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15 qy k $% st $tht$ tz8a BP R$tZRB$Isj 8BI RYs} R z by 4 z $R st s A$ s k o {BtRst srrz8 I B JZsj Bt sti ) ' z ) 4 z R$t w W z q w1xd qy tsz sj P JZ t{$ R z s PBZtI Ak tz8 ${sjjk RBj%$t Y str{ ti tsj JZs$Bt A jbb w W z U st z U ) ' \ U w1ed - _LqQ qy $8 I } ti t }B $Bt BP Y RBjZ$Bt x z w0d PBZtI $t ejzs$bt w1nd {st A PBZtI Ak RBj%$t s R {BtI B I B I$ts k I$& t$sj JZs$Bt Ys I R{ $A R s 8sRRTR} $ttisry}b RkR 8 E z [ x z L z x z L > z x z ) < z w1d y b$jj A srrz8 I Ys Y {B8}j }$ 9B j { ${ ZA R}BtR b$jj A IB8$ts I Ak `ZR $R h R 8BI R}BtR qy h R 8BI 8BIsj 8sRR $R E ) 8 U ( 8 U ' \ 1 wq DQq L - 1 _LqQ wq D&wq b U DQq w1md ( 7ZAR$Z$t PB Y h R 8BI RYs} sti $t s$t B% Y j ty BP Y }$ 9B j { ${ $% R E ) ' \ ^U 1 b ; R$t w 1 U W w W U L - _LqQ R$t 1 w1d qy 8BIsj Is8}$t PB Y h R 8BI $R } B}B $Btsj B Y {st$j % }B $Bt BP Y 8BIsj 8sRR qy {BtRst K $R Zt I B s b$y -} $8 tsj RZjR ^U ) K 1 b w W 1 U R$t ; w1d(d qy 8BIsj R$&t RR PB Y h R 8BI {B8 R P B8 Y I ht$$bt BP Y tsz sj P JZ t{k PB s 8 {Yst${sj RkR 8 > ) E 1 w1ddd qy Btjk PB { R Bt Y }$ 9B j { ${ ZA s IZ B Y $8}BR I %Bjs -{$s$bt 8 $R < ) 8 U ( \ o Q nd wp L b p 7 D ~ F &wf b U DQq qy 8BIsj w1d1d dx

16 7ZAR$Z$t PB Y h R 8BI RYs} sti $t s$t B% Y j ty BP Y }$ 9B j { ${ $% R < ) 8 ~ F w1dnd GY 8 $R s {BtRst I ht I sr 8 ) \ w W o Q nd wp L b p 7 D R$t U w1d;d G$Y Y 8sRR Is8}$t R$&t RR sti -{$s$bt 8R I ht I Y }$ 9B j { ${ ZA :R Ikts8${R s PZjjk I ht I qy PB{ZR {st tbb RY$P B Y Ikts8${R BP Y {st$j % A s8 1n ]st$j % s8 *kts8${r * R{ $A$t Y Ikts8${R BP Y V3 {st$j % JZ$ R R} {$sj {s {szr $ $R ss{y I B bb Ikts8${ {B8}Bt tr Y RYs, sti Y }$ 9B j { ${ ZA s js$% I$R}js{ 8 t {BB I$ts RkR 8 $R $t BIZ{ I qy I$R}js{ 8 t BP Y RYs, F X $R js$% B Y }$ 9B j { ${ ZA sti Y I$R}js{ 8 t BP Y {st$j % F $R$tZ t js$% BY A$8B }Y RYs, W j {$t Y A ti$t 8B8 t IZ B st t$sj PB { R Y JZs$Bt BP 8B$Bt BP Y {st$j % $R PBZtI Y BZY PB { Asjst{ >MH qy PBjjBb$t I $%s$bt b$jj A PB Y t sj s}}$t 8BI {sr ]Bts{ 8BI Ikts8${R s s I t s PB 8 BP s}}$t 8BI Ikts8${R ( 1 wf L F X L F D (wf L F X L F D '\ L K (0 1 F L o { (; F (0 (q ; } ) B z b K X (wf L F X L F D (0 ] &wq b UD w1dxd qy$r PB 8 BP Y }s $sj I$& t$sj JZs$Bt $R tb {BtIZ{$% B s RBjZ$Bt $t$t Y RYs, sti }$ 9B j { ${:R s{{ j s$bt sti % jb{$k 8R B Y $Y YstI R$I $% RU '\ [F LK F F Lo { (; F (q ; )>B z bk X wf LF X LF DH&wq budb'\ [F X b'\ [F bk F F X bk F F w1ded VR $t Y } %$BZR R {$Bt Y }s $sj I$& t$sj JZs$Bt $R RBj% I Ak Y 8 YBI BP R }s s$bt BP %s $saj R F wq,0d) 3 z)d zwfdx z w0d w1dd de

