M e t ir c S p a c es
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- Horace Warren
- 3 years ago
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Transcription
1 A G M A A q D q O I q 4 78 q q G q 3 q v- q A G q M A G M A D O I A 4 78 / 3 v D OI A G M / 3 54 D D v M q D M 3 v A G M 3 v M 3 5 A 4 M W q x v Z M * A D q q q v W q q q q D q q W q x - v Zá M J v v M q W q v q q q F q q - q - q W v A v F Dv q - - W ξ M W q x Uv P M v x I U UIL8zU U 3 z ä ˆ π W q J q v q I D M ˆ v W ˆ - - Uv v - -I - - U k x W I L 8 -z U U z v Av W A J q - v - z k x - W z- v v F ˆ v ˆ - - v A ˆ P é qq A v ˆ A J ˆ ˆ W Dv ˆ z ˆ ˆ M 4 ˆ 35 8 A x v ˆ 3 L ˆ z ˆ P ˆ I v A z ˆ I P q D G L M Dv ˆ Uv ˆ - v F v ˆ I M U π A 7 8 ˆ 4 U 4 53 v- I 3 L 8 z U π - z I π I z L W q j v - q 34 F v v ˆ I v W I ˆ ˆ z L ˆ z ˆ v W ˆ ; ˆ v ˆ ˆ ˆ ˆ ˆ A J ˆ v v ˆ k v v v I z - - L v v L ℶ v v - v - W v q v - v k v v v v v -L v - A - P v v v q Dv q W - W - v q v M q 4 v 35 v 8 q v A W 53 q v 3 v v q v - v q z q v v - q - - v - O W- q - I - q - v q v v q W- - z v L v ˆ I v q q ˆ q F v v ˆ v O v v k z α Y α v I - v Y Y A ˆ A q Y ˆ v q I q - q -k Y Y z q ˆ Y A q A- ˆ - kv q A * z - q q ˆ kv - - k - A 3 ˆ
2 3
3 D D M x v L Pé q L Y F > Y L Y + Mv k k Y I q vkkkv A k k ä ; G k v ; v - L z q v j v I x W v x ; L A z ; W v v A v v x v kk kkk v v L µ A > F > α + L k > α x L α Mv v v ; W v z v Y x α / + I v α? v z q M k v] > v j zk I z í k - < v k q v q I v Dv
4 D D M D q -- D M - - q x I v v Dv q D q 3 x L A ˆ j π v W L - -- P D v v - π L z L Y F - Y 33 L - - q q q q Y v L q Mv k k Y P q I q - L Y F > Y v-k- k-k--v- L ˆ k -- k q k - G k v q Y k q v L z q v j v q Mv q k ˆ k -I ˆ Y x W- - v- x L - - I - -A - - q - - q q v k z k k v A - k k W v v ; -- - q - - A - v k v x ˆ v q ----k- q k k k L - z - q v- - v q k I v - W v x A L - q q F z q q ˆ ; W v v L - k q q A v x v -L k q k Mv - v v v - q q q q W - v q q q - v Y x- - - q L q q q > I F q q > v? v z q + ] M k-v q k - - L v k ˆ j - -z k x - - I z k q k ˆ v k- L - ˆ q k q q v Mv q I- - v
5 Z M J W k > v q W < ˆ v ˆ A v W q W k ˆ ˆ < I q v q ˆ v v v ; L W W W ˆ q q q 4 L q < < L P q q q W q L Y q q F > Y q L ˆ W ˆ q q + ] v q v q q v v k 3 ] W k v A v x q O v z z z z L z q v ˆ x x v q q v k q v q z v v k v k Dv Z M J W k v q W v A v W q W k q - -D- -I v v v v v L W I v G v 4 L q L - P q q - W L Y F - Y L - - W q q v v q v v - v q k - -v -k- 3 q k W k v q k A v x v z W z z v v z z G L z q