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- もえり あきくぼ
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1 A hydrodynamc lmt of move-to-front rules and ts applcaton to web rankngs START
2 Move-to-front cf. Move-to-front N N 1( )
3 (move-to-front ) N =1,,N t 0 t X (N) (t) X (N) (0) = x (N) X (N) (t) = x (N) + ν (N) + t 0 N k=1 t 0 1 X (N) k (s 0)>X (N) (s 0) ν(n) k (ds) (1 X (N) (s 0)) ν (N) (ds), =1,,N, t 0 : (Ω, B(R + )) Z + ρ (N) =E[ν (N) ] X (N) =(X (N) 1,,X (N) N ) 2( )
4 = E[ ν (N) ((0,t]) = w (N) ρ (N) ρ (N) ] R + (ρ (N) ({t}) = 0) t ν (N) : (Ω, B(R + )) Z + ν (N) (A) ρ (N) (A) A B = ν (N) ω Ω ν (N) (A) ν (N) (B) ν (N) (ω)(ds) = (ω)((a, b]) t (a, b] j=1 1 {τ (N),j, j} F (s)ν(ds) = F (τ j ) 1 A A j t X (N) (t) = x (N) N t t + (ds)+ k=1 0 1 X (N) k (s 0)>X (N) (s 0) ν(n) k 0 δ (N) τ,j (ω) (ds) (1 X (N) (s 0)) ν (N) (ds) 3( )
5 τ (N),j {τ (N),j, j} 0 <τ (N),1 <τ(n),2 1) X (N) (τ (N),j )=1(, j) 2) X (N) (τ (N),j )=X (N) < (τ (N),j 0) + 1 (,j ) t=τ 1,1 t=τ 2,1 t=τ 1,2 t=τ 3,1 x (N) 3,0 =1,x(N) 2,0 =2, τ 1,1 <τ 2,1 <τ 1,2 <τ 3,1 < 1 4( )
6 (M.L.Tsetln, 1963) (Least-Recently-Used cachng) v.s. (?) top-to-random shufflng w 5( )
7 Move-to-front Amazon 2ch.net 6( )
8 Y (N) C (t) = 1 N λ (N) t = 1 N N =1 δ ρ (N) Y (N) C (t) y C(t) =1 N =1 ((0,t]) λ t (N ) 0 e s λ t (ds) (N ) Y (N) (N) C (t) E[ Y C (t) ] 0 P[ τ 1 >t]=p[ν((0,t]) = 0 ] = e ρ((0,t]] 1 τ (N),1 t 7( )
9 x (N) = =1,0 t<τ (N) N t k=1 0 1 X (N) k X (N) (t) 1 (s 0)>X (N) (s 0) ν(n) k (ds) = N =1 t =0 1 N N =1 1 τ (N),1 δ (N) ρ ((0,t]) λ t Y (N) C (t) y C(t) =1 (N) = NY t C (t) 0 e s λ t (ds) ( w ) y C (t) λ 8( )
10 ρ Y (N) µ (N) t = 1 N N =1 δ (ρ (N),Y (N) (t)) = 1 N (X(N) 1) µ (N) 1 N N =1 0 µ 0 (N ) 0 s<t N δ (N) ρ ((s,t]) δ ρ((s,t]) Λ(dρ); Λ(dρ) =µ 0 (dρ [0, 1)) M(R + ) t >0 µ (N) t µ t (N µ t 9( )
11 µ (N) t µ t µ t U(dρ, y, t) :=µ t (dρ [y, 1)) { e ρ((t t0(y,t),t]) Λ(dρ), 0 y y = C (t), e ρ((0,t]) U(dρ, ŷ(y, t), 0), y C (t) y<1. t 0 y A (t 0,t)=1 e ρ((t t 0,t]) Λ(dρ) ŷ y B (y, t) =1 M(R + ) M(R + ) y C (t) =y A (t, t) =y B (0,t) e ρ((0,t]) µ 0 (dρ [y, 1)) 10( )
12 Λ= r β δ ρβ, ρ β (A) = β A w β (u) du, w β,r β > 0 β r β =1, β r β w β (t) <, u α : [0, 1) R + : u β (y) =1 y U α (y, t) =U({ρ α },y,t) β U α t (y, t)+ w β (t) U β (y, t) U α y (y, t) = w α(t)u α (y, t), β U α (0,t)=r α U α (, 0) = u α ( ), (t 0,ŷ) (y A,y B,y C ) 1 t y α 11( )
13 (cf. Amazon.co.jp N = O(10 6 )) jump tal (y y C (t)) (µ 0 = U(,, 0)) randomness cf. TASEP 1 nvscd Burgers PDE 12( )
