Comparison of Response Surface and Kriging Models in the Multidisciplinary Design of an Aerospike Nozzle

NASA/CR-1998-206935 ICASE Report No. 98-16 Comparison of Response Surface and Kriging Models in the Multidisciplinary Design of an Aerospike Nozzle Timothy W. Simpson Georgia Institute of Technology Institute for Computer Applications in Science and Engineering NASA Langley Research Center Hampton, VA Operated by Universities Space Research Association National Aeronautics and Space Administration Langley Research Center Hampton, Virginia 23681-2199 Prepared for Langley Research Center under Contract NAS1-19480 February 1998

]!_Viy7!W!3 ie7_!w7e 7=i3V]e VW* iypywp!*en7 yw q<e =Nqy*y7]y_NyWViO *e7ypw!3 VW Vei!7_y e W!Ne qy!q<o G 7y_7!W ~ VAR s{ qy ZR BP R}BtR RZ Ps{ 8BI jr sti, $$t 8BI jr s {B8}s I PB s}} B-$8s$t tbtt stib8 I 8$t$R${ {B8}Z stsjkr R VP I$R{ZRR$t Y si$$btsj R}BtR RZ Ps{ s}} Bs{Y PB {BtR Z{$t }BjktB8$sj 8BI jr PB s}} B-$8s$Bt, $$t $R } R t I sr st sj ts$% Rs$R${sjT AsR I s}} B-$8s$Bt 8 YBI PB Y I R$t sti stsjkr$r BP {B8}Z -} $8 tr BY s}} B-$8s$Bt 8 YBIR s s}}j$ I B Y 8Zj$I$R{$}j$ts k I R$t sti stsjkr$r BP st s BR}$, tb99j by${y {BtR$RR BP s {B8}Zs$Btsj PjZ$I Ikts8${R 8BI j sti s P$t$ j 8 t stsjkr$r 8BI j e B stsjkr$r BP Y R}BtR RZ Ps{ sti, $$t 8BI jr $R } PB 8 I sjbt b$y s s}y${sj {B8}s $RBt BP Y s}} B-$8s$BtR 3BZ B}$8$9s$Bt } BAj 8R s PB 8Zjs I sti RBj% I ZR$t ABY s}} B-$8s$Bt 8BI jr GY$j t $Y s}} B-$8s$Bt {Yt$JZ {BtR$R tjk BZ} PB 8R Y BY $t Y$R -s8}j Y, $$t 8BI jrvzr$t Btjk s {BtRst PB Y ZtI jk$t jbasj 8BI j sti s pszrr$st {B js$bt PZt{$Btv} PB 8 sr b jj sr Y R {BtI B I }BjktB8$sj R}BtR RZ Ps{ 8BI jr k bb IR R}BtR RZ Ps{ 8BI jr, $$t 8Zj$I$R{$}j$ts k I R$t 7ZA` { {jsrr$p${s$bt V}}j$ I sti WZ8 ${sj YBIR d yt BIZ{$Bt ]Z t t$t $t stsjkr R jk Y s%$jk Bt Ztt$t {B8}j - sti BP t -} tr$% {B8}Z stsjkr$r {BI R * R}$ Y R sik sti {Bt$tZ$t BbY BP {B8}Z$t }Bb sti R} I Y {B8}j -$k BP Y R {BI R R 8R B, } }s{ b$y {B8}Z$t si%st{ R 7s$R${sj {Yt$JZ R s b$i jk ZR I $t t$t $t I R$t B {BtR Z{ s}} B-$8s$BtR BP Y R stsjkr$r {BI R Y R s}} B-$8s$BtR s Y t ZR I $t j$ Z BP Y s{zsj stsjkr$r {BI R BPP $t Y PBjjBb$t A t P$R qy k k$ ji $tr$y $tb Y js$btry$} A b t wbz}zd R}BtR R k sti w$t}zd I R$t %s $saj R - qy k } B%$I PsR stsjkr$r BBjR PB B}$8$9s$Bt sti I R$t R}s{ -}jb s$bt R$t{ Y {Y s}tbt Zt s}} B-$8s$BtR }js{ Y -} tr$% TBT Zt {B8}Z stsjkr R qy k Ps{$j$s Y $t s$bt BP I$R{$}j$t I } ti t stsjkr$r {BI R qy 8BR {B88Bt 8 YBI PB AZ$jI$t s}} B-$8s$BtR BP {B8}Z stsjkr R $R B s}}jk I R$t BP -} $8 tr w*!ed R}BtR RZ Ps{ wi7d 8BI jr sti RR$Bt stsjkr$r B AZ$jI R {BtI B I }BjktB8$sj s}} B-$8s$BtR BP Y {B8}Zs$Btsjjk -} tr$% stsjkr R 3B -s8}j Y ibazr ]Bt{ } e-}jb s$bt YBI wr >xh sti >EHD YsR A t I % jb} I B Ps{$j$s JZ${, %sjzs$bt BP I$PP t I R$t sj ts$% R $I t$pk $8}B st I R$t I $% R sti t s BAZR B}Tj % j I R$t R} {$P${s$BtR ZR$t *!e i7 8BI jr sti Y {B8} B8$R * {$R$Bt 7Z}}B _ BAj 8 >1xH $ YsR A t RZ{{ RRPZjjk s}}j$ I B Y 8Zj$BA` {$% I R$t BP s Y$Y R} I {$%$j str}b wr >xh sti >dhd s Ps8$jk BP p t sj V%$s$Bt s$ { sp >;(H s Z A$t j$p t$t >dmh sti s PjkbY j >11H yt BY bb, Y zs $saj ]B8}j -$k i R}BtR 7Z Ps{ BI j$t wz]i7d 8 YBI wr >d1h sti >dnhd ZR R stsjkr R BP %s k$t P$I j$k B IZ{ Y I R$t R}s{ B Y $Bt BP $t R sti AZ$jI R}BtR RZ Ps{ 8BI jr BP ~ W73 p sizs i R s {Y 3 jjbb 7kR 8R i sj$9s$bt NsAB sb k p B G GBBI ZPP 7{YBBj BP {Yst${sj et$t $t p B $s ytr$z BP q {YtBjBk Vjsts p B $s n(nn1t(;(x w((n{o} $R8s {Y IZD qy$r R s {Y bsr RZ}}B I Ak Y Ws$Btsj V BtsZ${R sti 7}s{ VI8$t$R s$bt ZtI WV7V ]Bt s{ WB WV7dTd;M( by$j Y szyb bsr $t R$I t{ s Y ytr$z PB ]B8}Z V}}j${s$BtR $t 7{$ t{ sti et$t $t wy]v7ed 7 ;(n WV7V Nstj k i R s {Y ] t <s8}bt zv 1nEMdT(((d d

$t{ sr$t s{{z s{k qy z]i7 8 YBI 8}jBkR *!e sti i7 8BI j$t {Yt$JZ R sti YsR A t RZ{{ RRPZjjk s}}j$ I B Y 8Zj$I$R{$}j$ts k b$t I R$t BP s Y$Y R} I {$%$j str}b wr >d;h sti >dhd B Y stsjkr$r sti I R$t BP {B8}BR$ {Z % I {Ystt j P s8 R >1;H sti B IZ{ tz8 ${sj tb$r $ty t $t R Z{Z sj stsjkr R wr >d;h sti >;xhd sti RYs} I R$t } BAj 8R ZR$t PjZ$I PjBb stsjkr$r >1H V %$ b BP R % sj s}}j${s$btr BP R}BtR RZ Ps{ R $t 8 {Yst${sj sti s BR}s{ t$t $t I R$t $R $% t $t >;dh qy ZR BP R}BtR RZ Ps{ R PB s}} B-$8s$t I 8$t$R${ w$ tbtt stib8d {B8}Z stsjkr R $R Rs$R${sjjk JZ R$BtsAj IZ B Y js{, BP stib8 B $t Y {B8}Z 8BI j w{p >;dhd V 8B s}} B} $s sti } Ys}R 8B XRs$R${sjjk RBZtI" 8 YBI PB s}} B-$8s$t I 8$t$R${ {B8}Z -} $8 tr $R Y BZY Y ZR BP, $$t >H 8BI jr by${y s sjrb P I B sr Y * R$t sti VtsjkR$R BP ]B8}Z e-} $8 tr w*v]ed 8BI jr wr >;H >1(H sti >nmhd qy %sj$i$k BP Y, $$t 8BI j $R tb I } ti t Bt Y -$R t{ BP stib8 B sti 8sk Y PB A A RZ$ I PB s}}j${s$btr $t%bj%$t I 8$t$R${ {B8}Z -} $8 tr 3Z Y 8B, $$t 8BI jr $t }Bjs A b t Iss }B$tR by${y 8sk A k$ ji 8B s{{z s RZjR R$t{ {B8}Z -} $8 tr k}${sjjk IB tb {Bts$t stib8 B w$ kbz Y Rs8 BZ}Z by t kbz ZR Y Rs8 $t}zd BB, >1H {Bt srr si$$btsj *!e sti i7 8BI j$t b$y *V]e 8BI jr yt Y X{jsRR${sj" I R$t sti stsjkr$r BP }YkR${sj -} $8 tr stib8 %s $s$bt $R s{{bzt I PB Ak R} si$t Y Rs8}j }B$tR BZ $t Y I R$t R}s{ sti Ak s,$t 8Zj$}j Iss }B$tR w }j${s RD R 3yp d 7s{,R sj >nmh Rs Ys Y {jsrr${sj tb$btr BP -} $8 tsj AjB{,$t }j${s$bt sti stib8$9s$bt s $ j %st by t $ {B8 R B I 8$t$R${ {B8}Z -} $8 tr YZR Rs8}j }B$tR RYBZjI A {YBR t B P$jj Y I R$t R}s{ qy k RZ R 8$t$8$9$t Y $t s I 8 st RJZs I B wy7ed B% Y I R$t $Bt Ak ZR$t y7etb}$8sj I R$tR RZ{Y sr Y Bt RYBbt $t Y B} $Y {B t BP 3yp d e-} $8 tsj * R$t yt}z R $tr s by${y B BAs$t BZ}Z d( (x -1 (( T(x Td( *!e\i7 BI j$t PB _YkR${sj e-} $8 tr V{{BZt PB zs $sa$j$k *V]e\ $$t PB ]B8}Z e-} $8 tr 7}s{ 3$jj$t d( (x -1 (( T(x Td( Td( T(x (( (x d( Td( T(x (( (x d( BI jr -d N sr 7JZs R 3$ -d s-$8z8 N$, j$ybbi er$8s yt -} tr$% 8BI j B R$8s BZ}Z s Zt $ I $t}z k d( (x k d( (x (( (( Td( T(x (( (x d( Td( T(x (( (x d( zsj$is$bt * 8$t P$ s{{z s{k -d T RR 3TRs$R${R i 1 i R$IZsj }jbr >1MH -d ] BRRT%sj$Is$Bt yt s I 8 st RJZs B >nmh 3yp d gle y 7XLzLW;5obpCELQq7z/yzQ;\gob 7/7z/wyQy 0QW LE>1HD 1

