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5 x o R n a π(a, x o ) A R n π(a, x o )
6 π(a, x o ) A R n a a x o x o x n X R n δ(x n, x o ) d(a, x n ) d(, ) δ(, ) R n x n X d(a, x n ) δ(x n, x o ) a = a A π(a, xo ) a a A = X = R π(a, x o ) = (x o + ρ) a a a π(a, x o ) a = x o + ρ a ρ 0 a x o x o d(a, x n ) = a x n δ(x n, x o ) = 1 κ (xn x o ) κ > 0 a = x o + ρ x n R (xo + ρ) x n 1 κ (xn x o ) x n { {x x n o + κ, x o + ρ} ρ 0 = {x o κ, x o + ρ} ρ < 0 ρ ρ κ
7 ρ
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9 (x, y) {0, 1} {0, 1} (0, 0) (0, 1) (1, 0) (1, 1) 0 1 (x, y) (x, y) L R (0, 0) (1, 1) (x w, y w ) L R v L (x w, y w ) = 1 {xw 0} λ L 1 {yw 0} v R (x w, y w ) = 1 {xw 1} λ R 1 {yw 1} λ L > 0 λ R > 0 1 { } (x L, y L ) L (x R, y R ) R
10 (x o, y o ) (x n, y n ) (x n, y n ) = (x o, y o ) j = L, R (x n, y n ) u ( (x n, y n ), (x j, y j ) (x o, y o ) ) = ( ( ) 1 {xn xj } + κ1 }) {xn xo γ 1{yn y j } + κ1 {yn yo } γ > 0 κ > 0 j x 1 γ κ γκ γ κ γ [γ, γ] 0 < γ < 1 < γ κ < 1 γ θ {θ l, θ r } θ γ [γ, γ] θ ϕ (x,y)[θ] (x, y) γ < 1 ϕ + (x,y)[θ] (x, y) γ > 1 γ
![j } + κ1 {yn yo } γ > 0 κ > 0 j x 1 γ κ γκ γ κ γ [γ, γ] 0 < γ < 1 < γ κ < 1 γ](/docs-images/47/20974790/images/page_10.jpg "θ {θ l, θ r } θ γ [γ, γ] θ ϕ (x,y)[θ] (x, y) γ < 1 ϕ + (x,y)[θ] (x, y) γ > 1 γ")
11 γ = 1 ϕ (x,y) [θ] + ϕ+ (x,y) [θ] = 1 (x, y) θ θ l θ r ϕ (0,1) [θ l] + ϕ + (1,0) [θ l] > 1 ϕ (0,1) [θ r] + ϕ + (1,0) [θ r] < 1 ϕ (0,0) [θ l] + ϕ + (1,1) [θ l] > 1 ϕ (0,0) [θ r] + ϕ + (1,1) [θ r] < 1 θ l L θ r R (x L, y L ) (x R, y R ) θ {θ l, θ r } (x o, y o ) (x n, y n ) (x o, y o ) L u ( (x n, y n ), (x L, y L ) (x o, y o ) ) > u ( (x n, y n ), (x R, y R ) (x o, y o ) ) (x n,y n ) (x n,y n ) R
12 L R (x L, y L ) = (0, 0) (x R, y R ) = (1, 1) (0, 0) (1, 1) (0, 1) γ < 1 (0, 0) γ > 1 (1, 1) (1, 0) γ < 1 (1, 1) γ > 1 (0, 0) (x L, y L ) = (0, 0) (x R, y R ) = (1, 1) (x o, y o ) = (0, 0) L (x o, y o ) = (1, 1) R (x o, y o ) = (0, 1) L γ R 1 R (x n, y n ) = (1, 1) κ L (x n, y n ) = (0, 0) κγ κ < 1 κγ > γ > 1 κγ > κ γ < 1 (x o, y o ) = (0, 1) γ < 1 L (x n, y n ) = (0, 0) γ > 1 κ > 1 > γ
13 κ > κγ (x o, y o ) = (0, 1) (x n, y n ) = (1, 1) R (x o, y o ) = (0, 1) γ < 1 (x n, y n ) = (0, 0) L γ > 1 (x n, y n ) = (1, 1) R γ = 1 (x o, y o ) = (1, 0) γ < 1 (x n, y n ) = (1, 1) R γ > 1 (x n, y n ) = (0, 0) L γ = 1 ) L θ (1 1 + ϕ (0,1) [θ] + 4 ϕ+(1,0) [θ] R L 1/ θ = θ l 1/ θ = θ r L R R (x R, y R ) = (1, 1) L (x L, y L ) = (0, 0) L 1 (0) 1 (1 + λl ) L (1, 1) (1+λ L ) L ) (0, 1) (1 1 + ϕ (0,0) [θ] + 4 ϕ+(1,1) [θ] 1/ θ = θ r 1/ θ = θ l L 1/ L 1 (λl ) 1 (1 + λl ) L ) (1, 0) (1 1 + ϕ +(0,0) [θ] + 4 ϕ (1,1) [θ] 1/ θ = θ l 1/ θ = θ r