14 (t = ) ρ((0,t]) = wt w λ(dw) =µ (dw [0, 1)) µ (dw [y, 1)) = e wt 0(y) λ(dw); 1 y = R + e wt 0(y) λ(dw) t I(t) C N (t) =X (N) I (N) (t) (t) [y, 1) tal P[ 1 N C N(t) y ] = P[ Y (N) (t) y ]P[ I (N) R w µ (dw [y, 1)) (t) = ] + R wλ(dw) + LRU-cachng cache fault Amazon.co.jp Pareto a, b > 0, λ([0,w]) = 1 (a/w) b (w a) (w = a(n/) 1/b ) y>0 w µ (dw [y, 1)) R + b>1 wλ(dw) = ab,0<b<1 = y =+0 R + b 1 b>1 13( )
15 1 Ω sampleω f f(ρ, y)µ (N) t (dρ dy) = f(ρ, y)µ t (dρ dy) lm N M(R + ) [0,1) M(R + ) [0,1) M(R + ) [0, 1) f = f n Ω n Ω = n Ω n y χ[y, 1) 1 N lm g(ρ (N) N N ) 1 (N) Y (ω)(t) y = g(ρ)µ t (dρ [y, 1)) =1 M(R + ) y y C (t) 1 N N =1 1 Y (N) (t)<y 1 (N) 0, a.s. ν ((t t 0 (y,t),t])>0 14( )
16 Amazon Amazon.co.jp 2ch.net (ameblo.jp) 15( )
17 Amazon.co.jp Amazon 2006 ML 16( )
18 rankng 500,000 Jun 07 Sep 07 Dec 07 Mar 08 date (FAQ) 17( )
19 Pareto x (N) =1,0 t<τ (N) Y (N) (t) =Y (N) C (t)+ 1 N t =0 NY C (t) x C (t) N N 0 e s λ t (ds) λ t Pareto (Zpf ) w (N) = a ( ) N 1/b ; a: b: x C (t) Ny C (t) N(1 b(at) b Γ( b, at)); Γ(z,p) = p e x x z 1 dx N, a, b 18( )
20 Amazon.co.jp (N, a, b )= (8 10 5, , 0.81) 500,000 rankng 1,000 2,000 hrs b<1 o(n) 19( )
21 2ch.net rankng 500,000 Jun 07 Sep 07 Dec 07 Mar 08 date rankng 500,000 Jan 09 May 09 Sep 09 date Amazon.co.jp 1 20( )
22 w (N) 21( )
23 λ t : w (N) (t) =w (N) a(t), w (N) > 0 λ (N) t = 1 N t δ (N) N w A(t) λ t; A(t) = a(u)du =1 0 a(t) 24 A(t) =t+ 22( )
24 2ch.net (2ch.net) web 1 move-to-front sage λ t 23( )
25 :00 18:00 00:00 06:00 12: N = /10/ jump y C (t) 2008 M2 24( )
26 A(t) = S (N) (t) n =1 t y C (t) 1 e ws(n) (t)/z(n) λ(dw); Z(N) = R + 0 a(u)du w (N) (t) =w (N) a(t) > 0 ρ (N) ((0,t]) = A(t) Z(N) N =1 w (N) M2 12:00 18:00 00:00 06:00 12:00 25( )
27 b y C (A 1 t) Pareto b =0.872 Amazon.co.jp 2ch.net b <1 26( )
28 Amazon.co.jp Chevaler, Goolsbee b =1.2 (Onlne bookstore ) Brynjolfsson, Hu, Smth b =1.148 (consumer welfare ) Onlne retal C. Anderson, The Long tal Amazon 27( )
29 2ch.net :00 18:00 00:00 06:00 12: Amazon.co.jp O(10 2 ) /1 (10 ) 9 /1 (30 ) (cf =20 /, 10 2 =1 / ) 28( )
30 Amazon.co.jp aa(t) 1 x C (t) NΓ(1 b)a b A(t) b + O(A(t)) 24 N, b, a ( 1.5 ) 2ch.net 29( )
31 Amazon.co.jp ( ) 0 MTF ( )
32 move-to-front (stochastc rankng process) nvscd Burgers PDE Amazon.co.jp 2ch.net Amazon.co.jp 2ch.net Amazon.co.jp 2ch.net 31( )
33 Stochastc rankng process long tal 32( )
34 (b <1) b<1 2ch b>1 b<1 33( )