VR RYBbt $t Y 8$IIj BP 3yp d R}BtR RZ Ps{ 8BI j$t k}${sjjk 8}jBkR j sr RJZs R RR$Bt B P$ s }BjktB8$sj 8BI j B Y Rs8}j I Iss, $$t 8BI jr s {YBR t B $t }Bjs Y Iss sti s P$ ZR$t 8s-$8Z8 j$, j$ybbi R$8s$Bt wr >1(HD zsj$is$bt BP i7 8BI jr $R AsR I BtU wsd R$t Rs$R${sj Yk}BY R$R wt RR sti 3TRs$R${RD I $% I P B8 B R$8s R BP Y %s $sa$j$k $t Y Iss wad }jb$t sti {Y {,$t Y R$IZsjR sti w{d {B8}Z$t i 1 Y s$b BP Y 8BI j RZ8 BP RJZs R B Y Bsj RZ8 BP RJZs R wr >1MHD 7s{,R sj >nmh sti G j{y sj >;H ABY Rs Ys Rs$R${sj R$t $R $ts}} B} $s by t $ {B8 R B I 8$t$R${ {B8}Z -} $8 tr by${y js{, stib8 B { BRRT%sj$Is$Bt sti $t s 8 st RJZs B {st A Z$j$9 I B srr RR Y s{{z s{k BP s, $$t 8BI j *V]e sti, $$t 8BI jr Ys% PBZtI j$8$ I s}}j${s$bt $t t$t $t I R$t } Ys}R A {szr BP Y js{, BP si$jk s%s$jsaj RBPbs B P$, $$t 8BI jr Y sii I {B8}j -$k BP P$$t s, $$t 8BI j B Y sii$$btsj PPB JZ$ I B ZR s, $$t 8BI j qb {js $Pk Y$R jsr }B$t } I${$Bt b$y s, $$t 8BI j JZ$ R Y $t% R$Bt sti 8Zj$}j${s$Bt BP R % sj 8s ${ R sti Y, $$t 8BI j IB R tb -$R sr s X{jBR ITPB 8" }BjktB8$sj JZs$Bt i7 8BI j } I${$Bt Btjk JZ$ R {B8}Zs$Bt BP R$8}j }BjktB8$sj JZs$Bt Bt{ s 8BI j YsR A t P$ qy Bsj $t Y$R }s} $R B -s8$t Y sii I {B8}Zs$Btsj -} tr JZ$ I B } PB 8, $$t sti {B8}s Y } I${$% {s}sa$j$k BP, $$t sti i7 8BI jr yt 7 {$Bt 1 st B% %$ b BP Y Rs$R${sj sti 8sY 8s${sj PBZtIs$BtR BP R}BtR RZ Ps{ 8BI j$t sti, $$t $R $% t yt 7 {$Bt n Y 8Zj$I$R{$}j$ts k I R$t BP st s BR}$, tb99j $R $t BIZ{ I $ R % R sr s R } BAj 8 B {B8}s i7 sti, $$t 8BI jr PB s}} B-$8s$Bt yt 7 {$Bt ; Y i7 sti, $$t 8BI jr s {BtR Z{ I PB Y s BR}$, tb99j -s8}j yt 7 {$Bt x PBZ B}$8$9s$Bt } BAj 8R s PB 8Zjs I sti RBj% I ZR$t Y i7 sti, $$t 8BI jr 7 {$Bt E {Bts$tR s I$R{ZRR$Bt BP BtB$t bb, 1 7s$R${sj V}} B-$8s$BtR PB ]B8}Z e-} $8 tr Z$jI$t s}} B-$8s$BtR BP {B8}Z stsjkr R k}${sjjk $t%bj% RU wsd {YBBR$t st -} $8 tsj I R$t B Rs8}j Y {B8}Z stsjkr$r {BI wad {YBBR$t s 8BI j B } R t Y Iss sti w{d P$$t Y 8BI j B Y BAR % I Iss qy s s %s $ k BP B}$BtR PB s{y BP Y R R }R sr RYBbt $t 3yp 1 sti RB8 BP Y 8B } %sj t Bt R Ys% A t Y$Yj$Y I n

EXPERIMENTAL DESIGN (Fractional) Factorial Central Composite Box-Behnken D-Optimal!*eN ]<!y]e Polynomial (linear, quadratic) Splines (linear, cubic) i sj$9s$bt BP s!*en 3yqqyWp Least Squares Regression Weighted Least Squares Regression SAMPLE APPROXIMATION TECHNIQUES Response Surface Methodology Orthogonal Array Plackett-Burman Hexagon Hybrid Latin Hypercube Select By Hand Random Selection 7B{YsR${ _ B{ RR Kernel Smoothing Radial Basis Functions Network of Neurons Rulebase or Decision Tree R N$t s =ta$sr I _ I${B Best Linear Predictor Backpropagation Log-Likelihood Entropy (info.-theoretic) Kriging Neural Networks Inductive Learning 3yp 1 x_z7r`xwl K`7qQ7z/y L?7Ey07LzX>;dH 7$8}RBt sj >;dh I$R{ZRR R % sj BP Y si%sts R sti I$RsI%sts R BP Y Y$Yj$Y I s}} Bs{Y R j$r I $t 3yp 1 ts8 jk R}BtR RZ Ps{ 8 YBIBjBk t Z sj t bb,r $tiz{$% j s t$t sti, $$t yt Y$R bb, Y 8BI j {YB${ sti 8BI j P$$t }B $BtR BP AZ$jI$t s}} B-$8s$BtR s Y } $8s k {Bt{ t R}BtR RZ Ps{ 8BI jr s I$R{ZRR I $t 7 {$Bt 1d sti, $$t 8BI jr $t 7 {$Bt 11 y $R srrz8 I Ys Y si YsR RB8,tBbj I BP *!e sti i7 8BI j$t sti j$j B tb,tbbj I BP, $$t 1d!% %$ b BP i R}BtR 7Z Ps{ BI j$t i R}BtR RZ Ps{ 8BI j$t {Yt$JZ R b B $$tsjjk I % jb} I B stsjk9 Y RZjR BP }YkR${sj -} $8 tr sti { s 8}$ ${sjjktasr I 8BI jr BP Y BAR % I R}BtR %sjz R i R}BtR RZ Ps{ 8BI j$t }BRZjs R s 8BI j BP Y PB 8U w dd kw-d )Pw-D Lε by kw-d $R Y Zt,tBbt PZt{$Bt BP $t R Pw-D $R s,tbbt }BjktB8$sj PZt{$Bt BP - sti ε $R stib8 B by${y $R srrz8 I B A tb 8sjjk I$R $AZ I b$y 8 st 9 B sti %s $st{ σ 1 qy $ti$%$izsj B R ε $ s s{y BAR %s$bt s sjrb srrz8 I B A $ti } ti t sti $I t${sjjk I$R $AZ I qy }BjktB8$sj PZt{$Bt Pw-D ZR I B s}} B-$8s kw-d $R k}${sjjk s jbb B I }BjktB8$sj by${y $R srrz8 I B A $Y j$t s sr $% t Ak e+w w1du w 1D B JZsI s${ sr $% t Ak e+w wndu ˆ y )β 0 + k i =1 β i x i w nd ˆ y )β 0 + k 2 β i x i + β i x ii + β ij x i x j i =1 k ii =1 i< j ;

qy }s s8 R β ( β $ β $$ sti β $` BP Y }BjktB8$sjR $t e+w7 w1d sti wnd s I 8$t I Y BZY j sr RJZs R RR$Bt by${y 8$t$8$9 R Y RZ8 BP Y RJZs R BP Y I %$s$btr BP Y } I${ I %sjz R y ˆ w-d P B8 Y s{zsj %sjz R kw-d yt B I B P$ Y 8BI j B Y BAR % I Iss ZR$t j sr RJZs R RR$Bt Y {B PP${$ tr BP e+w7 w1d sti wnd {st A R$8s I ZR$t e+w w;d w ;D β)> : H Td :k yt e+w w;d $R Y I R$t 8s $- BP Rs8}j I }B$tR sti k $R s {BjZ8t % {B {Bts$t$t Y {B R}BtI$t %sjz R BP Y R}BtR 3B 8B I s$jr Bt j sr RJZs R RR$Bt B }BjktB8$sj i7 8BI j$t R >1MH 11!% %$ b BP $$t 11d sy 8s${R BP $$t $$t B *V]e 8BI j$t }BRZjs R s {B8A$ts$Bt BP s }BjktB8$sj 8BI j }jzr I }s Z R BP Y PB 8 $% t Ak e+w wxdu wxd kw-d )Pw-D Lw-D by kw-d $R Y Zt,tBbt PZt{$Bt BP $t R Pw-D $R s,tbbt }BjktB8$sj PZt{$Bt BP - sti w-d $R Y sj$9s$bt BP s tb 8sjjk I$R $AZ I pszrr$st stib8 } B{ RR b$y 8 st 9 B %s $st{ σ 1 sti tbtt9 B {B%s $st{ qy Pw-D 8 $t e+w wxd $R R$8$js B Y }BjktB8$sj 8BI j $t s R}BtR RZ Ps{ sti } B%$I R s XjBAsj" 8BI j BP Y I R$t R}s{ $t 8stk {sr R Pw-D $R R$8}jk s, t B A s {BtRst 8 β wr >1(H >nmh sti >;HD GY$j Pw-D XjBAsjjk" s}} B-$8s R Y I R$t R}s{ w-d { s R XjB{sj$9 I" I %$s$btr RB Ys Y, $$t 8BI j $t }Bjs R Y t R Rs8}j I Iss }B$tR qy {B%s $st{ 8s $- BP w-d $R $% t Ak e+w wed w ED ]B%>w- $ Dw-`DH ) σ 1 iw>iw- $ -`DHD yt e+w wed i $R Y {B js$bt 8s $- sti iw- $ -`D $R Y R}s$sj {B js$bt PZt{$Bt A b t stk bb BP Y t R Rs8}j }B$tR - $ sti -` i $Rst R -t R Rk88 ${ }BR$$% I P$t$ 8s $- b$y Bt R sjbt Y I$sBtsj qy {B js$bt PZt{$Bt iw- $ -`D $R R} {$P$ I Ak Y ZR 7s{,R sj >nmh sti B Yj sti!b t >1(H I$R{ZRR R % sj {B js$bt PZt{$BtR qy pszrr$st {B js$bt PZt{$Bt $t e+w wd $R 8}jBk I $t Y$R bb, n dv k =1 w D iw- $ -`D ) -}w θ k x k i x k j 2 D qy θ, $t e+w wd s Y Zt,tBbt }s s8 R ZR I B P$ Y 8BI j t I% $R Y tz8a BP I R$t $ Y %s $saj R sti -, sti -,` s Y, {B8}Bt tr BP Rs8}j }B$tR - $ sti -` yt RB8 {sr R ZR$t s R$tj {B js$bt }s s8 $% R RZPP${$ tjk BBI RZjR wr >;H >n(h sti >nmhd _ I${ I R$8s R y ˆ w-d BP Y R}BtR kw-d s Zt $ I %sjz R BP - s $% t Ak e+w wmdu w MD y ˆ ) β ˆ L q w-di Td wkt3 β ˆ D x