v I x-- x v - -v k- - q k v - z v v -k v I q k k k k z z W v I- -v v M q- - - q- k v ---v W v x I v v q - v -k Ak Z M J W k > v W < π v A v π W W k π < D I v π v v v v ; L π W W π I v G v W π 4 L < < L µ - P é q q W π L Y F > Y L W π α α α + ] v v v v k 3] W k v A v x O v z W v z z v v z z G - - L z q v I x x v v k ] v z - v vk v k Dv - I k - k k z z W v I v v M q q k v v W v x Iv v q v k Ak v D M U v I U - J v I M U v J W k k F Pj G - D I P j AA F DM - 9 DM - 875
6 34
7 D D M D q D - M q Dq D M q q I x- I I q x x q x > > v x x x < ] x < x q W -- - x x A v j q F A- - - x x v x -A k x W A q x ] -A x A v j F x F A > W q x q q A q q k A A - x v x - A q Wx < x - F q A x q v λ > λ A xλ j - A v q A W - A > q µ A - - v - -- x-f - µ k v A - - G v x x F x µ < G v Y - µ F q U x > µu µ U x A U U Y q Y F q v q q q q q F q q q - - A k k k F k F > - q -k k - k - q k k - k k q Uq q U - q v - W v q k q - M -W-v k- L > W M µ -- G q v k q - - q v Y > q q L q W v q µx U q ˆ U µx x v v q x x v U q Y W v µ v Ax - q I x F q W v v A ; A k ˆ q W k A F > v µ A v I > A µ k ˆ A ˆ q x µ x W k k ˆ v x A v W q v k ˆ ˆ q U q µ A - q q v q v > q q W v k x M q x µ q ˆ v x v L > < W W v W v W v q > q v q x q ˆ v x q ˆ q ]
8 q v v A x q A 35
9 Z M J W k 3 v Z M M J q W k Z M J W k L v 3 3 v q v M M L > v v W L ; > > v M q ö W ˆ v M q ˆ ; ˆ - D k D v k 3 3 q v - k M - -k D q k D x k v v x k v q v D ˆ k ˆ v v 3 ö q q q W q W q ˆ W ; W q q ; D q < W ; q q W q x vq ] W v M q -- - q x q µ q k v Y Y W v M q q A v k z W zk ˆ k k ˆ L ; ˆ Y Y Y q q Y ˆ ] ; ˆ ] A v v v γ ] k--- z--z k-k-k -- L - Y γγ q q Y < q k q k W ˆ ; ˆ γ W q ˆ v v v L q q k q q v ] k P W Y ] W v YM q - v ; Y q v q Y L ; Y L A W z F vk v k L k k I z v z k q k q Y k q z L v k- P- Y -M - q W P Y xv - Y kkké ] q q v Y D q v 3 v v ] LL A Y µ L Pé q -- z--f-k-k v - - k- q σk Y > I q ] v ] Y z µ σ µ/ M --- P-x--v --- k-k W 3 q j z - q k kv D q 3 L A q v -A k - P - P é ˆ q ] q W P ˆ q - - q v Y - q Y q Lq > - v x q σ k ˆ > q k ; Y L ˆ - ; Y σ µ L ˆ zf k k q k I v 3 Y z q 3 M j z k Px A - q q P - - Y D q - q L 3 - q x L q q A q q P q q v q q q q q - q > 3 ]