35 End of sldes. Clck [END] to fnsh the presentaton. K. Hattor, T. Hattor, Stochastc Processes and ther Applcatons 119 (2009) K. Hattor, T. Hattor, Funkcalaj Ekvacoj 52 (2009) K. Hattor, T. Hattor, preprnt (2009). Y. Harya, K. Hattor, T. Hattor, Y. Nagahata, Y. Takeshma, T. Kobayash, preprnt (2010). Google twtter tetshattor END Bye
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2012.08.10 START 3 B(3, 0.5) N =8 3 2 1 0 1 3 3 1 w, =1, 2,...,N w 3 2 1 1 N 0 1 N 1( ) w, =1, 2,...,N w > 0 w = c log N, =1, 2,...,N, c>0 P[ [x, ) ]= N 1 { w x} = 1 N { Ne x/c } e x/c X w x 1 N 2( ) Zpf
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Amazon.co.jp 2008.09.02 START Amazon.co.jp Amazon.co.jp Amazon.co.jp Amazon Internet retailers are extremely hesitant about releasing specific sales data 1( ) ranking 500,000 100,000 Jan.1 Mar.1 Jun.1
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.............................
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20 21 2 8 1 2 2 3 21 3 22 3 23 4 24 5 25 5 26 6 27 8 28 ( ) 9 3 10 31 10 32 ( ) 12 4 13 41 0 13 42 14 43 0 15 44 17 5 18 6 18 1 1 2 2 1 2 1 0 2 0 3 0 4 0 2 2 21 t (x(t) y(t)) 2 x(t) y(t) γ(t) (x(t) y(t))
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)
chap9.dvi
9 AR (i) (ii) MA (iii) (iv) (v) 9.1 2 1 AR 1 9.1.1 S S y j = (α i + β i j) D ij + η j, η j = ρ S η j S + ε j (j =1,,T) (1) i=1 {ε j } i.i.d(,σ 2 ) η j (j ) D ij j i S 1 S =1 D ij =1 S>1 S =4 (1) y j =
201711grade1ouyou.pdf
2017 11 26 1 2 52 3 12 13 22 23 32 33 42 3 5 3 4 90 5 6 A 1 2 Web Web 3 4 1 2... 5 6 7 7 44 8 9 1 2 3 1 p p >2 2 A 1 2 0.6 0.4 0.52... (a) 0.6 0.4...... B 1 2 0.8-0.2 0.52..... (b) 0.6 0.52.... 1 A B 2
) 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
変 位 変位とは 物体中のある点が変形後に 別の点に異動したときの位置の変化で あり ベクトル量である 変位には 物体の変形の他に剛体運動 剛体変位 が含まれている 剛体変位 P(x, y, z) 平行移動と回転 P! (x + u, y + v, z + w) Q(x + d x, y + dy,
変 位 変位とは 物体中のある点が変形後に 別の点に異動したときの位置の変化で あり ベクトル量である 変位には 物体の変形の他に剛体運動 剛体変位 が含まれている 剛体変位 P(x, y, z) 平行移動と回転 P! (x + u, y + v, z + w) Q(x + d x, y + dy, z + dz) Q! (x + d x + u + du, y + dy + v + dv, z +
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TOP URL http://amonphys.web.fc.com/ 3.............................. 3.............................. 4.3 4................... 5.4........................ 6.5........................ 8.6...........................7
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..........