by k $R Y {BjZ8t % {B BP j ty t R by${y {Bts$tR Y %sjz R BP Y R}BtR s s{y Rs8}j }B$t sti 3 $R s {BjZ8t % {B BP j ty t R by${y $R P$jj I b$y Bt R by t Pw-D $R s, t sr s {BtRst yt e+w wmd w-d $R Y {B js$bt % {B BP j ty t R A b t st Zt $ I - sti Y Rs8}j I Iss }B$tR >- d - t R H sti $R $% t Ak e+w wd - 1 w D q w-d )>iw-- d D iw-- 1 D iw-- t R DH q yt e+w wmd ˆ β $R R$8s I ZR$t e+w wd(d w d(d ˆ β )w3 q i Td 3D3 q i Td k qy R$8s BP Y %s $st{ ˆ σ 2 BP Y Rs8}j }B$tR P B8 Y ZtI jk$t jbasj 8BI j wtb Y %s $st{ $t Y BAR % I Iss $R jpd $R $% t Ak e+w wdddu w ddd σ ˆ 2 ) (y -F β ˆ ) T R -1 (y -F β ˆ ) n s by Pw-D $R srrz8 I B A Y {BtRst ˆ β qy 8s-$8Z8 j$, j$ybbi R$8s R w$ XA R Z RR R"D PB Y θ, $t e+w wd ZR I B P$ Y 8BI j s PBZtI Ak 8s-$8$9$t e+w wd1d B% θ, k ( wr >;HD w d1d max θ k > 0 - [n s ln( σ ˆ 2 ) + ln(detr)] 2 BY σ ˆ 2 sti I i s PZt{$BtR BP θ, GY$j stk %sjz R PB θ, { s st $t }Bjs$% 8BI j Y "A R", $$t 8BI j $R PBZtI Ak RBj%$t Y,TI$8 tr$btsj Zt{BtR s$t I tbttj$t s B}$8$9s$Bt } BAj 8 $% t Ak e+w wd1d 111 V}}j${s$BtR BP *V]e sti $$t *V]e sti, $$t 8BI jr Ys% PBZtI j$8$ I ZR $t t$t $t I R$t s}}j${s$btr R$t{ $R $t BIZ{$Bt $tb Y j$ sz Ak 7s{,R sj >nmh p$zts >ddh YsR } PB 8 I s } j$8$ts k $t% R$s$Bt $tb Y ZR BP *V]e 8BI j$t PB Y 8Zj$I$R{$}j$ts k I R$t B}$8$9s$Bt BP s <$Y 7} I ]$%$j q str}b s$ { sp < -}jb R s x sti s d( %s $saj I R$t } BAj 8 BAR %$t Ys Y *V]e sti R}BtR RZ Ps{ 8BI j$t s}} Bs{Y R k$ ji R$8$js RZjR IZ B Y JZsI s${ ti BP Y R}BtR R!R$B sti V8Bt >n(h Ys% I % jb} I st - tr$bt BP *V]e 8BI j$t PB tz8 ${sj B}$8$9s$Bt by${y ZR R s 8Zj$Rs R s k PB P$t$t Y s{{z s{k BP Y 8BI j Y k Ys% s}}j$ I Y $ s}} Bs{Y B Y Y 8sj I R$t BP st 8A II I j { Bt${ }s{,s by${y YsR x I R$t %s $saj R G j{y sj >;EH I R{ $A s, $$ttasr I s}} B-$8s$Bt 8 YBIBjBk by${y Y k ZR B $I t$pk $8}B st %s $saj R I { {Z %sz sti $t s{$btr sti } BIZ{ s ZR PZj s}} B-$8s$Bt 8BI j PB bb 1( %s $saj } BAj 8R ZR$t Btjk n(tx( ZtR BP Y {B8}Z {BI Y k {js$8 Y $ 8 YBI {st {B} b$y Z} B n(t;( %s $saj R } B%$I I Ps{B R}s R$k {st A -}jb$ I BB, sj >nh RBj% s nd %s $saj Y j${b} BB R Z{Z sj I R$t } BAj 8 ZR$t st s}} B-$8s$Bt 8 YBI AsR I Bt, $$t BB, >1H - tir Y Y j${b} BB I R$t } BAj 8 B $t{jzi xe R Z{Z sj %s $saj R B -s8$t Y s B jsr${ sti Ikts8${ R}BtR BP Y BB q BRR sti qb {9Bt >;;H Ys% I % jb} I s tz8 ${sj B}$8$9s$Bt R s k by${y $t{b }B s R *V]e 8BI j$t sti }s t R s {Y 8 YBIR PB jbasj B}$8$9s$Bt ]B- sti FBYt >H Ys% I % jb} I Y 7 JZ t$sj * R$t PB!}$8$9s$Bt 8 YBI by${y E

ZR R jbb {BtP$I t{ ABZtIR Bt } I${ I %sjz R BP Y R}BtR PB Y R JZ t$sj R j {$Bt BP %sjzs$bt }B$tR IZ $t B}$8$9s$Bt BY s}} Bs{Y R Ys% RYBbt $8} B% 8 tr B% si$$btsj B}$8$9s$Bt s}} Bs{Y R by t s}}j$ I B s %s $ k BP RstIs I 8sY 8s${sj R } BAj 8R 1n!t zs $saj e-s8}j BP i R}BtR 7Z Ps{ sti $$t BI jr V R$8}j Bt %s $saj -s8}j A RR $jjzr s R Y I$PP t{ A b t Y s}} B-$8s$Bt {s}sa$j$$ R BP s R {BtI B I i7 8BI j sti s, $$t 8BI j 7Z sti i tszi >;1H PB 8Zjs I Y$R -s8}j B I 8BtR s RB8 BP Y j$8$s$btr BP ZR$t R {BtI B I i7 8BI jr R 3yp n qy k P$ s R {BtI B I R}BtR RZ Ps{ ZR$t j sr RJZs R RR$Bt B P$% Rs8}j }B$tR P B8 s PsA ${s I $YY B I PZt{$Bt b$y$t Y $Bt BP Y B}$8Z8 w- ) n1d V, $$t 8BI j ZR$t s {BtRst PB Y jbasj 8BI j sti Y pszrr$st {B js$bt PZt{$Bt BP e+w wd $R P$ B Y Rs8 P$% }B$tR Y B $$tsj PZt{$Bt Y P$% Rs8}j }B$tR sti Y i7 sti, $$t 8BI jr s RYBbt $t 3yp n y88 I$s jk %$I t P B8 3yp n $R Ps{ Ys Y, $$t 8BI j $t }Bjs R Y Iss }B$tR s}} B-$8s$t Y B $$tsj PZt{$Bt A Yst Y R}BtR RZ Ps{ 8BI j sti } I${$t st B}$8Z8 by${y $R 8Z{Y {jbr B Y s{zsj B}$8Z8 y $R $8}B st B tb${ Ys BZR$I BP Y I R$t R}s{ I P$t I Ak Y Rs8}j }B$tR w1( c - c ;xd t $Y 8BI j } I${R b jj sr -} { I Y, $$t 8BI j Z tr B Y ZtI jk$t jbasj 8BI j by${y $R s {BtRst qy$r $R k}${sj A Ys%$B PB s, $$t 8BI j Ps P B8 Y Rs8}j }B$tR Y, $$t 8BI j Z tr B Y ZtI jk$t jbasj 8BI j R$t{ Y $tpjz t{ BP Y Rs8}j }B$tR YsR -}Bt t$sjjk I {sk I sbsk BZR$I BP Y I R$t R}s{ ( E( Su's & Renaud's Fcn [42] Sample Points 2nd Order RS Model x( Kriging Model y ;( n( 1( d( dx 1x nx ;x xx Ex - 3yp n 5z8y 7yKq?yE qlw X LzXX` WyyzQ> 7/7z/ELQqX 7$- t % tjk R}s{ I }B$tR wtb $t{jzi$t Y Rs8}j }B$tRD s s, t P B8 b$y$t Y st w1( c - c ;xd B {Y {, Y s{{z s{k BP Y bb s}} B-$8s$Bt 8BI jr qy 8s-$8Z8 sarbjz B wi$pp t{ A b t Y s{zsj sti } I${ I %sjz RD Y s% s sarbjz B sti Y BB 8 st RJZs B w7ed by${y $RU w dnd BB 7e ) n error i =1 (y i -y ˆ i ) n error 2

