M e t ir c S p a c es
|
|
|
- Horace Warren
- 4 years ago
- Views:
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
29 D D M k M v v x x G G - - z G v v G v G A v γ G z v v z z v z - é G v v γ k v z v v ] G v v F U v G v v v I k A z z v ö v k G G I k G π π G P 7 G π - x v v P 8 L Y F > 4 Y L G π α α α ] x x G I x v k P x - G G x x v v v v v v 7 x v v v k k k q k
30 D D M D q D k- - M q * v v M v v k * - x * M v x v x q q G + G - z -- G ˆ 5 v x v G ˆ q- x v G A v z G G v v z q z G z v v - v G G ˆ v G v G z v v v - z v q v z v z k v z v- v q k q k G G v v v v ˆ -U- q v ˆ + v ˆ v v ˆ v ˆ v ] v I - - -k z--z q k k v z v - v- - v ] v k v v F k G -G ˆ I k G v G G v v P 7 v G q q x-- -v - - v P q k A 8 zz L Y F - 4 Y L - - v G v q q q q q v q k x-- -x - k q G ˆ - G I G k G ˆ ˆ q G q P q q 7 I -x -v k-p G - ˆ G G x q q x v 7 v q v x ˆ - P v ˆ v v q v x q v v ˆ v v v -q v q -- 8 k---k k q- - k- - L L v Y v L F L 3 x > 4 Y L ˆ
31 Z M J W k P v P x x π G - L z G I π L z G G < W π v / á > q v - x P v π v / W v v ; v L v π q I v L G v G v x v v A π L z < D A L F vx v x x W A P L v π q x v P 7 O q I v q v k v L x π W v π q 7 L A - W x A ˆ π ˆ W L > α ˆ + ] I W v v ˆ β α x L? π α
32 Z M J W k P- Z M v- J P W -x k -x v W k v q G L z P v P G A x v x I L z v L z G ˆ π W < G W G I 5 ˆ L z v G q v - G x W P v ˆ ˆ v v v > v q v L v v q I v v ˆ L ˆ G v / v G v v x ; ˆ ˆ v v A L z q D A ˆ L I v L F v x q - v v q G x x v L q v L q v L A 3 q ˆ L z 3 L 4 < q q D A W L A q F v x L v q x-- v- P v q x - ˆ x 7 O q I v q v k v q ˆ + q L x q W ˆ + v + q - q ˆ + ˆ 3 q 7 ˆ ] L A - - W - W x A A x-- q W L ˆ q k - x- v P q k L v - ˆ I W ˆ v v ˆ x v x- x L q 7 q? O q v-w-k v q A -v- I v q v ˆ ˆ q L x x- W v q q
33 D D M I -v v- D - -- q - D M - q - D D M W k I vv I v v q q x- W k α π > 7 ˆ -v W α v W k ˆ ˆ v > q v- -k -v - - z W v v - k q k 7 x- O q k v v k v W k z W v k α ˆ O q x- v q k -x W k α π > -v v k v z ˆ -k - ˆ k v z α v v v k ; k v k 7 z α v v-v-i O -v- 7 q q- k v v I v q W k - ˆ ˆ - > q x v v x 7 L L α < v < k α < L q ; L k Fk α v v v k > k Fk α Fk q Fk 7 v q Fk v v - ; - vvi - A v - v q µ A + v < < < 7 3 ˆ v L µ 7 q 3 v F v v α L F x v Fk - α v L -Fk F x v v < < < F-x L v I I - F k ] A z z F G v v q J k M q A k A A 34 z z k ˆ F G ] A z j J- D M- - L A A F k 34 q 8 M 5 v ] A q A k q q k A F z k j AD M L v ] Z M F ä M 5 v- M 97 P 47 9 P j A v M v 3 q k 3 59 q ˆ 4 k A A q ; ˆ A- - M 57] - Z M M 994 J F37 q q q k 4 q J k M Z P A M 99 F P - ] Z M + - P j v W - - A- < < M v < A v M q k q 9 k Z M M J q 7 ] q Z M q - q J 7 3 W -J k M-- F q - - v P A 9 z 9-3 v 49 L M q k q k F v 53 Z M - - v - A- v M q k 7 q q k F Z k M q J- ˆ k- F q v v z v q M F x v 53 q q 7 4
34 Z M J W k q Z k M 8 q J k W A k Z M J W k I v 44 P 8 ] 8 ] ï A A q - I - M k M vk 44 P M kä q k 9 q k k Fq 9 ] k Fq q q 9 ] k ] J Fq D L z q k q k J D L z ] J q D G F A L G F A z 48 5] 7 J P M z L z P Dé M L 973 q k q k J P M z 9 39 A ] Dx è J q P A M F z x U v x 973 I z 9 39 ] ö q P M A D zj M G L q L z P D M L 973 v I J M q999 9 A 3 ] Dv G A Dx v q q F P M 44 x U 39 v ] Gx 973 F W I L 9 F x U v x I ] M v v A qz j G A M ] q Dv k G q k M A zj G 4 5 ] ] G F W F W ä ä ä J L ˆ q I J M J L M ] j z P k P q k 3 q k Dv G v P é M A M x + 7 ] J L P M ] G U v x F W - Y k 8 ] J J q k 4 q k G F W L q 973 k 54 P 5 A M 8 v v q A M ] 998 j z P 9 ] k J k P P v P J M A + v - v q J A 5 77 M 7 ] J L ] z q k 5 q k G í k P F D W U v x 8 ] v J A I q k Pé A P q L é 9 J 3 L 4 M ] Y j 9 ] 973 J 5 k P 4 5 ] D Y k q J q A P k v q k - v j J z A v M P 85 - k P ] A M M A 7 M z ] k 88 P D P v L 9 3 P A 4 M ] Mk J M q ] k J 7 W q k k M P Y é J q q L j - - U 5 ń 997 k 3G F 4 A ] M P G Y k ] q k 8 q v k 44 D Av Y J k M J - A k P v U P v P v 995 ] O W A Y M k J A Pv 8 A M A 5 M ] 7 L 99 P 7 M 38 3 ] q k 9 q P k v J A M 37 k P 47 P 43 ] Mk 8 ] J M D Y k J A J J A W v k q q M v P q G F A? 3 J 3 D A 3 7 M ] J 85 5 A ] 39 M z P G - L z - v L z 44 q k M U q L v k 8 P 79 3 ] z 995 k P D ] O W v x Y k J A v A Pv I A P M v A M 7 I L ] 9 L 3 P ] Z W P M Wk q 4 4 v 97 G q k 47 x M 3 - Y k 989 q k Y j 8 ] D Y k 54 J A q A? q k D q k D k 9 ] J J A q P A v z v L q z v q M L ] A M q q x 7 v 99 M 7 38 I q k 3 q k P v 3 ] Z P W P q A Wk M 8 v G x Y 43 k 989 q k 4 q k Mk J M J W k 54 M P q G F A q k 5 q k M P G 44 Av M U v P 995 q k q k O W Y k J A Pv A M q k 7 q k L P M A M q k 8 q k D Y k J A q? D
Ayuntamiento de Madrid
9 v vx-xvv \ ü - v q v ó - ) q ó v Ó ü " v" > - v x -- ü ) Ü v " ñ v é - - v j? j 7 Á v ü - - v - ü
i r-s THE MEMPHIS, TENN., SATURDAY. DEGfMBER
N k Q2 90 k ( < 5 q v k 3X3 0 2 3 Q :: Y? X k 3 : \ N 2 6 3 N > v N z( > > :}9 [ ( k v >63 < vq 9 > k k x k k v 6> v k XN Y k >> k < v Y X X X NN Y 2083 00 N > N Y Y N 0 \ 9>95 z {Q ]k3 Q k x k k z x X
V o l u m e 5, N u m b e r 5 2, 1 6 P a g e s. Gold B e U ClUt Stamps Double Stamp D a y E v e r y Wednesday
1 6 5 J 9 6 " " z k ; k x k k k z z k j " " ( k " " k 8 1959 " " x k j 5 25 ; ; k k qz ; x 13 x k * k ( ) k k : qz 13 k k k j ; q k x ; x 615 26 ( : k z 113 99751 z k k q ; 15 k k k j q " " k j x x ( *»
Juan Juan Salon. EH National Bank. Sandwich Shop Nail Design. OSKA Beverly. Chase Bank. Marina Rinaldi. Orogold. Mariposa.
( ) X é X é Q Ó / 8 ( ) Q / ( ) ( ) : ( ) : 44-3-8999 433 4 z 78-19 941, #115 Z 385-194 77-51 76-51 74-7777, 75-5 47-55 74-8141 74-5115 78-3344 73-3 14 81-4 86-784 78-33 551-888 j 48-4 61-35 z/ zz / 138
LOWELL JOURNAL. DEBS IS DOOMED. Presldrtit Cleveland Write* to the New York Democratic Rilltors. friends were present at the banquet of
X 9 Z X 99 G F > «?« - F # K-j! K F v G v x- F v v» v K v v v F
oenofc : COXT&IBCTOEU. AU skaacst sftwer thsa4 aafcekr will be ehat«s«ai Bi. C. W. JUBSSOS. PERFECT THBOUGH SDFFEBISG. our
x V - --- < x x 35 V? 3?/ -V 3 - ) - - [ Z8 - & Z - - - - - x 0-35 - 3 75 3 33 09 33 5 \ - - 300 0 ( -? 9 { - - - -- - < - V 3 < < - - Z 7 - z 3 - [ } & _ 3 < 3 ( 5 7< ( % --- /? - / 4-4 - & - % 4 V 2
A n.. a l y.. s i s.. a n.. d.. G.. e.. o.. m.. e.. t r y.. i.. n.. M.. e t r i c.. S.. p a.. c e.. s \ centerline
G O I : 4 8 G 3 v- G G 6 9 4 O I : 4 8 / 3 v O I : G 4 3 8 / 6 94 3 v G 3 9 4 - J K w * w - J K v w w : - - v - - w wv w w - F I6 FI F 6 Uv w F Uv ˆ v v ˆ wv wk W w - - : W w - v - w v w H w - v w v 8
THE I Establiifrad June, 1893
89 : 8 Y Y 2 96 6 - - : - 2 q - 26 6 - - q 2 2 2 4 6 4«4 ' V () 8 () 6 64-4 '2" () 6 ( ) * 'V ( 4 ) 94-4 q ( / ) K ( x- 6% j 9*V 2'%" 222 27 q - - K 79-29 - K x 2 2 j - -% K 4% 2% 6% ' K - 2 47 x - - j
. ffflffluary 7, 1855.
x B B - Y 8 B > ) - ( vv B ( v v v (B/ x< / Y 8 8 > [ x v 6 ) > ( - ) - x ( < v x { > v v q < 8 - - - 4 B ( v - / v x [ - - B v B --------- v v ( v < v v v q B v B B v?8 Y X $ v x B ( B B B B ) ( - v -
LOWELL JOURNAL. LOWSLL, MICK., WSSDNaSDAY", FEB 1% 1894:
? jpv J V# 33 K DDY % 9 D Y D z K x p * pp J - jj Q D V Q< - j «K * j G»D K* G 3 zz DD V V K Y p K K 9 G 3 - G p! ( - p j p p p p Q 3 p ZZ - p- pp p- D p pp z p p pp G pp G pp J D p G z p _ YK G D xp p-
A WORD To V eteran Spiritualists.
%U g U v L ^ ; ^ g )! v ^ L 7 Y 3 393 8 & d z ^ k ^ dv g d d kd d g - d dx d d dd d - ~ ---------- v g g d - v d U g d d d Q v g - k g g vg d d g g g g g d g U j k g d k q g g v d - d g d! v g d g d d
David Burns and Matthias Flach. t y
4 Dv B F v 4 b Dv 4 B Dv B F v b F bk bk R F R q v q b R F L L - b q q - Eq: L T C O b q ˆ bk bk * T C O b TΩ bk + ψ T Ω bk T Ω T C T O bk bk + ˆ O w w ψ * R ˆ R T bk Ω bk T O ˆ w R k R bk bk R T C O bk
Discovery Guide. Beautiful, mysterious woman pursued by gunmen. Sounds like a spy story...