10 D D M I D v q D - M q I D D M I I v v q q q I q I - v ; q q v I q x v -- - I q q x q k k v v k v I k I v I q q k k x Zü Z k L 3 3 L 3 3 q A v µ k v I A - Z q - q- q < < τ F L q q F L L /q L - L q x -- q q 3 L 3 > q q L - q - A q x q µ q xτ q µ < q F x L ˆ q x < < P L x - xτ x q L ˆ P q L L ˆ x x x q q > q µ µ+τm q x M q x ˆ q q M M x q L /q q L q x ] q v x k - v q q q k v - xτ k- v q - v x τ µ x x + τ M q < µ < µ x x P q q L M q x q q q L qx M ˆ q q q M + q M ˆ q q ] xp 3 4 M q A - - P é q L < q M < ˆ q - L ˆ M / q I q ˆ q Yq v - L k x v -- - q - -- q L /q L -- -q- - L M x > v q x P 3 4 A x x/5 µ/q q P x < < L - q I ˆ q q x 4 U v Y L- - + I ˆ q x P - L q q W x q + < F x x q L M ˆ q - q - q q x 5 ˆ q q q x + < q q + < + 4 q U v ˆ - q I q - - Lα q q M q q + P- - - W - q 37 q P q q 3 4 v q v q A L q q v q < q < I 37 Y x L ˆ q
11 Z M J W k Z M v J W k Z M J W k v v P q L q ] v x P > x L q ˆ v x x < 5 P q x 4 > x/5 /q L L ˆ q L > > k 5 - v v x < v v k ] - x -v k k - k- x k - q k x k q x / 5 k k / q k < L k k k L L k ˆ > q k ˆ L 3 q k k q k < k k q x x k k k 5 j v k j 5 v j -q k k q q q x k x k k k /5 x j j /5 j k k k x k x k k k ˆ k k < < k k < ˆ k q k x k q k ] x k k k α x k k α k k q α k v k q k x k 5 x k v k q / 5 A x j ö q j j / 5 A q q j v k k k k q k α k α α α k q v µ q q q k q v q x k k < L L /q q L L z α L z q L ˆ W q A W P q A P- - k ˆ q k q > x k L q L k x k k ˆ x/5 q v x x k < x k / 5 - x q ] M x x /q 5 q v x A x q M L q q q M x k q ˆ L - ˆ k k ˆ q x L M q L x q ˆ < µ q / q q µ q ] - k L µ q k L ˆ x I / q k ; z v x k L v q 38 W k q q q A k P k I k
12 D D M I D q D M v q z D D M I I v z 4 q A q A k q q q A 4 µ < k v k A A A k k q < - -k + v A - - A k ˆ A k q v v k v D k 4 + L ] q A A v v x - q v v x v σ - x k D k A 4 k ˆ L σ k A k k q σ v v x k k k q v q q x > x vk x k x k k k k x q k - - k P 4 3 k k L x k - - q v χ x kσ k x A - v - v v P v q 4 3 P L L q W -- Aq D q q 4 q x σ v v v σ v q k P L q A q L σ W I v -k- v x x L x- - x k x I kx k q < k > v x v L > x x x x k k v k k x k k v x k j k k k q j k q k k k x k ˆ v k q k k k x k q k 4 k 4 x x k k ˆ k σ v v k x ˆ k x q - - v v - xk σ k I L x k -q L k P I q q 4 3 I I v I v L v I- - - L I v A - - L I L v v x k q x xk σ 3 x 3σ L k I v q k I I q k I P q q L x q k W q v q q q q k q I x k I k x k k 3 q x 3σ σ I ˆ I- - q - k ˆ x q ˆ I k ˆ L > x
13 Z M J W k W-- Z -- M - J --W W x-- -- k -- v q -- Z M J W k W W W x W v L x q v q ˆ q L x - P é q -P v-- --k v- - - L - ˆ x q k x A P v q k k k v q q W x - v-- - -F P q q q q v ; - L-k - -- L - - µ q k ˆ k v - A v k q q q > 4 3 W x < x ; v q F Lk x v ν F A x q k ˆ q > q q q D q k νx z < 43 v F k k L k x q > F v k x ; q D k z q z 4k 4 k x k x q ˆ x F k k L z q k q k x > L L F L z x ˆ χx 44 L x ; x q x D k v x k z ˆ z L x x k v k k F k L z ψ ] ψ F x x ] ψ x x x L ψ L L z k x k q L L x x x x x x L ξ k x F x ξ L x x L z L x x q x 4 4 k- z ξ x ν /α ψ xξ W q k L x L - x U v ξ F- - F A- k L z ξ x + ] ξ x ˆ 3 L x L ξ ξ L z L ξ ξ k z k L k W k q ˆ L ξ O L L L U z v F A - v ξ 4 L ν x /α µ L x α ν x x k k L x k v ˆ F x ˆ