by t B $R Y tz8a BP }B$tR w) ded s j$r I $t qv Ne d sr I Bt Y B stsjkr$r $t qv Ne d $ {st A {Bt{jZI I Ys Y, $$t 8BI j s}} B-$8s R Y B $$tsj PZt{$Bt A R$t{ $ YsR s jbb BB 7e s% s B sti 8s-$8Z8 B V 8B $t%bj% I 8Zj$I$R{$}j$ts k I R$t -s8}j $R I R{ $A I $t Y t - R {$Bt qv Ne d o L yzyqrx7xwl Lz8y 7yKq?yE q 1tI! I i7 BI j $$t BI j s- V 7w B D ndn; 1x( V% V 7w B D ddd (E BB 7e 1dxx d((; n V BR}$, WB99j * R$t e-s8}j qy 8Zj$I$R{$}j$ts k I R$t BP st s BR}$, tb99j YsR A t R j { I sr Y R } BAj 8 PB {B8}s $t Y } I${$% {s}sa$j$k BP i7 sti, $$t 8BI jr qy j$t s s BR}$, B{, t$t $R Y } B}ZjR$Bt RkR 8 } B}BR I PB Y z tz 7s >;nh ZRsAj jszt{y % Y${j $jjzr s I $t 3yp ; 3yp ; ~z0` C0y `XyKqqy`z_8_7qj70_q7zy y LX 7> L `qx7lzxrx0e>1dh qy s BR}$, B{, t$t {BtR$RR BP s B{, Y ZR {Bbj s BR}$, tb99j sti }jz AsR $BtR sr RYBbt $t 3yp x qy s BR}$, tb99j $R s Zt{s I R}$, B }jz tb99j Ys si`zrr B Y s8a$ t } RRZ sti $t s R b jj b$y jszt{y % Y${j R >n;h qy PjBb P$ ji R Z{Z {Yst R I s8s${sjjk P B8 jbb sj$zi B Y$Y sj$zi Bt Y R}$, RZ Ps{ sti $t Y AsR PjBb $Bt w{p >dxh >1H sti >nehd VII$$Btsj PjBb $R $t` { I $t Y AsR $Bt B { s st s BIkts8${ R}$, >deh by${y $% R Y s BR}$, tb99j $R ts8 sti $t{ sr R Y AsR } RRZ sti {Bt $AZ$Bt BP Y AsR $Bt B Y s BR}$, Y ZR ie]yi]=nvqy!w ]!GN 7<!] q<i=7qei w_iyvio 3N!GD e _VW7y!W 3VW Feq!=W*ViO Vei!7_y e W!Ne ]!Wq!=i 7<eVi NVOei ie]!_ie77y!w 7<!] V7e Nee* _N=p V7e ie]yi]=nvqy!w iepy!w M

3yp x \ LX 7>LE Lzz0XyzQWqLjW7qQ_y y0 7X07X>1dH qy stsjkr$r BP Y tb99j $t%bj% R bb I$R{$}j$t Rvs BIkts8${R sti R Z{Z RvR$t{ Y $R st $t s{$bt A b t Y R Z{Z sj I$R}js{ 8 tr BP Y tb99j RZ Ps{ sti Y } RRZ R {szr I Ak Y %s k$t s BIkts8${ PP {R qy ZR sti tb99j bsjj } RRZ {sj{zjs$btr s 8sI ZR$t {B8}Zs$Btsj PjZ$I Ikts8${R w]3*d stsjkr$r sti s j$t, I B s R Z{Z sj P$t$ j 8 t stsjkr$r 8BI j PB I 8$t$t tb99j b $Y sti R Z{Z sj $t $k V 8$RR$Bt s% s t$t R} {$P${ $8}ZjR sti t$t Y ZR\b $Y s$b s {sj{zjs I sti ZR I B R$8s % Y${j BRRTj$PTBPPTb $Y wpn!gd AsR I Bt Iss RZ}}j$ I Ak ib{, Ikt qy 8Zj$I$R{$}j$ts k IB8s$t I {B8}BR$$Bt $R $jjzr s I $t 3yp E B sj >1dH } B%$I sii$$btsj I s$jr Bt Y s BIkts8${ sti R Z{Z sj stsjkr R PB Y s BR}$, tb99j GLOW Contours ]3* *!VyW Engine Specific Impulse Thrust/Weight Ratio TRAJECTORY DOMAIN FEM STRUCTURES DOMAIN V7e3N!G!*eN *!VyW V7e Nee* 3yp E -`q07q7x7 q7zy rqley7zqle LX707Lz>1dH 3B Y$R RZIk Y I R$t %s $saj R s {BtR$I I PB Y 8Zj$I$R{$}j$ts k I R$t BP Y s BR}$, tb99j U Y ZR stj AsR Y $Y sti j ty sr RYBbt $t 3yp qy Y ZR stj $R Y t st{ stj BP Y sr P B8 Y {B8AZR$Bt {Ys8A BtB Y tb99j RZ Ps{ Y AsR Y $Y sti j ty P B Y RBj$I }B $Bt BP Y tb99j $R jp V JZsI s${ 8BI j $R { s I B t s %sjz R BP R}j$t,tB RZ Ps{ stj RjB} sti -$ stj by${y I P$t Y tb99j } BP$j {B R}BtI$t B R} {$P${ %sjz R BP Y ZR stj AsR Y $Y sti j ty 7s $t stj BIZj R}st 7}j$t,tB RZ Ps{ stj e-$ stj WB99j { t j$t N ty e-$ Y $Y 3yp ]LFFq/LE0 rqx7/z8y 7yKqX>1dH

BZtIR PB Y I R$t %s $saj R s R AsR I Bt $tpb 8s$Bt P B8 B $t ib{, Ikt sti %$saj tb99j } BP$j R P B8 Y JZsI s${ 8BI j AsR I Bt sjj {B8A$ts$BtR BP Y ZR stj Y $Y sti j ty b$y$t Y I R$t R}s{ 7 {BtI B I i7 8BI jr sti, $$t 8BI jr s I % jb} I PB s{y R}BtR vy ZR b $Y sti pn!gv$t Y t - R {$Bt B}$8$9s$Bt BP Y s BR}$, tb99j ZR$t Y i7 sti, $$t 8BI jr PB I$PP t BA` {$% PZt{$BtR $R } PB 8 I $t 7 {$Bt x ; V}} B-$8s$BtR PB Y V BR}$, WB99j _ BAj 8 qy Iss ZR I B P$ Y i7 sti, $$t 8BI jr $R BAs$t I P B8 s 1x }B$t B YBBtsj s sk wabr x n Bs stid P B8 >nnh qy Rs8}j }B$tR s $jjzr s I $t 3yp M sti s R{sj I B P$ Y Y I$8 tr$btsj I R$t R}s{ I P$t I Ak Y ABZtIR Bt Y Y ZR stj AsR Y $Y sti j ty N ty Vtj < $Y 3yp M CyE q L7z0XLWL 0_L/Lzyqy yr 7 {$Bt ;d {Bts$tR Y R}BtR RZ Ps{ 8BI jr by${y s P$ B Y Iss 7 {$Bt ;1 {Bts$tR Y, $$t 8BI jr e B stsjkr$r BP Y R}BtR RZ Ps{ sti, $$t 8BI jr $R I$R{ZRR I $t 7 {$Bt ;n sti s s}y${sj {B8}s $RBt BP Y s}} B-$8s$Bt 8BI jr $R $% t $t 7 {$Bt ;; ;d i R}BtR 7Z Ps{ BI jr qy i7 8BI jr PB b $Y Y ZR sti pn!g s BAs$t I ZR$t B I$ts k j sr RJZs R RR$Bt {Yt$JZ R sti F_ >nh qy {B R}BtI$t i7 8BI jr s $% t $t e+w7 wd;dtwded qy JZs$BtR Ys% A t R{sj I ss$tr Y AsR j$t I R$t IZ B Y } B} $ s k tsz BP RB8 BP Y Iss G $Y ) (Md( T (dde~s L (d1d~y L (dx1~j L ((Ex~s 1 T ((1x~s~Y L w d;d (((dn~y 1 T ((xn~s~j T ((dnd~y~j L ((n(d~j 1 qy ZR ) (EM L ((((nd~s L (((d~y L (((E(~j T (((dx~s 1 L (((d1x~s~y T w dxd (((dd~y 1 L (((d1x~s~j T (((dm~y~j T (((dex~j 1 pn!g ) (n( T ((1(~s L (((Ex~Y T ((1Ex~j L ((n(~s 1 T ((den~s~y L w ded ((d((~y 1 T ((11E~s~j L ((dxd~y~j L ((dx~j 1 qy i 1 i 1 TsI`ZR I sti BB 7e %sjz R PB s{y BP Y R R {BtI B I i7 8BI jr s RZ88s $9 I $t qv Ne 1 VR %$I t{ I Ak Y Y$Y i 1 sti i 1 TsI`ZR I sti jbb BB 7e %sjz R Y R {BtI B I }BjktB8$sj 8BI j s}} s R B {s}z s js }B $Bt BP Y BAR % I %s $st{ d(

qv Ne 1 -LQqQ7y/zLX07XLW X LzXX` WyELQqX px LzX -yx` G $Y qy ZR pn!g i 1 (ME (M (d i 1 TsI`ZR I ( (E (xn BB 7e dd10 ((d0 (1x0 ;1 $$t BI jr PB Y V BR}$, WB99j _ BAj 8 qy, $$t 8BI jr s AZ$j P B8 Y Rs8 1x Rs8}j }B$tR ZR I B P$ Y R}BtR RZ Ps{ 8BI jr $t 7 {$Bt ;d V {BtRst 8 w$ Y 8 st BP Y IssD $R R j { I PB Y ZtI jk$t jbasj 8BI j sti Y pszrr$st {B js$bt PZt{$Bt e+w wd $R Z$j$9 I PB Y jb{sj I }s Z R I 8$t I Ak Y {B js$bt 8s $- i yt$$sj $t% R$s$BtR % sj I Ys s R$tj θ }s s8 bsr $trzpp${$ t B s{{z s jk 8BI j Y Iss IZ B R{sj$t BP Y I R$t %s $saj R qy PB s R$8}j nt* -YsZR$% $I R s {Y b$y s P$tsAj R } R$9 bsr ZR I B P$tI Y 8s-$8Z8 j$, j$ybbi R$8s R PB Y Y θ }s s8 R t I I B BAs$t Y XA R", $$t 8BI j qy RZj$t 8s-$8Z8 j$, j$ybbi R$8s R PB Y Y θ }s s8 R PB Y b $Y Y ZR sti pn!g 8BI jr s RZ88s $9 I $t qv Ne n Y R %sjz R s PB Y R{sj I Rs8}j }B$tR qv Ne n x_0y y ye0 XWL > 7/7z/ELQqX px LzX G $Y qy ZR pn!g θ stj ) (x;md (n( nne1 θ Y $Y ) dn1n (x( 1;n θ j ty ) 1dM (Ex (xn G$Y Y R }s s8 R sti Y {B R}BtI$t 1x Rs8}j }B$tR Y, $$t 8BI jr s PZjjk R} {$P$ I V t b }B$t $R } I${ I ZR$t Y R θ %sjz R $t {B8A$ts$Bt b$y e+w7 wmdtwd(d qy s{{z s{k BP Y i7 sti, $$t 8BI jr $R -s8$t I $t Y t - bb R {$BtR Vt sii$$btsj 1x stib8jk R j { I }B$tR s ZR I B % $Pk Y s{{z s{k BP Y i7 sti, $$t 8BI jr e B $R I P$t I sr Y I$PP t{ A b t Y s{zsj R}BtR P B8 Y {B8}Z stsjkr$r kw-d sti Y } I${ I %sjz y ˆ w-d P B8 Y i7 B, $$t 8BI j qy 8s-$8Z8 sarbjz B Y s% s sarbjz B sti Y BB 7e e+w wdnd PB Y 1x stib8jk R j { I }B$tR s RZ88s $9 I $t qv Ne ; ;n e B VtsjkR$R BP i R}BtR 7Z Ps{ sti $$t BI jr qv Ne ; o L yzyqrx7xlwy L?7Ey07LzELQqX CLzQ5 Q px LzXC` Wy-LQqX G $Y qy ZR pn!g s- V 7w B D dx0 ((n10 nem0 V% V 7w B D 1;;0 ((d10 (xn0 BB 7e ;x;0 ((dx0 ((0 7/7z/-LQqXwj70_LzX0yz00 ED G $Y qy ZR pn!g s- V 7w B D d1n0 ((;M0 n;n0 V% V 7w B D 1xd0 ((d10 (x0 BB 7e ;n0 ((dm0 (M0 dd