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O x y z O ( O ) O (O ) 3 x y z O O x v t = t = 0 ( 1 ) O t = 0 c t r = ct P (x, y, z) r 2 = x 2 + y 2 + z 2 (t, x, y, z) (ct) 2 x 2 y 2 z 2 = 0
9 O y O ( O ) O (O ) 3 y O O v t = t = 0 ( ) O t = 0 t r = t P (, y, ) r = + y + (t,, y, ) (t) y = 0 () ( )O O t (t ) y = 0 () (t) y = (t ) y = 0 (3) O O v O O v O O O y y O O v P(, y,, t) t (, y,, t )
1 (Berry,1975) 2-6 p (S πr 2 )p πr 2 p 2πRγ p p = 2γ R (2.5).1-1 : : : : ( ).2 α, β α, β () X S = X X α X β (.1) 1 2
2005 9/8-11 2 2.2 ( 2-5) γ ( ) γ cos θ 2πr πρhr 2 g h = 2γ cos θ ρgr (2.1) γ = ρgrh (2.2) 2 cos θ θ cos θ = 1 (2.2) γ = 1 ρgrh (2.) 2 2. p p ρgh p ( ) p p = p ρgh (2.) h p p = 2γ r 1 1 (Berry,1975) 2-6
II ( ) (7/31) II ( [ (3.4)] Navier Stokes [ (6/29)] Navier Stokes 3 [ (6/19)] Re
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II 29 7 29-7-27 ( ) (7/31) II (http://www.damp.tottori-u.ac.jp/~ooshida/edu/fluid/) [ (3.4)] Navier Stokes [ (6/29)] Navier Stokes 3 [ (6/19)] Reynolds [ (4.6), (45.8)] [ p.186] Navier Stokes I Euler Navier
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H 0 H = H 0 + V (t), V (t) = gµ B S α qb e e iωt i t Ψ(t) = [H 0 + V (t)]ψ(t) Φ(t) Ψ(t) = e ih0t Φ(t) H 0 e ih0t Φ(t) + ie ih0t t Φ(t) = [
![H 0 H = H 0 + V (t), V (t) = gµ B S α qb e e iωt i t Ψ(t) = [H 0 + V (t)]ψ(t) Φ(t) Ψ(t) = e ih0t Φ(t) H 0 e ih0t Φ(t) + ie ih0t t Φ(t) = [](/thumbs/99/141438442.jpg "H 0 H = H 0 + V (t), V (t) = gµ B S α qb e e iωt i t Ψ(t) = [H 0 + V (t)]ψ(t) Φ(t) Ψ(t) = e ih0t Φ(t) H 0 e ih0t Φ(t) + ie ih0t t Φ(t) = [")
3 3. 3.. H H = H + V (t), V (t) = gµ B α B e e iωt i t Ψ(t) = [H + V (t)]ψ(t) Φ(t) Ψ(t) = e iht Φ(t) H e iht Φ(t) + ie iht t Φ(t) = [H + V (t)]e iht Φ(t) Φ(t) i t Φ(t) = V H(t)Φ(t), V H (t) = e iht V (t)e
K E N Z U 01 7 16 HP M. 1 1 4 1.1 3.......................... 4 1.................................... 4 1..1..................................... 4 1...................................... 5................................
http://www.ike-dyn.ritsumei.ac.jp/ hyoo/wave.html 1 1, 5 3 1.1 1..................................... 3 1.2 5.1................................... 4 1.3.......................... 5 1.4 5.2, 5.3....................