14 L 1/ 1(1) 1(1 + λl )
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17 A B R r R t = 0, 1,,..., A B A B A B(r) = [ r µ, r + ] µ r A B a t (r) {0, 1} a t (r) = 1 A r R t a t (r) = 0 A x n t (r) [0, 1] B x n t (r) ρ t (r) r B A r u t (r) = π t (ρ t (r)) v a t (r) π t (ρ t (r)) B r v > 0
![1} a t (r) = 1 A r R t a t (r) = 0 A x n t (r) [0, 1]](/docs-images/47/20974790/images/page_17.jpg "B x n t (r) ρ t (r) r B A r u t (r) = π t (ρ t (r)) v")
18 π t ( ) A A r ψ(r) = γ x n t (r) a t (r) 1 κ [xn t (r) x o t (r)] γ > 0 κ > 0 x o t (r) [0, 1] r x o t (r) = x n t 1(r) t > 0 x o 0(r) x o 0 : R [0, 1] x o t (r) 1 κ [xn t (r) x o t (r)] γ x n t (r) a t (r) B A r u t (r) + ψ(r) A r A A r
![1(r) t > 0 x o 0(r) x o 0 : R [0, 1] x o t (r) 1 κ [xn t](/docs-images/47/20974790/images/page_18.jpg "(r) x o t (r)] γ x n t (r) a t (r) B A r u t (r) + ψ(r) A r")
19 t A 0 t (r) = { r B(r) a t ( r) = 0}, A 1 t (r) = { r B(r) a t ( r) = 1}. r t + 1 t A 0 t (r) A 1 t (r) a t+1 (r) = { 0 ut (A 1 t (r)) < u t (A 0 t (r)) 1 u t (A 1 t (r)) u t (A 0 t (r)) A 0 t (r) = a t+1 (r) = 1 A 1 t (r) = a t+1 (r) = 0 A r r r a t (r) x o t (r) x n t (r) = { {x o t (r) + κ, 1} a t (r) = 1 {0, x o t (r) κ} a t (r) = 0 κ/ κ a t (r) x n t (r) κ [0, 1]
20 A π t ( ) ρ t (r) r π t (ρ) ρ t t > 0 v < π t (1) π t ( 1) t < t v > π t (1) π t ( 1) t t λ 0 λ 0 µ (α 0 (r), a 0 (r)) = { (1, κ) [ r λ 0 ], λ 0 (0, 0) λ 0 A
21 0 0 A t < t ρ t ( 1, 1) π t(ρ t ) v = π t ( 1 ) [0, 0] ( at+1 (r), x n t+1(r) ) { (1, {x n t (r) + κ, 1}) r [ λ t+1 =, λ t+1 ] (0, {x n t (r) κ, 0}) r / [ λ t+1, λ t+1 ] { λt + µ(1 ρ t ) t < t λ t+1 = {0, λ t µ} t t t A B t ρ t 1 A B t > t 0 0
22 λ 0 λ 0 µ v < π 0 (1) π 0 ( 1) λ ( µ, µ) v = π ( ) ( λ µ π 1 ) λ0 µ λ 0 λ λ 0 < λ A
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24 i = 1, R i x o i x n i x i
25 u i (x n i, x i x o i ) = (x n i x i ) e i (x n i x i ) κ i (x n i x o i ) i e i κ i x i x n i x n i x i e i > 0 i i x o i x n i i = 1, x i = x n i = α i x o i + (1 α i )x o i, α i = e i κ i + κ i κ i e i κ i + e i κ i + κ i. u i (x n i, x i x o i ) x n i x i 0 = x n i x i 0 = (x n i x i ) + e i (x n i x i ) + κ i (x n i x o i ), i = 1, (x n 1, x 1 ) (x n, x ) x n i = x i x i x n i x o i x o i α i i