3B Y b $Y sti pn!g R}BtR R Y, $$t 8BI jr Ys% jbb 8s-$8Z8 sarbjz B R sti jbb BB 7eR Yst Y i7 8BI jr YBb % Y s% s sarbjz B $R Rj$Yjk js PB Y, $$t 8BI jr $ti${s$t Ys Y s% s 8st$ZI BP Y } I${$Bt B $R js PB Y, $$t 8BI jr Yst Y i7 8BI jr VR PB Y ZR Y i7 8BI jr s Rj$Yjk A Yst Y, $$t 8BI jr s{{b I$t B Y %sjz R $t Y saj Y 8s-$8Z8 sarbjz B sti BB 7e s Rj$Yjk j RR by$j Y s% s sarbjz B R s RR t$sjjk Y Rs8 y $R tb RZ } $R$t Ys Y i7 8BI j } I${R Y ZR A $ YsR s % k Y$Y i 1 %sjz (M sti jbb BB 7e ((d0 y $R srrz $t B tb YBb % Ys Y, $$t 8BI j I R}$ ZR$t s {BtRst 8 PB Y ZtI jk$t jbasj 8BI j $R Btjk Rj$Yjk j RR s{{z s Yst Y {B R}BtI$t i7 8BI j y s}} s R Ys ABY s}} B-$8s$BtR } I${ srbtsajk b jj b$y Y, $$t 8BI jr Ys%$t s Rj$Y B% sjj si%sts A {szr BP Y jbb BB 7e %sjz R ;; p s}y${sj ]B8}s $RBt BP i R}BtR 7Z Ps{ sti $$t BI jr yt sii$$bt B Y B stsjkr$r BP 7 {$Bt ;n s s}y${sj {B8}s $RBt BP Y i7 sti, $$t 8BI jr YsR A t } PB 8 I B %$RZsj$9 I$PP t{ R $t Y bb s}} B-$8s$Bt 8BI jr yt 3yp7 Tdd nt* {BtBZ }jbr BP Y ZR b $Y sti pn!g sr s PZt{$Bt BP stj j ty sti AsR Y $Y s $% t yt s{y P$Z Y Rs8 {BtBZ j % jr s ZR I PB Y i7 sti, $$t 8BI jr RB Ys Y RYs} R BP Y {BtBZ R {st A {B8}s I 3yp px LzXX` WyyzQ> 7/7z/ELQqXWL 0_ `X0 yt 3yp $ {st A R t Ys Y {BtBZ R BP Y ZR PB Y i7 sti, $$t 8BI jr s % k R$8$js VR %$I t{ I Ak Y Y$Y i 1 sti jbb BB 7e %sjz R Y i7 8BI j P$R Y Iss JZ$ b jj sti $ $R srrz $t B tb Ys Y, $$t 8BI j R 8Aj R Y i7 8BI j % t Y BZY Y ZtI jk$t jbasj 8BI j PB Y, $$t 8BI j $R `ZR s {BtRst 8 d1

3yp d( px LzXX` WyyzQ> 7/7z/ELQqXWL j7/_0 qy {BtBZ R BP Y i7 sti, $$t 8BI jr PB b $Y $t 3yp d( s sjrb % k R$8$js AZ Y $tpjz t{ BP Y jb{sj$9 I } Z As$BtR {szr I Ak Y pszrr$st {B js$bt PZt{$Bt $t Y, $$t 8BI j {st A $t B A R t qy B stsjkr$r P B8 7 {$Bt ;n $ti${s I Ys Y, $$t 8BI j PB b $Y $R Rj$Yjk 8B s{{z s Yst Y i7 8BI j by${y 8sk RZj P B8 Y R8sjj jb{sj$9 I %s $s$btr V {XLE0 787j ozq87j 3yp dd px LzXX` WyyzQ> 7/7z/ELQqXWL tu5p qy t sj RYs} BP Y pn!g {BtBZ R $R Y Rs8 $t 3yp ddv YBb % Y R$9 sti RYs} BP Y I$PP t {BtBZ R }s ${Zjs jk sjbt Y j ty s-$r s JZ$ I$PP t qy ti %$ b sjbt Y j ty s-$r $t 3yp dd PZ Y Y$Yj$YR Y I$PP t{ R A b t Y bb 8BI jr WB${ sjrb $t 3yp dd Ys Y, $$t 8BI j } I${R s 8$t$8Z8 pn!g b$y$t Y I R$t R}s{ { t I s BZtI < $Y)T(M Vtj )( sjbt Y s-$r I P$t I Ak (1 c N ty c (M Y$R 8$t$8Z8 bsr % $P$ I Y BZY sii$$btsj -} $8 tr x!}$8$9s$bt =R$t i R}BtR 7Z Ps{ sti $$t BI jr qy Z R BP Y s{{z s{k BP Y i7 sti, $$t 8BI jr {B8 R by t Y s}} B-$8s$BtR s ZR I $t B}$8$9s$Bt y $R { Z{$sj Ys stk s}} B-$8s$BtR ZR I $t B}$8$9s$Bt } B% srbtsajk s{{z s j R Y k j si Y B}$8$9s$Bt sjb $Y8 $tb $BtR BP AsI I R$tR q ZR i $Bt s}} Bs{Y R wr >1nH sti >nxhd sti Y BI j sts 8 t P s8 bb, wr >;H sti >d(hd Ys% A t I % jb} I B trz Ys B}$8$9s$Bt dn

sjb $Y8R s tb j I sr sk Ak $ts{{z s s}} B-$8s$BtR yt Y$R bb, YBb % Y PB{ZR YsR A t Bt I % jb}$t Y s}} B-$8s$Bt 8BI jr }s ${Zjs jk Y, $$t 8BI jr sti tb Bt Y B}$8$9s$Bt $R jp 3BZ I$PP t B}$8$9s$Bt } BAj 8R s PB 8Zjs I sti RBj% I B {B8}s Y s{{z s{k BP Y i7 sti, $$t 8BI jru wdd 8s-$8$9 Y ZR w1d 8$t$8$9 b $Y wnd 8$t$8$9 pn!g sti w;d 8s-$8$9 Y ZR\b $Y s$b qy P$ R bb BA` {$% PZt{$BtR } R t si$$btsj R$tj BA` {$% R$tj I$R{$}j$t B}$8$9s$Bt } BAj 8R qy R {BtI bb BA` {$% PZt{$BtR s 8B {Ys s{ $R${ BP 8Zj$I$R{$}j$ts k B}$8$9s$Bt 8$t$8$9$t pn!g B 8s-$8$9$t Y Y ZR\b $Y s$b JZ$ R si T BPPR A b t Y s BIkts8${R sti R Z{Z R I$R{$}j$t R 3B s{y BA` {$% PZt{$Bt {BtR s$t j$8$r s }js{ I Bt Y 8s$t$t R}BtR R PB $trst{ {BtR s$tr s }js{ I Bt Y 8s-$8Z8 sjjbbsaj b $Y sti pn!g sti Y 8$t$8Z8 sjjbbsaj Y ZR\b $Y s$b by t 8s-$8$9$t Y ZR <Bb % tbt BP Y {BtR s$tr s s{$% B A$tI$t $t stk BP Y P$tsj RZjR es{y B}$8$9s$Bt } BAj 8 $R RBj% I ZR$tU wsd Y i7 8BI j s}} B-$8s$BtR sti wad Y, $$t 8BI j s}} B-$8s$BtR PB Y ZR b $Y sti pn!g qy B}$8$9s$Bt $R } PB 8 I ZR$t s p t sj$9 I i IZ{ I p si$ t wpipd sjb $Y8 qy I$PP t Rs $t }B$tR s ZR I PB s{y BA` {$% PZt{$Bt wy jbb 8$IIj sti Z}} ABZtIR BP Y I R$t %s $saj RD B srr RR Y s% s tz8a BP stsjkr$r sti si$ t {sjjr t { RRs k B BAs$t Y B}$8Z8 I R$t b$y$t Y $% t I R$t R}s{ Y RBjZ$BtR PB s{y BA` {$% PB s{y s}} B-$8s$Bt {Bt% B Y Rs8 B}$8Z8 I R}$ Y $t$$sj Rs $t }B$t qy Rs8 }s s8 R w$ R } R$9 Bj st{ {BtR s$t %$Bjs$Bt {D s ZR I b$y$t Y pip sjb $Y8 PB s{y B}$8$9s$Bt qy B}$8$9s$Bt RZjR s RZ88s $9 I $t qv Ne x * R$t %s $saj sti R}BtR %sjz R Ys% A t R{sj I sr s } { ts BP Y AsR j$t I R$t IZ B Y } B} $ s k tsz BP RB8 BP Y Iss s-$8$9 qy ZR qv Ne x 5 07E7Fy07Lz X`q0X`X7z/ X LzXX` WyyzQ> 7/7z/ELQqX V% ' BP V% ' BP z $P$ I VtsjkR$R p si$ t!}$8z8 * R$t _ I${ I!}$8Z8!}$8Z8 0 e B ~ ]sjjr ]sjjr Vtj ((E qy ZR d((de d((dn ((10 pc 1 ; < $Y T(;nn G $Y (;x( (;E T(10 -LQqX N ty d((( qy \G d(d;d d(dn; ((0 pn!g (1; (x T(nE0 Vtj (ExE qy ZR d((de d((d; ((10 7/7z/ E1 x < $Y T(E1 G $Y (nmx (dxx 1xd0 -LQqX N ty d((( qy \G d(dx d(1d( T(xd0 pn!g (E( (EMn ((M0 $t$8$9 G $Y Vtj (M(( qy ZR (x (x T((d0 pc 1 n < $Y Td((( G $Y (xm; (;E ddm0 -LQqX N ty Td((( qy \G d(xnn d(xxx T(1d0 pn!g (ne ((E (n(0 Vtj d((( qy ZR (Ex (xe ((M0 7/7z/ ;n ;E < $Y T(Mn G $Y (1x (;;n n0 -LQqX N ty Td((( qy \G d(x(e d(xem T(x0 pn!g (M1; (d; T((0 $t$8$9 pn!g Vtj (EdE qy ZR d((dn (x (xe0 pc n(e nnn < $Y Td((( G $Y (ME (MEd ;(0 -LQqX N ty d((( qy \G d(1xd d(1me T(n;0 pn!g (EE( d(d;e T;0 Vtj (E; qy ZR d((( d(((e ((;0 7/7z/ xe Enn < $Y T(Mnn G $Y ((E( (Mn1 nx0 -LQqX N ty (EE qy \G d(11m d(n(1 T(10 pn!g (Ex (EM( T((x0 s-$8$9 qy ZR\G $Y is$b Vtj ((E qy ZR d((de (x (x0 pc 1 ; < $Y T(;nn G $Y (;x( ((n ;de0 d;