Dv G W C T Gp, A T Af Hk T 39 Sp. M Mx Hk p j p v, f M P v...(!) Af Hk T 39 Sp, B,,, UNMISSABLE! T - f 4 p v 150 f-p f x v. Bf, k 4 p v 150. H k f f x? D,,,, v? W k, pf p f p? W f f f? W k k p? T p xp
S p e c i a l M a t r i c e s. a l g o r i t h m. intert y msofdiou blystoc
M D O : 8 / M z G D z F zw z z P Dẹ O B M B N O U v O NO - v M v - v v v K M z z - v v MC : B ; 9 ; C vk C G D N C - V z N D v - v v z v W k W - v v z v O v : v O z k k k q k - v q v M z k k k M O k v
Educjatipnal. L a d ie s * COBNWALILI.S H IG H SCHOOL. I F O R G IR L S A n B k i n d e r g a r t e n.
- - - 0 x ] - ) ) -? - Q - - z 0 x 8 - #? ) 80 0 0 Q ) - 8-8 - ) x ) - ) -] ) Q x?- x - - / - - x - - - x / /- Q ] 8 Q x / / - 0-0 0 x 8 ] ) / - - /- - / /? x ) x x Q ) 8 x q q q )- 8-0 0? - Q - - x?-
R for beginners. 2 The few things to know before st. 8 Index 31
; & & & 8 * ( 0 " & 9 1 R f Eu l 1 W R? 3 T fw kw f 5 3-4.1 T
LOWELL. MICHIGAN, THURSDAY, AUGUST 16, Specialty Co. Sells to Hudson Mfg. Company. Ada Farmer Dies When Boat Tips
K N» N - K V XXXV - N 22 N 5 V N N q N 0 " " - x Q- & V N -" Q" 24-?? 2530 35-6 9025 - - K ; ) ) ( _) ) N K : ; N - K K ) q ( K N ( x- 89830 z 7 K $2000 ( - N " " K : K 89335 30 4 V N
Una aad Ark«m*. I cuim tie la.-seit HTni«.ent 9. Twenty.? S 3 S 3 CLOTHS, MEMPHIS, TENN., SATURDAY. JANUARY 18, 1873.
8! (!> > > ( v 7 q! v Y vq! >5! #! g k gg y y k Q G [x y k xv < zg > 9 _ 7 v ) 6 4 { k & x > 5! k & \ ) >% G > k k x k< G < q k>{> y k k kk k 2 k y y k ( y k y y Y g
SYLPH E D I T I O N S 2016
SYLPH EDITIONS 2016 A WORD FROM THE PUBLISHER J k, z b bk: J Pk T P Hz, v z P b Hz b J Pk. I, bk z b v : b. Sbq b v v vv b v vb. W k b bk, bk b b. T bk b v bj : v T C S Rk v - bk. N b T M,, 29, T C S v.
S O A O lllllu O, W E D N E S D A Y N E X T ; D E C 2 9 t h. R E D U C T I O N S. 3 1, 3 2, 3 3, R o b e r t s o n S t., 2 & 3 Q a r e m o n t,
2» q» Z - - Qk»Q») v Q [ z -? ( 27 2 - ( q - < 5 75 7 v v 50 Q > vk 3 Q - -v- 2 3 7> 27
NOTES ON SCHAUDER ESTIMATES. r 2 x y 2
NOTES ON SCHAUDER ESTIMATES CRISTIAN E GUTIÉRREZ JULY 26, 2005 Lemma 1 If u f in B r y), then ux) u + r2 x y 2 B r y) B r y) f, x B r y) Proof Let gx) = ux) Br y) u r2 x y 2 Br y) f We have g = u + Br
Two Posts to Fill On School Board
Y Y 9 86 4 4 qz 86 x : ( ) z 7 854 Y x 4 z z x x 4 87 88 Y 5 x q x 8 Y 8 x x : 6 ; : 5 x ; 4 ( z ; ( ) ) x ; z 94 ; x 3 3 3 5 94 ; ; ; ; 3 x : 5 89 q ; ; x ; x ; ; x : ; ; ; ; ; ; 87 47% : () : / : 83
LOWELL. MICHIGAN, OCTOBER morning for Owen J. Howard, M last Friday in Blodpett hospital.
G GG Y G 9 Y- Y 77 8 Q / x -! -} 77 - - # - - - - 0 G? x? x - - V - x - -? : : - q -8 : : - 8 - q x V - - - )?- X - - 87 X - ::! x - - -- - - x -- - - - )0 0 0 7 - - 0 q - V -
LOWELL WEEKLY JOURNAL
G $ G 2 G ««2 ««q ) q «\ { q «««/ 6 «««««q «] «q 6 ««Z q «««Q \ Q «q «X ««G X G ««? G Q / Q Q X ««/«X X «««Q X\ «q «X \ / X G XX «««X «x «X «x X G X 29 2 ««Q G G «) 22 G XXX GG G G G G G X «x G Q «) «G
wi& be demonstrated. Ilexbert Arkro,
8( P C B E L B A k> D A 10 O N O k jk \ CH 12 B R Z G kxj7~53> P C C 20 A A P O P 3 x G H kv 7 B5! &$ L N M k APO HM M B / Bk K j R 3(330 C BH& B k C j 2jB A D C & Dk M L 12 H R > APO k L E k M k APO M
(EccL HUt, Mosheim, p. 40.) AGC3. Rgnres. We shall now proceed to show two things:
P K K P / P V -K VX - x K D K GFF G D G DKX X P P F D K 8 6 Y X X X P 9 ] K V Y 0 - D 00 D P F G K K PXVK P > G K K V v v v v PK P v D > v Y v D P > P v v - v x V D - ()zx q - & 9 K x K > % x v - - P x
Whitney Grummon. She kick started a fire in my soul Teaching me a tool to cleanse my mind That ll last a life time. That s how I will remember
W Gmm S kk f m T m m m T f m T I mmb N m p f p f f G L A f b k, b k v M k b p:, bb m, m f m, v. A b m, f mm mm f v b G p. S m m z pp pv pm f, k mk, f v M. I m, I m, fm k p x. S f 45 m m CMS, I p mf,. B
P A L A C E P IE R, S T. L E O N A R D S. R a n n o w, q u a r r y. W WALTER CR O TC H, Esq., Local Chairman. E. CO O PER EVANS, Esq.,.