26 1 r1 x (x o 1, x o ) r x 1 x o i e i κ i α i e i i i κ i
27 x n i i r i (x n i) = e i x n i + κ i x o i, i = 1, e i + κ i e i + κ i x 1 [0] = x o 1 x [0] = x o x 1 [t] = e 1 e 1 + κ 1 x [t 1] + κ 1 x [t] = e e + κ x 1 [t] + x o e 1 + κ 1, 1 t > 0 κ i x o e + κ, t > 0 x i [t] i t x o 1 x o x o 1 x o {x 1 [t]} t {x [t]} t x n 1 x n x i [t] = (τ 1 τ ) t x o + [ ] [ ] τ i (1 τ i )x o i + (1 τ i )x o 1 (τ 1 τ ) t i i = 1, 1 τ 1 τ τ i = e i /(e i + κ i ) (0, 1) i = 1, x i[t] = τ i(1 τ i )x o i + (1 τ i )x o i, i = 1, t 1 τ 1 τ
28 τ i i = 1, x n i i = 1, (x n 1, x n ) (x o 1, x o ) (x o 1, x o ) α i 0 1 x i [t]
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38 R (x R, y R ) = (1, 1) L (x L, y L ) = (0, 1) L 1 L 1 λl L (0, 0) 1 λl R (x R, y R ) = (1, 1) L (x L, y L ) = (1, 0) L 1 L 1 λl L (0, 0) 1 λl L (x L, y L ) = (0, 0) R (x R, y R ) = (1, 0) (0, 0) L (1, 0) R (0, 1) L γ R 1 γ L (x n, y n ) = (0, 0) γκ R (x n, y n ) = (1, 0) κ γκ 1 γ < γ < γκ κ γκ < γκ (0, 1) (0, 0) L (1, 1) (1, 0) R R 1 R 1 λr R (1, 1) 1 1 λr L (x L, y L ) = (0, 0) R (x R, y R ) = (0, 1) (0, 0) L (0, 1) R (1, 0)
39 (0, 0) L (1, 1) (0, 1) R R 1 1 λr R (1, 1) 1 1 λr R (x R, y R ) = (0, 1) L (x L, y L ) = (1, 0) (1, 0) (0, 1) R (0, 0) L (1, 0) κ R (0, 1) γκ γ > 1 (0, 0) (1, 0) L γ > 1 (0, 1) R γ > 1 (1, 1) (0, 1) R γ > 1 (1, ) 0) L L θ 1 (1 + ϕ +(0,0) [θ] + 4 ϕ (1,1) [θ] 1 θ = θ r 1 θ = θ l 1 L 1 λl L (0, 0) (0, 0) L (0, 1) R (1, 1) (0, 1) R (1, 0) (0, 0) L L 1 λl R (x R, y R ) = (1, 0) L (x L, y L ) = (0, 1) (0, 1) L (1, 0) (0, 0) γ L 1 R L (0, 1) γκ R (1, 0)
40 κ γ > 1 γ < 1 < κ γκ < κ (0, 0) R γ < 1 L γ > 1 (1, 1) L γ < ) 1 R L θ (1 1 + ϕ (0,0) [θ] + 4 ϕ+(1,1) [θ] 1 θ = θ l 1 θ = θ r L 1 L 1 λl L (0, 0) 1 1 L (x L, y L ) = (1, 0) R (x R, y R ) = (1, 0) 1 L λl L (0, 0) (1, 0) L (1, 1) R (0, 0) (1, 0) L (0, 1) (1, 1) R R 1 λr R (x R, y R ) = (0, 1) L (x L, y L ) = (0, 1) 1 L λ L L (0, 0) L 1 λl R (x R, y R ) = (1, 1) L (x L, y L ) = (1, 1) 1 L 1 λ L L (0, 1) 1 λl L (x L, y L ) = (0, 0) R (x R, y R ) = (0, 0) 1
