 11 2.4....................... 12 3 15 3.1..........

More information

x () g(x) = f(t) dt f(x), F (x) 3x () g(x) g (x) f(x), F (x) (3) h(x) = x 3x tf(t) dt.9 = {(x, y) ; x, y, x + y } f(x, y) = xy( x y). h (x) f(x), F (x

x () g(x) = f(t) dt f(x), F (x) 3x () g(x) g (x) f(x), F (x) (3) h(x) = x 3x tf(t) dt.9 = {(x, y) ; x, y, x + y } f(x, y) = xy( x y). h (x) f(x), F (x [ ] IC. f(x) = e x () f(x) f (x) () lim f(x) lim f(x) x + x (3) lim f(x) lim f(x) x + x (4) y = f(x) ( ) ( s46). < a < () a () lim a log xdx a log xdx ( ) n (3) lim log k log n n n k=.3 z = log(x + y ),

More information

0.6 A = ( 0 ),. () A. () x n+ = x n+ + x n (n ) {x n }, x, x., (x, x ) = (0, ) e, (x, x ) = (, 0) e, {x n }, T, e, e T A. (3) A n {x n }, (x, x ) = (,

0.6 A = ( 0 ),. () A. () x n+ = x n+ + x n (n ) {x n }, x, x., (x, x ) = (0, ) e, (x, x ) = (, 0) e, {x n }, T, e, e T A. (3) A n {x n }, (x, x ) = (, [ ], IC 0. A, B, C (, 0, 0), (0,, 0), (,, ) () CA CB ACBD D () ACB θ cos θ (3) ABC (4) ABC ( 9) ( s090304) 0. 3, O(0, 0, 0), A(,, 3), B( 3,, ),. () AOB () AOB ( 8) ( s8066) 0.3 O xyz, P x Q, OP = P Q =

More information

2

2 1 6 11 17 33 40 46 50 56 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 etc, 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 Agricultural Society 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53

More information

オートマトンと言語理論 テキスト 成蹊大学理工学部情報科学科 山本真基 ii iii 1 1 1.1.................................. 1 1.2................................ 5 1.3............................. 5 2 7 2.1..................................

More information