: 2005 ( ρ t +dv j =0 r m m r = e E( r +e r B( r T 208 T = d E j 207 ρ t = = = e t δ( r r (t e r r δ( r r (t e r ( r δ( r r (t dv j =
72 Maxwell. Maxwell e r ( =,,N Maxwell rot E + B t = 0 rot H D t = j dv D = ρ dv B = 0 D = ɛ 0 E H = μ 0 B ρ( r = j( r = N e δ( r r = N e r δ( r r = : 2005 ( 2006.8.22 73 207 ρ t +dv j =0 r m m r = e E(
7 π L int = gψ(x)ψ(x)φ(x) + (7.4) [ ] p ψ N = n (7.5) π (π +,π 0,π ) ψ (σ, σ, σ )ψ ( A) σ τ ( L int = gψψφ g N τ ) N π * ) (7.6) π π = (π, π, π ) π ±
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7 7. ( ) SU() SU() 9 ( MeV) p 98.8 π + π 0 n 99.57 9.57 97.4 497.70 δm m 0.4%.% 0.% 0.8% π 9.57 4.96 Σ + Σ 0 Σ 89.6 9.46 K + K 0 49.67 (7.) p p = αp + βn, n n = γp + δn (7.a) [ ] p ψ ψ = Uψ, U = n [ α
.2 ρ dv dt = ρk grad p + 3 η grad (divv) + η 2 v.3 divh = 0, rote + c H t = 0 dive = ρ, H = 0, E = ρ, roth c E t = c ρv E + H c t = 0 H c E t = c ρv T
NHK 204 2 0 203 2 24 ( ) 7 00 7 50 203 2 25 ( ) 7 00 7 50 203 2 26 ( ) 7 00 7 50 203 2 27 ( ) 7 00 7 50 I. ( ν R n 2 ) m 2 n m, R = e 2 8πε 0 hca B =.09737 0 7 m ( ν = ) λ a B = 4πε 0ħ 2 m e e 2 = 5.2977
6 2 T γ T B (6.4) (6.1) [( d nm + 3 ] 2 nt B )a 3 + nt B da 3 = 0 (6.9) na 3 = T B V 3/2 = T B V γ 1 = const. or T B a 2 = const. (6.10) H 2 = 8π kc2
![6 2 T γ T B (6.4) (6.1) [( d nm + 3 ] 2 nt B )a 3 + nt B da 3 = 0 (6.9) na 3 = T B V 3/2 = T B V γ 1 = const. or T B a 2 = const. (6.10) H 2 = 8π kc2](/thumbs/92/109118076.jpg "6 2 T γ T B (6.4) (6.1) [( d nm + 3 ] 2 nt B )a 3 + nt B da 3 = 0 (6.9) na 3 = T B V 3/2 = T B V γ 1 = const. or T B a 2 = const. (6.10) H 2 = 8π kc2")
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K E N Z U 2012 7 16 HP M. 1 1 4 1.1 3.......................... 4 1.2................................... 4 1.2.1..................................... 4 1.2.2.................................... 5................................
IA hara@math.kyushu-u.ac.jp Last updated: January,......................................................................................................................................................................................
構造と連続体の力学基礎
II 37 Wabash Avenue Bridge, Illinois 州 Winnipeg にある歩道橋 Esplanade Riel 橋6 6 斜張橋である必要は多分無いと思われる すぐ横に道路用桁橋有り しかも塔基部のレストランは 8 年には営業していなかった 9 9. 9.. () 97 [3] [5] k 9. m w(t) f (t) = f (t) + mg k w(t) Newton
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1 1 y = y() y, y,..., y (n) : n y F (, y, y,..., y (n) ) = 0 n F (, y, y ) = 0 1 y() 1.1 1 y y = G(, y) 1.1.1 1 y, y y + p()y = q() 1 p() q() (q() = 0) y + p()y = 0 y y + py = 0 y y = p (log y) = p log
24 I ( ) 1. R 3 (i) C : x 2 + y 2 1 = 0 (ii) C : y = ± 1 x 2 ( 1 x 1) (iii) C : x = cos t, y = sin t (0 t 2π) 1.1. γ : [a, b] R n ; t γ(t) = (x
![24 I ( ) 1. R 3 (i) C : x 2 + y 2 1 = 0 (ii) C : y = ± 1 x 2 ( 1 x 1) (iii) C : x = cos t, y = sin t (0 t 2π) 1.1. γ : [a, b] R n ; t γ(t) = (x](/thumbs/94/118744578.jpg "24 I ( ) 1. R 3 (i) C : x 2 + y 2 1 = 0 (ii) C : y = ± 1 x 2 ( 1 x 1) (iii) C : x = cos t, y = sin t (0 t 2π) 1.1. γ : [a, b] R n ; t γ(t) = (x")
24 I 1.1.. ( ) 1. R 3 (i) C : x 2 + y 2 1 = 0 (ii) C : y = ± 1 x 2 ( 1 x 1) (iii) C : x = cos t, y = sin t (0 t 2π) 1.1. γ : [a, b] R n ; t γ(t) = (x 1 (t), x 2 (t),, x n (t)) ( ) ( ), γ : (i) x 1 (t),
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数論 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/008142 このサンプルページの内容は, 第 2 版 1 刷発行当時のものです. Daniel DUVERNEY: THÉORIE DES NOMBRES c Dunod, Paris, 1998, This book is published