? ( # [ ( 8? [ > 3 Q [ ««> » 9 Q { «33 Q> 8 \ \ 3 3 3> Q»«9 Q ««« 3 8 3 8 X \ [ 3 ( ( Z ( Z 3( 9 9 > < < > >? 8 98 ««3 ( 98 < # # Q 3 98? 98 > > 3 8 9 9 ««««> 3 «>
LOWELL JOURNAL. MUST APOLOGIZE. such communication with the shore as Is m i Boimhle, noewwary and proper for the comfort
- 7 7 Z 8 q ) V x - X > q - < Y Y X V - z - - - - V - V - q \ - q q < -- V - - - x - - V q > x - x q - x q - x - - - 7 -» - - - - 6 q x - > - - x - - - x- - - q q - V - x - - ( Y q Y7 - >»> - x Y - ] [
SPIRITUALISM. forces. of Spirit, A n stiy a e d f r o m a C o m m o n rhey. n o d and H en so S ta n d p o in t. Lea d s i 1 T U A L I.S M.
~ 3 : K G V 7 G GG 2 3 9 3» < V ; j z_! V 9 7 ' ; > : ; _ < - «-] 88 _ K _ [ -] ZZ - - _ [ ) G K < ' - - ( - '! j () - -] < : : < :?! q z ; [ > # : - 2 - - j ; :!_ - ] ' z ; : j G - j j - [ _ j! { q -
Y k p p Y < 5 # X < k < kk Strauss PDEs 2e: Section Exercise 2 Page 1 of 6. Solve the completely inhomogeneous diffusion problem on the half-line
Strauss PDEs 2e: Section 3.3 - Exercise 2 Page of 6 Exercise 2 Solve the completely inhomogeneous diffusion problem on the half-line v t kv xx = f(x, t) for < x
Tsung-Ming Huang. Matrix Computation, 2016, NTNU
Tsung-Ming Huang Matrix Computation, 2016, NTNU 1 Plan Gradient method Conjugate gradient method Preconditioner 2 Gradient method 3 Theorem Ax = b, A : s.p.d Definition A : symmetric positive definite
Daily Register Q7 w r\ i i n i i /"\ HTT /"\I AIM MPmf>riAnpn ^ ^ oikiar <mn ^^^*»^^*^^ _.. *-.,..,» * * w ^.. i nr\r\
![Daily Register Q7 w r\ i i n i i /\ HTT /\I AIM MPmf>riAnpn ^ ^ oikiar <mn ^^^*»^^*^^ _.. *-.,..,» * * w ^.. i nr\r\](/thumbs/77/75517320.jpg "Daily Register Q7 w r\ i i n i i /\ HTT /\I AIM MPmf>riAnpn ^ ^ oikiar <mn ^^^*»^^*^^ _.. *-.,..,» * * w ^.. i nr\r\")
$ 000 w G K G y' F: w w w y' w-y k Yk w k ' V 0 8 y Q w \ /"\ /"\ > ^ ^ k < ^^^*»^^*^^ _*-» * * w ^ \\ Y 88 Y Y 8 G b k =-- K w' K y J KKY G - - v v -y- K -y- x- y bb K' w k y k y K y y w b v w y F y w
"INDEPENDENT IN AI.L THINOS. NEUTRAI. IN NOTHINO' LOWELL, MICHIGAN, JAM AHV, 19, WHOLE NO. 290.
> HS U H V V 8 W HG J HV 9 899 WH 29 H G S J G W W W WS 4 5 6 898 K H q $ U S S U G 8 G H - J W U S G Y K - «H - W S HW W»U W 8 W H WS H G U Y Y J H q x U 2 VV GV W H W H G 8 H S G K W W W H J? 5? G S-
N e w S t u d e n t. C o u n c i l M e n
ZV. XX L GG L 3 942. 25 J b D b v D G... j z U 6 b Y DY. j b D.. L......&. v b v. z " 6 D". " v b b bv D v.... v z b.. k."... 92... G b 92. b v v b v b D ( 6) z v 27 b b v " z". v b L G. b. v.. v v. D
ACHD Roadways to Bikeways Update June Hills Gate Dr. Ec ho Summit Pl. Star Ridge Ln. Sunrise View Ln. Eagle Pointe Pl.
v U v G G q G G z j v Q v v v v v v G v U v v v z K K z v J v v v G v v 16 z z v q v G v J J K:\_j\20\20987 - U\\ 1-4_24. - - 3:46 6/2/2017 O ( O) O z O O v v v v J J J G v O G J v z zz G v v Q zz / /
Lower Austria. The Big Travel Map. Big Travel Map of Lower Austria.