14 O α α 4
15 D D M v L ξ ν ν L k L ξ L ξ W v ξ M ξ k v ξ k v ; x v v ξ W ξ α F > I λ λ I λ x λxλ I I λ λ v 7 ] W v v α < α k ξ I α ξ #ν < ξ α ; α α F v ξ ξ x ξ α ννx < 45 W ξ x ξ xξ k x + ν α ψ x ψ k W x x x k x x k k x vl k k ξ ξ x ξ α x α I v x α W ννx < x x α ν <
16 D D M - -- D - - q - - D M q v ν < F x x F L x L q v q q + x < +3 k L L x L 4 x x ˆ W v x M k k ] v L x L ˆ x x k W v v x x v M v x x k W x F 34 ] I I x v x ˆ I I 34 k- ] v q k W v v x I x x k ˆ x v ; q x v v x W x q F v F q > 4 5 I x x x x x I x W x L x x x x x L k I I x k v ] v x W v v ˆ < k W x x I x x # < ] x x k k x - L k x -k q ˆ x ˆ x x x F v I v x x x x x ˆ ˆ x x < 4 5 W x x W F x x F x x x x x q x k ] 3 4 x + x q k
17 Z M J W k Z M k J W k x Z M J W k k k k x x q x v x x F x + ν q α x A v + k ˆ F k ] A v x k v x F v F F x A v x x α ν x k x q v α < α v x W v ˆ v x x k k k ˆ k ˆ kkv q k v ˆ ˆ W ˆ Y k ˆ v v v v ˆ ˆ A λ ˆ v --k-k-k-k--- λ +x v x A k-k-- x v-- -- k λ v Y k k U x ˆ < k A v v W k v v v Y v A k Y k k k k v k v v v v k I q x Y v v x v L A v v q - x v q q q W + x v v - U-x- --k -A v k v q x A q k Y ˆ q q v x ˆ q q ; k Y v Ux k A v W v v k I > Y v v L Y q v v ; α Y q v v v v W q I α v W α ; 4 ˆ v Y q ˆ v α < α I v W L v W q k q W α v W 47 W v W v ; v L ˆ ; ˆ q v α W v q x v W W q k ˆ ; > 4 v I W ˆ ; ˆ x α ννx < 48 q q v v v W 4 7 ν W F W q ˆ v v x ˆ ; ˆ 4 v L q 4 4 W ˆ < I W L -- -v - ; x D Z q - - v q ; q L + v W q L x W W L α v L Z 49 v ; x ˆ 4 F x q L 4 4 q W L - 8 v D Z q
18 D D M D -k-- q D --F- M q L- ---v D D M P q k k k F k F Lv ˆ L P v L x 3 L k 3 L x L α ννx < v L Z 4 v k L Z 4 q 4 Z L L x L L x < q Z x L L x 4 L α ννxl < - Z v L L P x v A v L Z Z 4 5 P L - x L L ˆ v Φ x L q x v 4 4 A Z L v P Z Φ q v α < v -L ˆ v --A- v--- -L-L L - -x-- -- Z ΦL + α δα 4 - q k W- L- q - q L 4 5 q k α L x P L L L P x A v ˆ LL ˆ L P Z x x v A q Z x W L P q q ˆ x Φ L q < v L x 4 3 Φ Z Z L x δ x L L v x Z L P L + ˆ ˆ ˆ L x L α L F Z x α L Z L x 43 L q ˆ x L Z L x F L A v ˆ LL x L L q x x x L x L α ννxl L x Z Z W L L x x P L 5 q L x P I Z v v L x F -I I - -v - - v v - v v - - Z - -- F I - L x L - - v - -- ˆ L - q v - F q x 4 L 3 5 v A q F W k L 5 F A 43 Z L x ˆ α ˆ W k α π > L Z L x ˆ ˆ L 43 x q x ˆ x <