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22 R}BtR IZ B Y RYs, s{{ j s$bt $R PBZtI Ak I$& t$s$t ejzs$bt w1;1d R x w+ z D)b \ xf X Q n w W Q {BR +.; E F n z L * X F w1;md qy % jb{$k R}BtR IZ B Y RYs, % jb{$k $R PBZtI R$8$js jku R E w+ z D)b \ EF X Q 1 w W Q R$t +.; E F 1 z L * X F w1;d 1E *$& t$s$bt b t qs}}$t BI sti ]Bts{ BI qy Ikts8${R Rs I $t 7 {$Bt 1; s}}jk B Y V3 PZt{$Bt$t $t ABY s}}$t sti {Bts{ 8BI VR Y }$ 9B j { ${ ZA { s R s {BtRst js sj % jb{$k Y A$8B }Y RYs, % ${sjjk -{$ R Y {st$j % t s $R tsz sj P JZ t{k qy VB8${ 3B { $T { BR{B} R}BtIR B Y RZ Ps{ } Bhj Ak 8 srz $t Y $} I$R}js{ 8 t sti {sj{zjs$t Y BB 8 st RJZs $} s8}j$zi qy B A b t Y s{zsj i7 $} s8}j$zi sti Y I R$ I $} s8}j$zi $R P I B s _y* {Bt Bjj by${y $t Z t % ${sjjk s{zs R Y }$ 9B j { ${ ZA 3$Z 1T1 RYBbR s R{Y 8s${ BP Y {Bt Bj jbb} =tj$, $t s}}$t RMS Tip Amplitude Set Point K*Kd(s) Ki(s) PID Controller x' = Ax+Bu y = Cx+Du State-Space Cantilever Tip Displacement Calculate_RMS_Amplitude 3$Z 1T1U V jb{, *$s s8 BP Y V3 $t qs}}$t BI 8BI Y A$8B }Y RYs, IB R tb -{$ Y V3 {st$j % $t {Bts{ 8BI < t{ Y Btjk I$& t{ A b t s}}$t 8BI Ikts8${R sti {Bts{ 8BI Ikts8${R $R Y T 8B%sj BP Y Y$ I sti PBZ Y -{$s$bt 8R P B8 Y ` 8s $- $t ejzs$bt w1nxd qy }$ 9B j { ${ ZA { s R s {BtRst js sj % jb{$k sti Y {st$j % I 4 {$Bt R}BtIR $t } B}B $Bt B $R R$&t RR qy B A b t Y s{zsj {st$j % $} }BR$$Bt sti Y I R$ I I 4 {$Bt $R R t B s _y* {Bt Bjj by${y $t Z t s{zs R Y % ${sj 8B$Bt BP Y }$ 9B j { ${ ZA 3$Z 1Tn RYBbR s R{Y 8s${ BP V3 B} s$bt $t {Bts{ 8BI 11

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28 nnd FBYtRBtT tisjjtiba R V s ]sj{zjs$bt qy FBYtRBtT tisjjtiba R wf id ]Bts{ qy B k $R s {Bt$tZZ8 8BI j BP Y }YkR${R BP jsr${ siy R$% {Bts{R >d;h qy Y B k $t{b }B s R siy R$Bt B } B%$I st $8} B% I {sj{zjs$bt BP Y sj s s BP {Bts{ 3B s }s sabj${ sr} $k F i Y B k $% R Y sj s s BP {Bts{ B A >dnh } w W] 1bn npy \ W ) $ B z Ln$p y L E$p y B z Lwn$p y D 1 ;o wned qy I$& t{ A b t s R}Y ${sj sti s }s sabj${ sr} $k $t sj s s BP {Bts{ $R t T j$$aj >dxh Z tr <BZRBt ]s }${, sti {YsjR, ZR s t s h ji R{stt$t B}${sj 8$T { BR{B} B 8 srz P ${$Bt qy $tr Z8 t } B%$I R st si%sts B% Y V3 Ak I {BZ}j$t Y tb 8sj sti P ${$Bt PB { by$j 8s$ts$t$t tstb8 j ty R{sj R sti st sr} $k Bt }jsts RZ Ps{ B8 k qy k }B st -{ jj t s 8 t A b t -} $T 8 tsj P ${$Bt 8 srz 8 tr sti s F i AsR I BbI ttqsab P ${$Bt {sj{zjs$bt nn1 sz$rt*zisj V s ]sj{zjs$bt qy sz$rt*zisj w*d Y B k I R{ $A R {Bts{R $t by${y siy R$Btsj sti jsr${ {Bts{ PB { R s {B8}s saj >deh V I$8 tr$btj RR }s s8 * B% tr Y str$$bt P B8 s }Z jk I k jsr${ < 9$st {Bts{ B Bt $t by${y siy R$Bt IB8$ts R $t s F i k} {Bts{ X ~ ;py 1 dbn * ) wnd o 1 FL n F i Y B k $R 8BR s}}j${saj by t *kx sti siy R$Bt IB8$ts R Y sr} $k B RZ Ps{ $t s{$bt < 9$st Y B k } B%$I R Y A R 8BI j by t *c(3d sti I k jsr${ {Bts{ $R 8BR R$t$h{st qy sz$rt*zisj Y B k } B%$I R st $t 8 I$s Y B k PB by t * z d qy 8BI j {Bt% R B < 9$st ]Bts{ qy B k sr siy R$Bt t k s}} Bs{Y R 9 B sti {Bt% R B Y F i 8BI j sr $ -{ IR Y jsr${ {Bts{ t k Nst9!:7Y s sti G jjsti s Z Ys Y * Y B k $R 8BR s}} B} $s PB st V3 b$y s RYs } $} >d1h qy sz$rt*zisj Y B k {st A RZ88s $9 I sr st &B B s{{z s jk hti Y s s BP jsr${ {Bts{ sti Y s s BP siy R$Btsj $t s{$bt 3$Z nt; RYBbR Y si$zr BP jsr${ {Bts{ y sti Y si$zr BP siy R$Btsj $t s{$btr qy bb si$${sta PBZtI 1M

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34 YB $9Btsj I$R}js{ 8 tr js$% B s{y BY > I? NsRjk Y $R s }B t$sj A b t Y sr} $k sb8 sti % k RZ Ps{ sb8 * ht$t s {BB I$ts % {B n )w?,fd Y Bsj }B t$sj $R Y t $% t Ak ~ x ) 3 7 L 3 7 ~?7 wmn b n 7 MDL d 1 >?w? b? D 1 L 3 7 d 1 >I? >w? 7Ld b? 7Ld,( D b w? 7 b? 7,( DH 1 L 3 7 d 1 >?w? 7 b? 7,( D 1 L B z F d 1 > FwF 7 b F 7,( D 1 wndd qy $t s{$bt }B t$sj A b t Y sr} $k sti $ti$%$izsj sb8 $R I R{ $A I Ak s N tts ITFBt R _B t$sj b$y 6)(M; z sti F L )1xE #V d B z s{{bztr PB Y - tsjjk s}}j$ I tb 8sj PB { y $R sjrb $% t Ak B z ) 3 7 } (~F7 (F ] ) 3 7 > F wf 7 b F 7,( D wn1(d G$Y Y }B t$sj PZt{$Bt I R{ $A I sab% Y JZs$Bt BP 8B$Bt BP Y {st$j % $} $t Y - I$ {$Bt A {B8 R >1dH E[? L 3 7 (~?7 (? L B z (F (? L > w? b? D ) ( wn1dd qy ZjIZ8 sti ]$ s{$ 8BI j YB BZYjk $t{b }B s R 8stk BP Y } $t t t $ R y I $% R Y js sj RZ Ps{ PB { P B8 st - tr$% R BP t k RZ88s$BtR qy$r RZjR $t s 8sY 8s${sj I R{ $}$Bt Ys {s}z R Y JZsj$s$% tsz BP tstbr{sj RZ Ps{ $t T s{$btr y I R{ $A R Y R${,TRj$} A Ys%$B RB8 $8 R BAR % I $t {Bts{ 8BI R{stR y sjrb } I${R s PB { Ys $R s $8 R b s j RR sti si$sas${ qy 8BI j I R{ $A R I$RR$}s$Bt sr st t k strp P B8 Y sr} $k sb8 B Y %$A s$btsj t k BP Y RZ Ps{ sb8r qy %$A s$bt BP sb8r $R Y JZ$%sj t BP Y s t k Ys {st tb A {B% I nx1 pksjbtqyb8sr BI j pksjb sti qyb8sr } B}BR I s R$8}j bb I$8 tr$btsj RZ Ps{ $t s{$bt 8BI j PB Y VB8${ 3B { ${ BR{B} y R$jj ZR R st t k }B t$sj B I 8$t Y RZ Ps{ PB { AZ $ IB R tb s{{bzt PB Y & {R BP Y $ti$%$izsj sb8r BP Y RZ Ps{ ytr si $ d yt 7 {$Bt n; Y N tts ITFBt R }B t$sj bsr I R{ $A I sr Y % ${sj I$Rst{ sbsk P B8 s }jsts RZ Ps{ BP sb8r y sjrb JZsjjk I R{ $A R Y }B t$sj $t s si$sj I$ {$Bt sbsk P B8 Bt B 8stk sb8r n;