-LQqX N ty d((( qy \G d(d;d d(dn T(nd0 pn!g (1; d(11m T;n0 Vtj (ExE qy ZR d((de d((d; ((10 7/7z/ E1 x < $Y T(E1 G $Y (nmx ((En nxe0 -LQqX N ty d((( qy \G d(dx d(1nd T(n0 pn!g (E( (EEE (1x0 ~\wld L 0 E7zQ7y0X0_y00_ELQq7XL8 Q707z/,ywTD7zQ7y0X0_y0707X`zQ Q707z/ qy PBjjBb$t BAR %s$btr {st A 8sI AsR I Bt Y Iss $t qv Ne x \8 y/z`ek LW yzyqrx7xyzq / yq7z0yqqxu yt t sj Y i7 8BI jr JZ$ P b stsjkr$r sti si$ t {sjjr B s{y$ % Y B}$8Z8 Yst Y, $$t 8BI jr IB qy$r {st A s $AZ I B Y Ps{ Ys Y i7 8BI jr s R$8}j R {BtI B I }BjktB8$sjR by sr Y, $$t 8BI jr s 8B {B8}j - glz8 /z y0xu VjYBZY tb RYBbt $t Y saj B}$8$9s$Bt ZR$t Y i7 8BI jr tir B {Bt% 8B JZ${,jk Yst by t ZR$t, $$t 8BI jr qy$r {st A $tp I P B8 Y s% s tz8a BP si$ t {sjjr by${y $R Bt B Y {sjjr P b PB Y i7 8BI jr 5 07E`EQX7/zXU qy B}$8Z8 I R$tR BAs$t I P B8 Y i7 sti, $$t 8BI jr s RR t$sjjk Y Rs8 PB s{y BA` {$% PZt{$Bt $ti${s$t Ys ABY s}} B-$8s$BtR R ti Y B}$8$9s$Bt sjb $Y8 $t Y Rs8 t sj I$ {$Bt qy js R I$R{ }st{k $R Y j ty PB Y 8$t$8$9 pn!g B}$8$9s$Bt i7 8BI jr } I${ Y B}$8Z8 pn!g B{{Z R s Y Z}} ABZtI Bt j ty wldd by$j Y, $$t 8BI jr k$ ji (EE qy$r I$PP t{ $R %$I t $t 3yp dd h Q70QL 07EyyzQ Q707Lz L XU qb {Y {, Y s{{z s{k BP Y } I${ I B}$8s Y B}$8Z8 I R$t %sjz R PB stj Y $Y sti j ty s ZR I sr $t}zr $tb Y B $$tsj stsjkr$r {BI R sti Y } { ts I$PP t{ A b t Y s{zsj sti } I${ I %sjz R $R {B8}Z I qy } I${$Bt B $R j RR Yst x0 PB sjj {sr R sti $R (x0 B j RR $t Y JZs R BP Y RZjR yt RZ88s k Y t t $Y 8BI j {BtR$R tjk BZ} PB 8R Y BY sti Y I$PP t{ $t } I${$% {s}sa$j$k BP s{y 8BI j PB s{y BA` {$% PZt{$Bt $R JZ$ R8sjj x_> 7/7z/ELQqX WL EyXjqqyX0_ XLzQL Q pcelqqx8z0_l`/_0_/qlkyq L 07LzLW0_> 7/7z/ELQq7XLzqryLzX0yz0!tB$t bb, B $8} B% 8BI j s{{z s{k sti {Y {,$t si JZs{k BP P$ $R I s$j I $t Y t - R {$Bt E ]jbr$t i 8s,R sti 3ZZ GB, qy$r bb, } R tr s } j$8$ts k $t% R$s$Bt $tb Y ZR BP, $$t sr st sj ts$% Rs$R${sjTAsR I s}} B-$8s$Bt {Yt$JZ PB 8BI j$t tbtt stib8 I 8$t$R${ {B8}Z -} $8 tr V Y %s $saj t$t $t I R$t -s8}j $R ZR I B {B8}s Y s}} B-$8s$Bt {s}sa$j$k BP R}BtR RZ Ps{ 8BI j$t sti, $$t qy -s8}j $R Y 8Zj$I$R{$}j$ts k I R$t BP st s BR}$, tb99j by${y $t{jzi R s ]3* sti s P$t$ j 8 t 8BI j G$Y Y$R R$8}j k sj$r${ t$t $t -s8}j Y ZR BP, $$t 8BI jr sr st sj ts$% s}} B-$8s$Bt {Yt$JZ YsR A t I 8BtR s I V Y$R }B$t Y $R $t{bt{jzr$% %$I t{ B Rs Ys Bt s}} B-$8s$Bt 8 YBI $R 8B si%sts BZR Yst stby YBb % Y, $$t 8BI jr ZR$t Btjk s {BtRst ZtI jk$t jbasj 8BI j sti s pszrr$st {B js$bt PZt{$Bt } PB 8 sr b jj sr Y R {BtI B I R}BtR RZ Ps{ 8BI jr qy s R % sj R s {Y $RRZ R B sii RR PB Y s}}j${s$bt BP, $$t sti *V]e 8 YBIR PB BY wsti js D t$t $t I R$t } BAj 8R B7007z/y> 7/7z/ELQqU 3$$t s, $$t 8BI j JZ$ R RBjZ$Bt BP st,ti$8 tr$btsj Zt{BtR s$t I tbttj$t s B}$8$9s$Bt } BAj 8 e+w wd1d $t B I B I 8$t Y 8s-$8Z8 j$, j$ybbi R$8s R BP Y θ }s s8 R PB Y XA R", $$t 8BI j _s t R s {Y 8 YBIR sti R$8Zjs I stt sj$t sjb $Y8R s {Z tjk A $t 8}jBk I B } PB 8 Y$R B}$8$9s$Bt 3B R8sjj } BAj 8R b$y js$% jk P b Rs8}j }B$tR Y$R B}$8$9s$Bt $R sy $%$sj <Bb % sr Y R$9 BP Y } BAj 8 dx