41 1 λ R R (0, 1) (0, 1) R (0, 0) L (1, 1) (0, 1) R (1, 0) (0, 0) L R λr R (x R, y R ) = (0, 0) L (x L, y L ) = (1, 1) (0, 0) R (1, 1) L (1, 0) γ L 1 R L (x n, y n ) = (1, 1) γκ R (0, 0) κ γ > 1 γ < 1 < κ γκ < κ (1, 0) (0, 0) R γ < 1 1 < γ < γκ κ < γκ (1, 1) L γ > 1 (0, 1) (1, 1) L γ < 1 ) (0, 0) R L (1 1 + ϕ +(0,1) [θ] + 4 ϕ (1,0) [θ] 1 θ = θ r 1 θ = θ l L 1 λl L (0, 1) (0, 1) L (0, 0) R (1, 1) (0, 1) L (1, 0) (0, 0) R L 1 λl R (x R, y R ) = (0, 1) L (x L, y L ) = (1, 1) (0, 1) R (1, 1) L (1, 0)
42 (1, 1) L (0, 0) (0, 1) R L 1 1 λl L (0, 1) 1 λl R (x R, y R ) = (1, 0) L (x L, y L ) = (1, 1) (1, 0) R (1, 1) L (0, 1) (1, 1) L (0, 0) (1, 0) R L λl L (0, 1) 1 L 1 λl L (x L, y L ) = (0, 1) R (x R, y R ) = (0, 0) (0, 0) R (0, 1) L (1, 1) (0, 1) L (1, 0) (0, 0) R R λr R (0, 1) 1 1 R (x R, y R ) = (0, 0) L (x L, y L ) = (1, 0) (0, 0) R (1, 0) L (0, 1) (0, 0) R (1, 1) (1, 0) L L 1 1 L (0, 0) 1 0
43 [ λ 0, λ 0 ] t [ λ t, λ t ] t + 1 [ λ t+1, λ t+1 ] λ t+1 x n t (r) ( ) R R u t (R) u t R t < t λ t µ r 0 r < 0 r [ 0, λ t ] µ A 0 t (r) = a t+1 (r) = 1 r > λt + µ A1 t (r) = a t+1 (r) = 0 r ( λt µ, λt + µ ] { ) u t (A 1 t (r)) = u t ( {0, r µ }) = ( π t 1 r λ t/ µ v r > λ t / π t (1) v r λ t / π t (ρ) ρ u t ( r) r = {0, r µ } B(r) ( ρ t {0, r µ }) 1 r λ t / 1 r λt/ µ r > λ t / u t (r) u t (A 0 t (r)) = ε 0 + π t = ε 0 + π t ( ( λt ρt + ε)) ( ( 1 µ ( λ t + ε) ( λt µ ))) = π t ( 1 ) π t ( ) v < π t (1) π t ( 1 ) t < t u t (A 1 t (r)) u t (A 0 t (r)) r λ t / r > λ t / u t (A 1 t (r)) u t (A 0 t (r)) ( π t 1 r λ ) ( ) t/ 1 v π t µ
44 r = λ t / r = (λ t + µ)/ v > 0 π t (ρ) ρ r t 1 r t λ t / µ = ρ t r t = λ t + µ(1 ρ t ) r t = λ t+1 / t < t t t λ t µ r [ 0, λt ] µ A 0 t (r) = a t+1 (r) = 1 r > λ t + µ A1 t (r) = a t+1 (r) = 0 r ( λ t µ, λ t + ] µ ut (A 1 t (r)) u t (A 0 t (r)) v > π t (1) π t ( 1) π t(ρ) ρ u t (A 1 t (r)) < u t (A 0 t (r)) r ( λ t µ, λ t + µ ] A t + 1 [ λ t + µ, λ t µ ] 0 < λ t < µ A 1 t (r) = r > λ t + µ a t+1 (r) = 0 r > λ t + µ r [ 0, λ t + µ ] { u t (A 0 t (r)) = π ( λt t + ε) πt (1/) λ = t µ/ ε 0 + π t (λ t /µ) λ t < µ/ r 0 u t (A 1 t (r)) u t (0) = π t (λ t /µ) v λ t < µ/ r 0 a t+1 (r) = 0 v > 0 u t (A 1 t (r)) < u t (A 0 t (r)) λ t µ/ u t (A 1 t (r)) < u t (A 0 t (r)) π t (1/) > π t (1) v > π t (λ t /µ) v λ t < µ π t (ρ) ρ a t+1 (r) = 0 r 0 λ t = 0 A 1 t (r) = a t+1 (r) = 0 r
α α λ α = = λ λ α ψ = = α α α λ λ ψ α = + β = > θ θ β > β β θ θ θ β θ β γ θ β = γ θ > β > γ θ β γ = θ β = θ β = θ β = β θ = β β θ = = = β β θ = + α α α α α = = λ λ λ λ λ λ λ = λ λ α α α α λ ψ + α =
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