v v v :,000, v v v v, v j, Z ö V v! ö +4/4/000 000 @ : / : v v V, V,,000 v v v v v v 08 V, v j?, v V v v v v v v,000, V v V, v V V vv /Z, v / v,, v v V, v x 6,000 v v 00,000 v, x v U v ( ) j v, x q J J
LOWELL WEEKLY JOURNAL. ^Jberxy and (Jmott Oao M d Ccmsparftble. %m >ai ruv GEEAT INDUSTRIES
? (») /»» 9 F ( ) / ) /»F»»»»»# F??»»» Q ( ( »»» < 3»» /» > > } > Q ( Q > Z F 5
LOWELL WEEKLY JOURNAL
KY Y 872 K & q $ < 9 2 q 4 8 «7 K K K «> 2 26 8 5 4 4 7»» 2 & K q 4 [«5 «$6 q X «K «8K K88 K 7 ««$25 K Q ««q 8 K K Y & 7K /> Y 8«#»«Y 87 8 Y 4 KY «7««X & Y» K ) K K 5 KK K > K» Y Y 8 «KK > /» >» 8 K X
T i t l e o f t h e w o r k : L a M a r e a Y o k o h a m a. A r t i s t : M a r i a n o P e n s o t t i ( P l a y w r i g h t, D i r e c t o r )
v e r. E N G O u t l i n e T i t l e o f t h e w o r k : L a M a r e a Y o k o h a m a A r t i s t : M a r i a n o P e n s o t t i ( P l a y w r i g h t, D i r e c t o r ) C o n t e n t s : T h i s w o
r*tt7v Progress, Ibe Ur)ft>ersal LaWof J^atare; Th>oagbt, fbe 3olA>er)t of Jier Problems. CHICAGO, SEPTEMBER MRS. ADA FOYE.
7v P U)> L ^; > 3>) P L' PBR 3 892 45 p p p j j pp p j ^ pp p k k k k pp v k! k k p k p p B pp P k p v p : p ' P Bk z v z k p p v v k : ] 9 p p j v p v p xp v v p ^ 8 ; p p p : : x k p pp k p k v k 20
[2] (a) Develop and describe the piecewise linear Galerkin finite element approximation of,
![[2] (a) Develop and describe the piecewise linear Galerkin finite element approximation of,](/thumbs/88/117157910.jpg "[2] (a) Develop and describe the piecewise linear Galerkin finite element approximation of,")
269 C, Vese Practice problems [1] Write the differential equation u + u = f(x, y), (x, y) Ω u = 1 (x, y) Ω 1 n + u = x (x, y) Ω 2, Ω = {(x, y) x 2 + y 2 < 1}, Ω 1 = {(x, y) x 2 + y 2 = 1, x 0}, Ω 2 = {(x,
Baby Beauty Contest Judging Today In WR Recreation Halt
MO BOOM JO R 7OM OJJM JC 20 946 MG 2 O H K F C O Ck C U VMR B G DON U M L H Y v C M G 2 v COMMNDNG MG-2 R R5-C k k C G - R k < v : L C B Z - v C R L C D H - v M -2 - «v G z F - MG-2 v j v v K O G - C
HEAGAN & CO., OPP. f>, L. & W. DEPOT, DOYER, N. J, OUR MOTTO! ould Iwv ia immediate vltlui. VEEY BEST NEW Creamery Butter 22c ib,
#4 NN N G N N % XX NY N Y FY N 2 88 N 28 k N k F P X Y N Y /» 2«X ««!!! 8 P 3 N 0»9! N k 25 F $ 60 $3 00 $3000 k k N 30 Y F00 6 )P 0» «{ N % X zz» «3 0««5 «N «XN» N N 00/ N 4 GN N Y 07 50 220 35 2 25 0
Gwinnett has an amazing story to share, spanning 200 years from 1818 until today.
I B, Lm, W - D I C Dm 15, 1818, W C, m D I. T m m m Ck Ck m Jk C. B m, 30, A 20. T mk, B, v v m C. m, m 1776, C C. O A 2, 1776, D I,. C v 437 q m xm 280,000. D 1980, C k, m v. A, 2010, j v 800,000 j m
LOWELL WEEKLY JOURNAL.
> LLL KLY L L x L L L L G K Y F 7 2 K LKL Y K «F «««««q 5 $ ) / «2 K) ««) 74 «G > x «LY K «! «KL K K K K K! ««x > x K! K ) 2 K «X! «K LK >> < >«««) «< >>«K«KLK < «4! «««#> ««!
«4 [< « ' Liberty and Umou Ono and Inseparablo "
3 5? #< q 8 2 / / ) 9 ) 2 ) > < _ / ] > ) 2 ) ) 5 > x > [ < > < ) > _ ] ]? <
" W I T H M A L I C E T O W A - P t D N O I S T E A - I S T D O H A n i T Y F O R. A L L. " A TENDERFOOT. an awful storm." At this juncture,
v «> X k < W L W - P N - Y F R L L / L N LWLL N UNY PR 9 WL N - [N v v NRF N -Nv j k q v v k k v k Rk x - v N W k - WLL PN NG NV k Rk G v Y L v k (?)! V W k ) W k v k P UL W Pj$ V G k v -) v k W j v k
1 r. Published on 28 January Abstract. will be discussed period Recently frequency jumps
L R R 6 L L R R 6 R ˆ R - - ˆ 6 ˆ ˆ ˆ q q R R G P S G P S N A 4 N A D P U D C P U C B CO 89 -z 9 B CO 89 z9 U S R A q q q G q P q S U S A N A N A @ N A W W A 8 J A D 8 J P U C P 8 J P 8 J A A B CO 89 z
A Cluster-based Approach for Biological Hypothesis Testing and its Application
-b B J k, J S Y, M D S, D B I Uv- Uv, F W, I, US {kj,j,@} b v b, v N, O, F b v, v, vv b W z, β-,, b b v q W,, b b b v b : b v b β-, b b b I,,,, b-,, I INRODUION qk b v [] O G Lk,,, k, v, b vv b [] v v
a s*:?:; -A: le London Dyers ^CleanefSt * S^d. per Y ard. -P W ..n 1 0, , c t o b e e d n e sd *B A J IllW6fAi>,EB. E D U ^ T IG r?