19 Z M J W k P Z M A W J W - k - - Z M J W k P P A W q A W q q q q -- - q q α v q W k q q v q α v W k α π q L j j q L j j α q v q v - W W π v W > k ˆ x-j x j ˆ j j q q j ] j q k π Y j q L k Y π j j q I q q q v q I - α v Y v v - π > q q xj q j q j α v < - ˆ j -k Y q k π ˆ > v k Y π v Y Y I q k Y k α ˆ π j < ˆ j v q j j j q j P - ˆ F < -P - F β v ˆ α A A > -- q > q k Y ˆ W k W α k π > β L Y q L q -- α W k k α π > k ˆ ˆ j < ] α β D -- - φ - β ] - q D j q k q j q q k q P q q q α q φq α + q F q q q q q q α 3 q O - O < - φ - - α > β β α φβ A M q v β > M v L L v W k ˆ > β ˆ 5 > q L φ β + -q q β > 5 α q 5 q φ q W k ˆ ˆ 44 > ] φq > 5 44 q q q D q ] q q + q & q
20 D D M v L α < α k α v 8k x α < k < F vk z W v v W > L δ > A > k v W < δ < 53 δ W v j j π W 54 j W 5 v x j j I I J π π W I j J 5 j 55 j j v j j L τ > δ k α τ π χπ j j F δ M P - L q j q /5 j µ I j J vv I xv I q 57 j J π π j j α I v π L z j Ij J F
21 D D M -v - D q - - D M q L v π j k - v- v - - -δv -- q k 8 k- x q L q q q k < - k F- ˆ q v v k- - q k z 8 x q q k < α k ˆ < F τ π W q α+ q v k I v j J v W /5 L A q α+ α q W x /5 j J q ˆ v v W v I W α I q q L 5 3 > A ˆ > k ˆ 45 ˆ W W q v < j j W q ˆ 5 ˆ 4 < q 5 j W 5 x j j I q I J q W q v q j j ˆ q I j J 5 j 5 j j v v q ˆ j -q 5 4 j L j k W 5 v x j q j j 5 J I q F q q P ˆ q L ˆ q W j v q q I 5 j ˆ J j v q j I j J -v-v I x-v j ˆ j ˆ k v v j ˆ j ˆ I j J j L > j I j J j v q 5 j k v ˆ q ˆ v j ˆ L z j 5 L L I j J j L 3 I j F F j M v v- - P
22 Z M J W k I-v - Z - M - J - - W k Z M J W k k I v I v L k α τ π v k k ˆ ˆ L v k ] k α τ π k α π - L k 5 α k 5 k ˆ - ˆ -- ; - -D A x- k ˆ ˆ D A W ˆ π A x- --x x - v- W v A W k ˆ < ; x q x q k 5 v v v v q x- v -x x- v -x x- W k α π > ˆ D v v α ˆ + ˆ W α ˆ + ˆ ˆ < v x- ˆ > W ] α v ˆ q k x- v - - α ˆ A I W q < x α < I W x q v W v -- α < v- - v v v I v I v v v W vk ˆ v ˆ v > v v v v ] α ˆ v x- v k -- k v- -k - -k - k 5 3 I v k k 5 3 q ˆ + W I W π k ˆ < α k W - - W - - π α - W v z k W x W > ] I k q v x W v - - z x 4 I k v - v x q 4 < I W q ˆ q q W v < v v I v v v v k k q q k q 5 3 I q k ˆ W
23 D D M A v v x j v z v j P ; - A v k v v x v v z F ńk W ] ń k L q q D v ] q - v q q v q I < k ] A - P é q v > k4] π k j π k - v v v A x j x L > α ] k Y L k α x v x v k v k k P é q v - ] π k α O 3 F W v q v k q L + W D x v I x x x+x + +ωx ωxx x +x x x + q - v q q v á x x 4 + /4