$t{ sr R sti Y tz8a BP Rs8}j }B$tR $t{ sr R Y sii I PPB t I I B BAs$t Y XA R", $$t 8BI j 8sk JZ${,jk A $t B BZb $Y Y A t P$ BP AZ$jI$t Y s}} B-$8s$Bt Cq07z/ y > 7/7z/ ELQqU yt Y$R -s8}j s {BtRst $R ZR I PB Y jbasj }B $Bt BP Y, $$t 8BI j AsR I Bt Y RZ{{ RR BP Y bb, $t >n(h >nh sti >;H <Bb % ZR$t s jbasj }BjktB8$sj 8BI j PB Pw-D $tejt wxd 8sk PZ Y $8} B% Y s{{z s{k BP Y, $$t 8BI j p$zts >ddh } PB 8R s } j$8$ts k $t% R$s$Bt BP RZ{Y st s}} Bs{Y sti P$tIR Ys 8$t$8sj $8} B% 8 t bsr BAs$t I h Q707z/j70_y> 7/7z/ELQqU =tj$, i7 8BI j } I${$Bt } I${$Bt b$y s, $$t 8BI j JZ$ R Y $t% R$Bt sti 8Zj$}j${s$Bt BP R % sj 8s ${ R Y R 8s ${ R Bb sr Y tz8a BP Rs8}j }B$tR $t{ sr R 3B js } BAj 8R } I${$Bt b$y Y, $$t 8BI j 8sk A {B8 {B8}Zs$Btsjjk -} tr$% $t sti BP $R jp 3Z Y 8B $ $R 8B I$PP${Zj B jbb, s s, $$t 8BI j sti I 8$t Y PP {R BP Y I R$t %s $saj R Bt Y R}BtR wrd R$t{ Y jbasj 8BI j $R ZRZsjjk s, t sr s {BtRst sti s{y } I${$Bt }B$t $R RR t$sjjk Y RZ8 BP -}Bt t$sjjk I {sk$t PZt{$BtR AsR I Bt i ~yq7qy07z/y> 7/7z/ELQqU G$Y i7 8BI jr i 1 %sjz R sti R$IZsj }jbr {st A ZR I B srr RR 8BI j P$ sti s{{z s{k 7$t{, $$t 8BI jr $t }Bjs Y Iss Y s tb R$IZsjR sti sj ts$% {Y {,R 8ZR A $8}j 8 t I B %sj$is Y 8BI j yt Y$R -s8}j st sii$$btsj 1x stib8 Iss }B$tR s ZR I B {Y {, 8BI j si JZs{k YBb % 8B PB 8sj s}} Bs{Y R -$R!B sj >ndh sti >n1h sti O R$jkZ sti _s s >;MH Ys% I % jb} I s sk R$stT%sj$Is I RZ Bs s}} Bs{Y by${y ZR R sii$$btsj %sj$is$bt }B$tR B 8s, JZsj$s$% srr RR8 tr BP Y JZsj$k BP Y s}} B-$8s$Bt 8BI j sti } B%$I Y B ${sj ABZtIR Bt Y js R I$R{ }st{k A b t Y 8BI j sti Y s{zsj {B8}Z stsjkr$r Vt sj ts$% 8 YBI by${y IB R tb JZ$ sii$$btsj }B$tR $R j s% TBt TBZ { BRR %sj$is$bt >1EH es{y Rs8}j }B$t ZR I B P$ Y 8BI j $R 8B% I Bt s s $8 Y 8BI j $R AZ$j b$ybz Y Rs8}j }B$t sti Y I$PP t{ A b t Y 8BI j b$ybz Y Rs8}j }B$t sti s{zsj %sjz s Y Rs8}j }B$t $R {B8}Z I PB sjj BP Y Rs8}j }B$tR W $Y s}} Bs{Y bsr $8}j 8 t I $t Y$R -s8}j IZ B Y $t{ sr I {B8}Zs$Bt PPB JZ$ I ;X7/z LW? 7Ez0X WL K`7qQ7z/ > 7/7z/ ELQqXU V Y I R$tR by${y s A RZ$ I PB Rs8}j$t {B8}Z -} $8 tr sti AZ$jI$t, $$t 8BI jr Yst PB Rs8}j$t }YkR${sj -} $8 tr sti AZ$jI$t i7 8BI jr2 qy B}$t$BtR Bt Y s}} B} $s -} $8 tsj I R$t %s k Y Btjk {BtR trzr s{y I YZR Ps $R Ys I R$tR PB tbtt stib8 I 8$t$R${ {B8}Z stsjkr R RYBZjI A R}s{ P$jj$t yt Y$R -s8}j B YBBtsj s skr s ZR I B AZ$jI s}} B-$8s$Bt PBjjBb$t Y bb, Ak BB, sj >nh sti >;H p$zts >ddh ZR R *TB}$8sj I R$tR B P$ Y$R, $$t sti i7 8BI jr 7s{,R sj >nmh RZ R ZR$t y7etb}$8sj I R$tR sti B Yj sti!b t >1(H I$R{ZRR 8$t$8s- 8s-$8$t Ns$t Yk} {ZA sti R{ s8aj I t I R$tR PB {B8}Z -} $8 tr * R}$ Y sii I {B8}j -$k BP P$$t ZR$t sti %sj$is$t s, $$t 8BI j Y }B t$sj s$tr $t 8BI j s{{z s{k `ZR$Pk {Bt$tZ I $t% R$s$Bt $tb Y s}} Bs{Y qy, $$t RBPbs ZtI I % jb}8 t b$jj Ps{$j$s Y ZR sti %sj$is$bt BP, $$t 8BI jr $t{ sr$t Y $ s s{$% t RR PB t$t $t s}}j${s$btr 3$tsjjk PZZ bb, Bt Y s BR}$, tb99j I R$t } BAj 8 $t{jzi R -}sti$t Y R{B} BP Y } BAj 8 B $t{jzi 8B I R$t %s $saj R sti R}BtR R sti $t% R$s$t Y $8}s{ BP I {B8}BR$t Y } BAj 8 $tb $R I$R{$}j$t R Ak AZ$jI$t s}} B-$8s$Bt 8BI jr BP s{y I$R{$}j$t R }s s jk sti -s8$t$t Y PP { BP I$PP t 8Zj$I$R{$}j$ts k I R$t PB 8Zjs$BtR w >dh sti >MHD Bt Y RBjZ$Bt de

V{,tBbj I8 tr qyst,r B * FBYt B _e sti q$8byk sz k s d NVi77 RZI t PB Y $ Y j} b$y Y s BR}$, tb99j } BAj 8 B Fs{, *Ztt PB Y$R srr$rst{ b$y WV7qiVW sti B * qbtk p$zts PB Y$R Y j}pzj {B88 tr\rz R$BtR sti } 8$RR$Bt B ZR %$R sti $8} B% Y$R *V]e RBPbs ie3eiew]e7 >dh i F VNNyWp VW* ] V GyN yw7!w o?`07lzlwe`q07q7x7 q7zy rqx7/zl 07E7Fy07Lzy Ly_X Lz LEELz 0X0 LKqEX EY VyVV\=7V3\WV7V\y77! 7k8}BR$Z8 Bt Zj$I$R{$}j$ts k VtsjkR$R sti!}$8$9s$bt jj %Z GV VyVV d 7 } 8A ;TE de }} ;1dT;n VyVVTET ;(nnt]_ >1H V F!! ei gyxx0`q7x7zqx7/zyzqyzyqrx7xlwle `0? 7Ez0X _ B{ I$tR BP Y 7 {$Bt Bt _YkR${sj sti et$t $t 7{$ t{ R V8 ${st 7s$R${sj VRRB{$s$Bt de >nh vvv V i ]!WW F e *ewwy7 _ * 3iVW * 7eiV3yWy z q!i]!w VW* qi!77eq -`q07tq8q QX7/z L 07E7Fy07LzU y 4L7z/b{4-bp7 LqqyKL y078 Li0 de 3$tsj i }B y77qe]<tet(nd qy B $t ]B8}stk 7 sj GV de >;H vvv V i ]!WW F e *ewwy7 _*3iVW qi!77eq VW* z q!i]!w tqlkyqelqq7z/ WL L 07E7Fy07LzU 4L7z/b{4-bp7 LqqyKL y078 Li0 qy B $t ]B8}stk 7 sj GV dx dx 3$tsj i }B y77qe]<txt(n1 >xh G ]<ew F VNNeW *Vziy7 VW* 3 y7qiee \Lz 0? ql y07lze0_lqwl Q0 E7z7z/ LK`X00L Sq8qX 7W7y07LzX et$t $t!}$8$9s$bt 1Ew1D de }} dntdxm >EH vvv F VNNeW VW* 3 y7qiee \ LK`X0Lz 0? ql y07lze0_lqwl z_yz7z/ LQ`07870r 7zLz` z0xrx0exqx7/z ]Bt{Z t et$t $tu i R s {Y sti V}}j${s$BtR xwnd d }} 1(nT1d >H * * ]! VW* 7 F!<W C;5U y X0y07X07yq E0_LQ WL /qlkyq L 07E7Fy07Lz $t _ B{ I$tR BP Y y]v7e\wv7v Nstj k GB,RYB} Bt Zj$I$R{$}j$ts k!}$8$9s$bt W Vj -sti B% sti <ZRRs$t$ IR <s8}bt zv 7yV s {Y dntde dx }} ndxtn1 >MH e F ]ivei F e *ewwy7 Fi _ * 3iVW i NeGy7 VW* p i 7<= yw h LKqE WL E`qy07Lz WL E`q07Q7X7 q7zy r L 07E7Fy07Lz 7yV FBZ tsj BP!}$8$9s$Bt ;w;d d; }} >H x;te W V ]ie77ye C0y07X07XWL C y07yq;y0y i %$R I FBYt G$j k m 7BtR W b OB, dn >d(h F e *ewwy7 VW* z q!i]!w -yzy/7z/ y L?7Ey07Lz ELQqX7z L 07E7Fy07Lz $t _ B{ I$tR BP Y y]v7e\wv7v Nstj k GB,RYB} Bt Zj$I$R{$}j$ts k!}$8$9s$bt W Vj -sti B% sti <ZRRs$t$ IR <s8}bt zv 7yV s {Y dntde dx }} nn(tn; >ddh V V py=wqv \7 yw0e`q07q7x7 q7zy rqx7/zl 07E7Fy07Lz `X7z/ QX7/z LW? 7Ez0X 0_L r yzq X LzXX` WyELQq7z/ _Y* *$RR s$bt V* ] t i }B WB T(xT(d * }s 8 t BP V BR}s{ sti!{ st et$t $t z$ $t$s _Bjk {Yt${ ytr$z sti 7s =t$% R$k js{,raz zv d >d1h vvv z VNV VW!z * <Vy pi!77vw G<V7!W VW* N q GVq7!W P7z/QX7/z WL y _7/_TX Q 787q 0 yzx L 0 `X7z/ y QX7/z LW? 7Ez0X E0_LQLqL/r EY VyVV\=7V3\ WV7V\y77! 7k8}BR$Z8 Bt Zj$I$R{$}j$ts k VtsjkR$R sti!}$8$9s$bt jj %Z GV VyVV d 7 } 8A ;TE de }} demtdmn VyVVTET;((dT]_ d