? 9 > 25? < ( x x 52 ) < x ( ) ( { 2 2 8 { 28 ] ( 297 «2 ) «2 2 97 () > Q ««5 > «? 2797 x 7 82 2797 Q z Q (
Tornado, Squalls Strike Kinston Area
q k K A V N 28 #/K N /WANE CO A AON-CHEY ON A N F W N H W D M D H U x 30 M k k M D 945 E M A A k - A k k k A C M D C 030 D H C C 0645 000 200 W j A D M D k F E- HAUNNG CALL - A A x U M D M j A A 9000 k
PanHomc'r I'rui;* :".>r '.a'' W"»' I'fltolt. 'j'l :. r... Jnfii<on. Kslaiaaac. <.T i.. %.. 1 >
5 28 (x / &» )»(»»» Q ( 3 Q» (» ( (3 5» ( q 2 5 q 2 5 5 8) 5 2 2 ) ~ ( / x {» /»»»»» (»»» ( 3 ) / & Q ) X ] Q & X X X x» 8 ( &» 2 & % X ) 8 x & X ( #»»q 3 ( ) & X 3 / Q X»»» %» ( z 22 (»» 2» }» / & 2 X
LIGHT DUTY DIFFERENTIAL
B F FF PP P # /............................4...................................4-5 F.....................................5.....................................6-7 P PP Z.....................................7...................................7
Pithy P o i n t s Picked I ' p and Patljr Put By Our P e r i p a tetic Pencil Pusher VOLUME X X X X. Lee Hi^h School Here Friday Ni^ht
G G QQ K K Z z U K z q Z 22 x z - z 97 Z x z j K K 33 G - 72 92 33 3% 98 K 924 4 G G K 2 G x G K 2 z K j x x 2 G Z 22 j K K x q j - K 72 G 43-2 2 G G z G - -G G U q - z q - G x) z q 3 26 7 x Zz - G U-
LOWELL J O U R N A L
O O V X 5 O G O X G O K O K FG O O K F; K F OK 5 O K $GOO «OKK O G F G G G G ( v v Gvz O O *«* K ] F F K v v v : v : F OG O OK O G?;;::OO O K O O vv v q >v v V v / (}»* v v v: v vv?? O ; Q
s f o r s o l v i n g t h e n o n l i n
M M R M q q D O : q 7 8 q q q M q x- q M M M 9 R R D O : 78 / x q D MO : M 7 9 8 / D q P F x z M q M q D T P - z P G S F q q q q q q q D q q PZ w - z q - P q q q w q q q w q q w z q - w P w q w w - w w
Linear Analysis Lecture 5
Linear Analysis Lecture 5 Inner Products and V Let dim V < with inner product,. Choose a basis B and let v, w V have coordinates in F n given by x 1. x n and y 1. y n, respectively. Let A F n n be the
and A I L j T O S O L O LOWELL, MICHIGAN, THURSDAY, AUG. 1, 1935
Y D D Y 5 VD D Y D D - ( D K D ( > Kz j K D x j ; K D D K x z ( D K D ( ; ) ( ) V DY - j! ) : x x x j K D K j DY 95 Y-D Y D D j 5 4 V 89 j j j j 89 j 4998 9 j K 8 j V x j K x x 5 x x x j - K 4- -D K 4-
Sticky News. Also our Facebook page is now live.
Sk Nw k j v #07 WINTER 2011 Fm Ow C W! W w bk w v b v m m b k w v m m Y w m m w v v m! T P C Sm B, T C, Gvv H K R w b v M C S A Fbk w v YI v v w m bk m b m w A H O w bk w w v w m m b m v qk w I w k ABC
lidmbtr Ftderal Dtposit Iniuranct C^rptratim
3 6 2 v v v v v J J : : $3 $ v J v x z " " v v Q j v v z v 2 J v v v v v v v ( v v ) v v v v ( v v v x v v v v x x! v J v v x 3 v v v v v v " v 7 ( v ) z j 3 q J J v v j v v v v x z v v x v v j x v; v
LOWHLL #WEEKLY JOURNAL.
# F 7 F --) 2 9 Q - Q - - F - x $ 2 F? F \ F q - x q - - - - )< - -? - F - - Q z 2 Q - x -- - - - 3 - % 3 3 - - ) F x - \ - - - - - q - q - - - - -z- < F 7-7- - Q F 2 F - F \x -? - - - - - z - x z F -
" W I T H I v r ^ L I O E T O W A R D I S T O K T E A I S T D O H ^ n i T Y F O R. A.LL,.'
" H v L A D K A D H Y F ALL VL V 20 LLL K UY H VB 3 9 HL 20 v p v B) H H p p P p A [G p D D-! P [ V 2 76 B ) - F v v K q v F G - (v p x Y - v 0 2 9 v> pp V H! ) v < 37 v LDAL H G 0 9 " pp p H \ p - >"
nd A L T O SOLO LOWELL. MICHIGAN. THURSDAY. APRIL Spring Activities Heads Up and Forward (Editorial By " T h e Committee'')
- 6 7 8 9 3-6 7 8 9 3 G UDY 3 93 VU XXXV U XY F K FD D j V K D V FY G F D Y X K X DD Y j \ V F \ VD GD D U Y 78 K U D Y U Y 484?35 V 93 7 4 U x K 77 - D :3 F K > 6 D x F 5 - - x - G 7 43 8 D $35 K F $5
CLASSIFICATION AND PRINCIPLE OF SUPERPOSITION FOR SECOND ORDER LINEAR PDE
CLASSIFICATION AND PRINCIPLE OF SUPERPOSITION FOR SECOND ORDER LINEAR PDE 1. Linear Partial Differential Equations A partial differential equation (PDE) is an equation, for an unknown function u, that
E S T A B L IS H E D. n AT Tnn G.D.O. r.w.-bal'eu. e d n e s d a y. II GRANVILLE HOUSE. GATJDICK ROAD. MEADS. EASTBOUENk
K q X k K 5 ) ) 5 / K K x x) )? //? q? k X z K 8 5 5? K K K / / $8 ± K K K 8 K / 8 K K X k k X ) k k /» / K / / / k / ] 5 % k / / k k? Z k K ] 8 K K K )» 5 ) # 8 q»)kk q»» )88{ k k k k / k K X 8 8 8 ]
LOWELL STORES SERVE THRONGS OF LOV PEOPLE ON FRIDAY NIGHT
J p M 879 61 p 260 M G W j p : b p pp M M K p b J M G * p P p b p p D W P p b G 14 b p qp j b p p p J p z M- K W W G Gbb Wb M J W W K G J D D b b P P M p p b p p b b p J W ; p jb b p x b p p b b W Pp pp
3 Operations on One R.V. - Expectation
0402344 Engineering Dept.-JUST. EE360 Signal Analysis-Electrical - Electrical Engineering Department. EE360-Random Signal Analysis-Electrical Engineering Dept.-JUST. EE360-Random Signal Analysis-Electrical
LOWELL WEEKLY JOURNAL
Y -» $ 5 Y 7 Y Y -Y- Q x Q» 75»»/ q } # ]»\ - - $ { Q» / X x»»- 3 q $ 9 ) Y q - 5 5 3 3 3 7 Q q - - Q _»»/Q Y - 9 - - - )- [ X 7» -» - )»? / /? Q Y»» # X Q» - -?» Q ) Q \ Q - - - 3? 7» -? #»»» 7 - / Q
KEEP PACE WITH. Volume 3, Number.38, 12 Pages. at Michigan State university.