24 D D M D q D M q A v A + q v q L j - A + v 47 v x -z v P q - A j ˆ - v- -k v - v x v v q q k z q v z- q k F k W P ˆ q k q ] k k L q q D v q k q k q ˆ q ; q A q v q q v q v k v v x v q v I q z q q k F q k k q k A P q v -k 4 k W ] ˆ k j k q v q v v ] ˆ ˆ q A x v q q j ˆ - -x L v q k I k Y ˆ < L k q k q k q q k ] ˆ -x - P q v x v - > v k v- -k q k k k P q j ˆ v O k 3 F v W A v ˆ x q q q v- -k- q k j ˆ q L q q W D x x L > v ] x k Y * x x x L ˆ x x k x x x x ] x x k q q q v q * q x v v x v k x
25 Z M J W k Z M J W k I k Z M J W k k á I k k q P q ˆ P é q v < k x ˆ v q - x- - - k- q + k k P ] q - v q < - x k δ x x > x x á ˆ δ δ q δx q δ x A > v * q A z * q ω I v q A v q z x v A z A z v ; A ˆ v A z ω v v á z z x v A z q ˆ + z q I ; v v O z x v F x v 3 v z ˆ q ˆ ˆ ˆ v ; π π z π π I π ˆ L z v π v L z ö F F x v q 3 v - j P ˆ + π P A z π ; L > ˆ ˆ + * + I ˆ L z + + v L z v F - - F x j v q ˆ M P v 3 v z ˆ ˆ π P P A L ˆ - ˆ ˆ ˆ P ] j I v - - π M v v ˆ ˆ A I π L z v P v 48 L z P F j - I v - q q j P q q v - ˆ ˆ A v P A ˆ 48 L
26 D D M D 3 q D M q D D M L z - Y G q 3 q 3 L z Y Gv Y -L L z v ˆ Y Y L > + v v k v ˆ Y q L ˆ ˆ α > ] + v * q q v v ˆ ˆ F z -- ] α ] α F Y z -L Y 4 L > 4 αv 3 q 3 3 ] v 3 v q k 3 α ˆ α * q x q q q x I á F - v - z ˆ 4 ˆ Y Mv v L ˆ I ˆ π L z > 4 v π Dv v 3 Mv 3 v v P q q 4 L z +π + ˆ q Dv q 3 v P π L P 4 x + L M v x + + π P φ q P j v P ˆ 4 > L - - π I v L ˆ I - x M v x - - P π P + v - + j -- á v Ov L q z q q ˆ ˆ + Dv A v v k v x ˆ v - I x P q q 5 q q 4 L z Y Gv v ˆ Y ˆ L + > + v + & - + & Ov α ] q v A--v P -- q -- q L - k q x + q q + α + α v ˆ + 49 L q 5 M v q x q L ˆ z + - ˆ Y + G P P ˆ Y q q -L ˆ q q v v ˆ q v q ˆ k q q v ˆ ˆ ˆ + v * q q ˆ q q q I q q q q x
27 Z M J W k Av + z q x x D + α α F x x α 3 W α x v A v A v x v k > 5 x vv α + + k > < q v z M v q v v α α + ] v k v 4 F z A x z z A v - z W - v z q - v k x x W - v v v x x v ; A v γ ] z γ γ W γ - é z z v j v I k - é á ; v v L x z ; z v x z W π
28 Z M J W k Av Z M J W k z π q I Av k ˆ + z π -x-x q ] ] q 5 q k x x q q ˆ D 4 F x -x ˆ q q q q 3 ˆ + F W-x x v x - - -A v * ˆ ˆ A q q v - - x- -v - q W x v 5 k A ˆ v * q v ˆ -x - v- - v- - - v k A ˆ v x v q - - v z M v q ˆ k v v ˆ > v 5 q k q k v v x v v 4 F z ˆ ˆ A x z z A ˆ + v ˆ k ˆ < z + ] W q v ˆ z v v ˆ k q v x v x + ] v W v v v v x v x v q v ˆ A v q k q k z 4 q F ˆ z W A x z q A v z z z v j v k W v q v v L x z k x * x z v x * z
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