>dnh vvv z VNV VW!z V=3VWW 7 =ipee pi!77vw i q <V3q V G<V7!W VW* N q GVq7!W ~y 7yKqTLE q?70r X LzX X` Wy QX7/z LW yz ICgx LzW7/` y07lz $t _ B{ I$tR BP Y y]v7e\wv7v Nstj k GB,RYB} Bt Zj$I$R{$}j$ts k!}$8$9s$bt W Vj -sti B% sti <ZRRs$t$ IR <s8}bt zv 7yV s {Y dntde dx }} n;mtne >d;h vvv F *=*NeO i WVi*=]]y pi!77vw i q <V3q V G<V7!W VW* N q GVq7!W ]L7Xr y LQrzyE7 X LzX yzq XELL0_ y L?7Ey07LzX 7z ICgx QX7/z xy VyVV\ =7V3\WV7V\y77! 7k8}BR$Z8 Bt Zj$I$R{$}j$ts k VtsjkR$R sti!}$8$9s$bt _sts8s ]$k 3N VyVV 1 7 } 8A T d; }} dddtdd1m VyVVT;T;nET]_ >dxh p <VpeVWW ]TV 7]<NeO e!*ywq7!z VW* V 7! Vq]< ywe ]LFFqWqLjW7qQyzyqrX7Xj70_ y 07`qy /y Q0Ln;T q`/tq`x0 LzW7/` y07lzx FZjk de VyVV _s} ET1x; >deh 7 3 yv]! enny7 z i NVi7!W VW* i z =iio U7R`7QT L qqyz0 L>0z/7zXU0_7 X0y0`XyzQ W`0` FBZ tsj BP 7}s{ { sp sti ib{, R ; * { 8A de }} dxetdxm( >dh V=3VW z VNV VW!z 7 N =ipee V V py=wqv pi!77vw G < V7!W VW* N q GVq7!W ~y 7yKqTLE q?70r X LzXX` Wyy L?7Ey07LzX WL j7z/ X0 `0` yqj7/_07z ICgx QX7/z n;y V BR}s{ 7{$ t{ R $t sti e-y$a$ i tb Wz FstZs k dxtdm de VyVVTET((M >dmh _ W!]< F VNNeW VW* 3 y7qiee glzw7/` 7z/ 0` K7z L `qx7lz XrX0EX `X7z/ LK`X0 Lz 0? ql y07lz VZZR dmt11 de $t VI%st{ R $t * R$t VZB8s$Bt * *Zs I y %$t ]V V7e _s} WB ET*eq]\*V]Td1Mx >dh vvv F VNNeW 3 y7qiee VW* * Vziy7 x_ LKqELWX7F7z LK`X0QX7/z $t VI%st{ R $t * R$t VZB8s$Bt 7s{ s8 tb ]V V7e 7 } 8A d;td d _s} WB *eq]\*v]tnmn >1(H F i!e<nei VW* V!GeW gle `0? 7Ez0X $t <stiabb, BP 7s$R${R 7 pybry sti ] i isb IR ejr %$ 7{$ t{ W b OB, de }} 1EdTn(M >1dH F F!iqe V!7VNV7 < F *=WW WVNe VW*i!z G G 3!NNeqq p e!iyewq VW* V < <V*y* -`q07q7x7 q7zy r y Ly_ 0L y LX 7> zlffq QX7/z WV7V q {Yt${sj 8B stiz8 dd(n1e WV7V Nstj k i R s {Y ] t <s8}bt zv 3 A Zs k d >11H = NV=qeW7]<NVpei < V e7]<ewv=ei VW* 3 y7qiee -`q07lki078wqrj_qqx7/zuy;5ot KyXQLz 0? ql y07lz0yx> $t VI%st{ R $t * R$t VZB8s$Bt * *Zs I 7s{ s8 tb ]V V7e 7 } 8A d;td d _s} WB *eq]\*v]tned >1nH i NeGy7 \0 `X0 /7LzW yejl >WL Eyzy/7z/y L?7Ey07LzELQqX7zz/7z 7z/L 07E7Fy07Lz EY VyVV\=7V3\WV7V\y77! 7k8}BR$Z8 Bt Zj$I$R{$}j$ts k VtsjkR$R sti!}$8$9s$bt jj %Z GV VyVV 1 7 } 8A ;TE de }} d(xntd(xx VyVVTET;d(dT]_ >1;H < V7!W i q <V3q V VW* e i F!<W7!W \zyqrx7xyzqqx7/zlwle LX70_yzzqW yex xy VyVV\WV7V\=7V3\y77! 7k8}BR$Z8 Bt Zj$I$R{$}j$ts k VtsjkR$R sti!}$8$9s$bt _sts8s ]$k 3N VyVV 1 7 } 8A T d; }} d(1ntd(;( VyVVT;T;nEnT]_ >1xH 3 y7qiee! 3 <=p<e7 VW* V iv7 x_ LE LE7X Q7X7Lz X` L 0 LKqE yzq 0_ yqy 078 q7zy L/ yee7z/ yq/l 70_E $t 7 Z{Z sj!}$8$9s$btu 7sZR sti _ B8$R _ s8s I VyVV GsRY$tBt *] dn }} 1;T1M >1EH q F yq]<enn VW* *!iiy7 4yrX7yz QX7/z yzq yzyqrx7x LW LE `0? 7Ez0XU 0jL?yE qx 7s$R${s 7$t${s 1 d1 }} nxtn >1H q F =ennei VW* G _ 7=Ne 4yX7 WqLj _y y0 7X07X LW y q7zy y LX 7> zlffq X/Ez0 V7e WB% 8A d1 _s} 1TGV\V BT1 dm

>1MH i < Oei7 VW* * ]!Wqp!eiO px LzX C` Wy -0_LQLqL/rU h LXX yzq h LQ`0 5 07E7Fy07LzJX7z/;X7/zQo? 7Ez0X FBYt G$j k m 7BtR W b OB, dx >1H i WVi*=]]y pi!77vw zvn!ivwy V *V*!We VW* i q <V3q V 5 07E7Fy07Lz E0_LQX WL zlztxell0_ L zl7xr LKi078 W`z07LzX 7z Wq`7Q QX7/z LKqEX d1y VyVV ]B8}Zs$Btsj 3jZ$I *kts8${r ]BtP t{ 7st *$ B ]V VyVV d FZt dt11 dx }} 1dT n1 >n(h y p!7y! VW* ] < V!W \zz/7z 7z/QX7/zE0_LQLqL/rj70_E`q07X0y/4yrX7yzX` L/y0X yzql 07EyqXyE q7z/ i R s {Y $t et$t $t * R$t Mw;D de }} dmt1(e >ndh F!qq! _ViV7]<yz!y= 7 Oe7yNO=iq VW* V q _VqeiV 4yrX7yzT8yq7Qy0Q LE `0 T X7E`qy07Lz X` L/y0X WL L 07E7Fy07Lz yzq QX7/z $t _ B{ I$tR BP Y y]v7e\wv7v Nstj k GB,RYB} Bt Zj$I$R{$}j$ts k!}$8$9s$bt W Vj -sti B% sti <ZRRs$t$ IR <s8}bt zv 7yV s {Y dntde dx }} nemtn1 >n1h vvv * NVW*VW VW* V q _VqeiV \ X` L/y0y Ly_ 0L 0_? 7Ez0yqL 07E7Fy07Lz LW E`q07qEz0y7 WL7qX EY VyVV\=7V3\WV7V\y77! 7k8}BR$Z8 Bt Zj$I$R{$}j$ts k VtsjkR$R sti!}$8$9s$bt jj %Z GV VyVV 1 7 } 8A ;TE de }} dn1ntdnnn VyVVTET;dnMT ]_ >nnh V!GeW 5 0_L/Lzyq y yrx WL LE `0? 7Ez0X 7z0/ y07lz yzq 87X`yq7Fy07Lz 7s$R${s 7$t${s 1 d1 }} ;nt;x1 >n;h p z i iv! pz0q8ql Ez0X7z L>0zLFFqLzW7/` y07lzx Vi7 FBZ tsj 7 } 8A ded }} d;mmtd;; >nxh F 3 i!*iyp=e F e iewv=* VW* N q GVq7!W x `X0 /7Lzy`/Ez0Qqy/ yz/7yze0_lqxwl XR`z07yq X LzXX` Wyy L?7Ey07Lz yzq L 07E7Fy07Lz $t VI%st{ R $t * R$t VZB8s$Bt * *Zs I 7s{ s8 tb ]V V7e 7 } 8A d;td d _s} WB *eq]\*v]tnn >neh i i!en p <VpeVWW ] 7<NeO p i=nne VW* * VW7 y hq`/ zlffq WqLjW7qQ yq`qy07lzxwl CCx5y q7y07lzx VyVV _s} xt1m; FZjk dx >nh F 7V] 7 7 7]<yNNei VW* G F GeN]< ;X7/zX WL LE `0? 7Ez0X q {YtB8 ${R ndwdd 3 A Zs k dms }} ;dt; >nmh vvv G F GeN]< q F yq]<enn VW* < _ GOWW ;X7/z yzq yzyqrx7x LW LE `0? 7Ez0X 7s$R${sj 7{$ t{ ;w;d dma }} ;(T;nx >nh 7V7 O-hJX t`7q z R$Bt nd 7V7 ytr$z ]s k W] dx >;(H q G 7y_7!W G]<eW F VNNeW VW* 3 y7qiee glz 0`yqQX7/zLWyWyE7qrLW LQ`0X 0_ L`/_ 0_ `X LW 0_ LK`X0 Lz 0? ql y07lz E0_LQ EY VyVV\=7V3\WV7V\y77! 7k8}BR$Z8 Bt Zj$I$R{$}j$ts k VtsjkR$R sti!}$8$9s$bt jj %Z GV VyVV 1 7 } 8A ;TE de }} dxnxtdx;x VyVVTET;dEdT]_ >;dh vvv F _e_nyw7 y _ W!]< VW* F VNNeW 5z 0_ `X LW X0y07X07X 7z QX7/z yzq 0_ 7E q7y07lzx WL Q0 E7z7X07 LE `0? 7Ez0X * R$t qy B k sti YBIBjBkT*q: 7s{ s8 tb ]V V7e 7 } 8A d;td d _s} WB *eq]\*qtnmmd >;1H F 7= VW* F e iewv=* \`0LEy07Q7WW z07y07lz7z LK`X0L 07E7Fy07Lz EY VyVV\=7V3\WV7V\ y77! 7k8}BR$Z8 Bt Zj$I$R{$}j$ts k VtsjkR$R sti!}$8$9s$bt jj %Z GV VyVV d 7 } 8A ;TE de }} 1(dT1dx VyVVTET;((xT]_ >;nh 7GeeqVW ~z0` C0y U 9^X0z0` rx yx_`00q _B}Zjs 7{$ t{!{ba de }} ;1T; >;;H G qi!77eq VW* z q!i]!w ]`E 7yqL 07E7Fy07Lz`X7z/LE `0? 7Ez0X i }B WB qit(1 * } BP ]B8}Zs$Btsj sti V}}j$ I sy 8s${R i${ =t$% R$k <BZRBt q d d

>;xh p zewqei i q <V3q V VW* F < 7qViWe7 Fi glzx0 `07Lz LW X LzX X` WyX WL QX7/z L 07E7Fy07Lz y q7y07lzx EY VyVV\=7V3\WV7V\y77! 7k8}BR$Z8 Bt Zj$I$R{$}j$ts k VtsjkR$R sti!}$8$9s$bt jj %Z GV VyVV d 7 } 8A ;TE de }} x;mtxe; VyVVTET ;(;(T]_ >;EH G F GeN]< i F =] F 7V] 7 < _ GOWW q F yq]<enn VW* *!iiy7 C z7z/, Q707z/,yzQLE `0? 7Ez0X q {YtB8 ${R n;wdd 3 A Zs k d1 }} dxt1x >;H vvv qt O= 7 VWp VW* F 7V] 7 gle `0? 7Ez0XWL R`yq70rLz0 LqKr y ye0 QX7/z FBZ tsj BP +Zsj$k q {YtBjBk 11wdD FstZs k d( }} dxt11 >;MH 7 Oe7yNO=iq VW* V q _VqeiV C` L/y0X WL z`e 7yq X7E`qy07LzX L 07E7Fy07Lz LW QQrT LEL0 _y0?_yz/ X s {Y dx }} 1ndT1x ]B8}Z YBIR $t V}}j$ I {Yst${R sti et$t $t d1dwdt;d 1(