2 3, 98! W \G \ q vk \ b v \(, v v ;, ): j:!, ; W, j v ; ;, \ ;, : z W, x,, G, 38 G v W W WW Y G W X Q G 82, v v G b Y v : W G : Y G X W Y 32 WG G G WG G X x x v v k v x b b b b b b 3 (x ) x, b b, W, v
A. H. Hall, 33, 35 &37, Lendoi
7 X x > - z Z - ----»»x - % x x» [> Q - ) < % - - 7»- -Q 9 Q # 5 - z -> Q x > z»- ~» - x " < z Q q»» > X»? Q ~ - - % % < - < - - 7 - x -X - -- 6 97 9
LOWELL JOURNAL CRESP0 REIGNS. MICE DESTROY #10,000 CASH. T O W E L L S T A T E B A N K,
N V 2 2 7 2 9 2 K K «KN < K KY KK K KN ( *
- >,- V v ' V" S.T T~T .. RAHWAY NEWS RECORD -CLARK PATRIOT PAGE 10 THURSDAY, JULY 22, 1971 THURSDAY, JULY 15 VOL. 149, NO. 29
> V V Y O K O G Y Y kj > «) > k : \ \\ V) Q K! \ : = < \ \ \ \V :! < VG O O OKO O O O OVG KO B K V G G O O $ G OK O Y V O >K K : j k k 6 Y OO >«Y k k k z : B OO G Bk k G k G O k > G! x OOO O k Y Y 6 }
Module-3: Kinematics
Module-3: Kinematics Lecture-20: Material and Spatial Time Derivatives The velocity acceleration and velocity gradient are important quantities of kinematics. Here we discuss the description of these kinematic
WILLPOWER! yalerep.org. WILL POWER! is supported by YALE REPERTORY THEATRE STUDY GUIDE WRITERS EDITORS SPECIAL THANKS
2016 G YALE REPERTORY THEATRE J B A D V N M D TUDY GUIDE WRITER WILL POWER! 2015 16 E U A P I Nw A F J M F T B Y D, MFA 16 P D L AH P Y D, MFA 17 P D EDITOR A Bk L M R C L A P M PECIAL THANK N H, J K,
A L T O SOLO LOWCLL. MICHIGAN, THURSDAY. DECEMBER 10,1931. ritt. Mich., to T h e Heights. Bos" l u T H I S COMMl'NiTY IN Wilcox
G 093 < 87 G 9 G 4 4 / - G G 3 -!! - # -G G G : 49 q» - 43 8 40 - q - z 4 >» «9 0-9 - - q 00! - - q q!! ) 5 / : \ 0 5 - Z : 9 [ -?! : ) 5 - - > - 8 70 / q - - - X!! - [ 48 - -!
MEEN 618: ENERGY AND VARIATIONAL METHODS
JN Reddy - 1 MEEN 618: ENERGY AND VARIATIONAL METHODS WORK, ENERGY, AND VARIATIONAL CALCULUS Read: Chapter 4 CONTENTS Work done External and internal work done Strain energy and strain energy density Complementary
" W I T H M I A L I O E T O W A R D istolste A N D O H A P l t T Y F O B, A I j L. ; " * Jm MVERSEO IT.
P Y V V 9 G G G -PP - P V P- P P G P -- P P P Y Y? P P < PG! P3 ZZ P? P? G X VP P P X G - V G & X V P P P V P» Y & V Q V V Y G G G? Y P P Y P V3»! V G G G G G # G G G - G V- G - +- - G G - G - G - - G
f;g,7k ;! / C+!< 8R+^1 ;0$ Z\ \ K S;4 i!;g + 5 ;* \ C! 1+M, /A+1+> 0 /A+>! 8 J 4! 9,7 )F C!.4 ;* )F /0 u+\ 30< #4 8 J C!
393/09/0 393//07 :,F! ::!n> b]( a.q 5 O +D5 S ١ ; ;* :'!3Qi C+0;$ < "P 4 ; M V! M V! ; a 4 / ;0$ f;g,7k ;! / C+!< 8R+^ ;0$ Z\ \ K S;4 "* < 8c0 5 *
OVER 150 J-HOP To Q JCATS S(MJ) BY NOON TUESDAY CO-ED S LEAGUE HOLDS MEETING
F F V à y y > * y y y! F! * * F k y è 2 3 U D Y F B U Y 3 * 93 G U P B PU FF; JH H D V 50 JHP QJ (J) BY UDY P G y D; P U F P 0000 GUU VD PU F B U q F' yyy " D Py D x " By ; B x; x " P 93 ; Py y y F H j
See, Sketch, Shoot. A Study Abroad program offered by Coastline Community College and ACCENT International Consortium for Academic Programs Abroad
R 17!! 0 2 5 2 l J 5 2 J S, Sk, S A S A ff Cl C Cll ACCENT Il C f A P A ROME Il Y I Wk 1 J 24 J 28 Av R, Il f -l. O ACCENT f lv R. L, PS. Il l l.* S v Nl M, Nl Gll f M A, Gll B, V, Cl R F. T v f l k Il
Applications of the Maximum Principle
Jim Lambers MAT 606 Spring Semester 2015-16 Lecture 26 Notes These notes correspond to Sections 7.4-7.6 in the text. Applications of the Maximum Principle The maximum principle for Laplace s equation is
Quantum Theory. Thornton and Rex, Ch. 6
Quantum Theory Thornton and Rex, Ch. 6 Matter can behave like waves. 1) What is the wave equation? 2) How do we interpret the wave function y(x,t)? Light Waves Plane wave: y(x,t) = A cos(kx-wt) wave (w,k)
Probe fire that killed 23
V ' ( WUY J Y JUY 88 P k z ' ' F x k J K Y - P k k k Pz Pk k k 'J Pk k U k k - - k k Pz " " k x k k k W k k k ' z " x - " z k k k x j k k k k x k zz "' ' k " k k k» «K VU G k - k z k U k x (P) - P z
March Algebra 2 Question 1. March Algebra 2 Question 1
March Algebra 2 Question 1 If the statement is always true for the domain, assign that part a 3. If it is sometimes true, assign it a 2. If it is never true, assign it a 1. Your answer for this question
Lowell Dam Gone Out. Streets Turned I n t o Rivers. No Cause For Alarm Now However As This Happened 35 Years A&o
V ()\\ ))? K K Y 6 96 Y - Y Y V 5 Z ( z x z \ - \ - - z - q q x x - x 5 9 Q \ V - - Y x 59 7 x x - Y - x - - x z - z x - ( 7 x V 9 z q &? - 9 - V ( x - - - V- [ Z x z - -x > -) - - > X Z z ( V V V
Assessment Exemplars: Polynomials, Radical and Rational Functions & Equations
Class: Date: Assessment Exemplars: Polynomials, Radical and Rational Functions & Equations 1 Express the following polynomial function in factored form: P( x) = 10x 3 + x 2 52x + 20 2 SE: Express the following
LOWELL JOURNAL.. TOOK H BR LIFE.
( \ R 277 v G v R 7 889 C? K R F Y C G F R C K 6 RYC K C K K 8 9 2 K C CK» R C G RR F v K K v Rk k v k x k Y QR FF F RKR C k \ R 4 ( k R F G q 5 R Y Y FR v R ; k k Y 8 K k : F K CK{ 8 k K x K K 2 K «v
Tracing High-z Galaxy Kinematics
T H- Gxy K v b k q Ey Wk THE KMOS 3D TEAM PI: NM Fö Sb D W, JT M, S Wy, E Wy, K B, A B, R B, G B, J C, R Dv, M Fb, M F, R G, S Kk, J Kk, P L, D L, I Mv, E N, D R, R S, S S, LJ T, K Tk, P v Dkk, + I C T!
A b r i l l i a n t young chemist, T h u r e Wagelius of N e w Y o r k, ac. himself with eth
6 6 0 x J 8 0 J 0 z (0 8 z x x J x 6 000 X j x "" "" " " x " " " x " " " J " " " " " " " " x : 0 z j ; J K 0 J K q 8 K K J x 0 j " " > J x J j z ; j J q J 0 0 8 K J 60 : K 6 x 8 K J :? 0 J J K 0 6% 8 0
DIFFERENTIAL EQUATIONS
DIFFERENTIAL EQUATIONS DIFFERENTIAL EQUATIONS NON-LINEAR LINEAR (in y) LINEAR W/ CST COEFFs (in y) FIRST- ORDER 4(y ) 2 +x cos y = x 2 4x 2 y + y cos x = x 2 4y + 3y = cos x ORDINARY DIFF EQs SECOND- ORDER
FICH~:s lciithyo\l~~trio~es.
PB FCNyM UNLP T g vg wk b b y y g b y F wk v b m b v gz w my y m g E bv b g y v q y q q ó y P mv gz y b v m q m mó g FCH CTHYOTROES P W P -C b } k < HP- qe q< - - < - m T
UP and ENTRIES. Farmers and WivUs to Hold Old-Fashioned Meeting Here
LD : g C L K C Y Y 4 L LLL C 7 944 v g 8 C g 85 Y K D L gv 7 88[ L C 94 : 8 g Cg x C? g v g 5 g g / /»» > v g g :! v! $ g D C v g g g 9 ; v g ] v v v g L v g g 6 g (; C g C C g! v g gg gv v v 8 g g q»v
UNIQUENESS OF POSITIVE SOLUTIONS OF THE HEAT EQUATION
Nishio, M. Osaka J. Math. 29 (1992), 531-538 UNIQUENESS OF POSITIVE SOLUTIONS OF THE HEAT EQUATION Dedicated to Professor Masanori Kishi on his 60th birthday MASAHARU NISHIO (Received July 5, 1991) 1.
For H. S. Athletes. 49 Boy Scouts Initiated Here
LD B V L LY L L ( 700 v v v * x Dv L v v B v «v U B v z v v- - - v v v 0 v D U v v v v B X v x v v U v v 0000 v 0000 v x v v U ) YU > v v v v YD L Y x v q -z : v v v v v x v v B L L Y-D LLL Y X L DD UDY
2 Two-Point Boundary Value Problems
2 Two-Point Boundary Value Problems Another fundamental equation, in addition to the heat eq. and the wave eq., is Poisson s equation: n j=1 2 u x 2 j The unknown is the function u = u(x 1, x 2,..., x
Lecture #8: Quantum Mechanical Harmonic Oscillator
5.61 Fall, 013 Lecture #8 Page 1 Last time Lecture #8: Quantum Mechanical Harmonic Oscillator Classical Mechanical Harmonic Oscillator * V(x) = 1 kx (leading term in power series expansion of most V(x)
Introduction to Probability and Stocastic Processes - Part I
Introduction to Probability and Stocastic Processes - Part I Lecture 2 Henrik Vie Christensen vie@control.auc.dk Department of Control Engineering Institute of Electronic Systems Aalborg University Denmark