35 RZ88s $9 R Y RsbTBBY A Ys%$B b$y s {B8A$ts$Bt BP R$tZRB$IR Ys s{ sr 3BZ $ R $ R 8R qy RZ Ps{ B sr} $k }B t$sj $t Y js sj I$ {$BtR $R $% t sr >11HU w W w W] w W w W 1$ 1$ 1$ 1$ ~?r ) y d }{BR? L{BR r L y 1 {BR? {BR r q q q q wn11d VR $t Y } %$BZR 8BI j Y YB $9Btsj RZ Ps{ PB { $R $% t Ak Y I$ {$Btsj I $%s$% b$y R} { B Y R{stt$t I$ {$Bt nb?r ) b (~?r (?? b (~?r (r r wn1nd {szr Y$R Y R$R $t% R$s R RZ Ps{ PB { R $t `ZR Bt I$ {$Bt Y RZ Ps{ sr} $k }B t$sj $R IZ{ I PB s Bt I$8 tr$btsj R{stU 7$8$js jk Y st t$sj PB { A {B8 R s }Z R$tZRB$IU w W 1$ ~? ) y n {BR? L y ; wn1;d q w W B? ) B É 1$ R$t? q wn1xd qy $} Rs8}j $t s{$bt sjbt IB R tb I R{ $A Y YB $9Btsj 8B$Bt BP Y V3 {st$j % yr Ikts8${ RsA$j$k I } tir Bt Y Bsj t k BP Y RkR 8 by${y $t Z t I } tir Bt Y I PB 8s$Bt BP Y {st$j % yp Y {BB I$ts % {B R s {Yst I B $t{jzi `ZR YB $9Btsj I$ {$Bt n )w?,r D Y t ~ x ) ~?r L d 1 wn b n D wn b n D wn1ed qy Ikts8${R RsA$j$k {BtI$$BtR s Y t I ht I sr Y PBjjBb$tU (~ x (?? L (~ x (r r ) ( wn1d d,1 w ( wn1md d,1 s Y $ t%sjz R BP Y < RR$st ( 1 ~ x b(? (r >1dH!% Y {BZ R BP s k}${sj V3 {Bts{ 8BI R{st Y RsA$j$k {BtI$$BtR s tb sjbskr 8 VR s RZj Y V3 RYBbR s Zjs RsbTBBY }s t BP ZtRsAj $ % R$Aj nx

36 `Z8}R qy 8BI j sjrb I R{ $A R Y si$sas${ tsz BP st t$sj RZ Ps{ PB { R pksjb sti qyb8sr } R t %$I t{ $t by${y Y $ 8BI j s R b$y -} $8 tsj V3 R{stR qy 8BI j sjrb s R b$y Y ZjIZ8 sti ]$ s{$ 8BI j AZ I R{ $A R Y }Y tb8 ts 8B RZ{{$t{jk nxn FBYtRBt sti GBBIYBZR BI j FBYtRBt sti GBBIYBZR } B}BR I s Bt I$8 tr$btsj 8BI j % k R$8$js B Ys BP pksjb sti qyb8sr V }B t$sj PZt{$Bt $R R$jj ZR I B I 8$t Y RZ Ps{ PB { s B8 ${ {BtR s$t $R sii I B } I${ Y B{{Z t{ BP Y ZtRsAj Rj$}R BP Y {st$j % sti Y js sj Ikts8${R BP Y V3 s $t{jzi I sr b jj qy 8BI j $R AZ$j Z}Bt s %s $ k BP RBZ { R {Bth 8$t Y R$tZRB$Isj tsz BP Y js sj }B t$sj PZt{$Bt YBt sti qb8st, $% Y $t s{$bt }B t$sj AsR I Z}Bt h R } $t{$}j R {sj{zjs$btr >1nH stby s ${j Y k b$y qyb8sr Rs Ys PB s $% t tb 8sj PB { Y $t s{$bt }B t$sj $R >1;H w W ~? ) ~ É 1$ {BR X q yt wn1d qy st t$sj RZ Ps{ PB { $R Y t PBZtI B s b$y Y Bt I$8 tr$btsj pksjb sti qyb8sr RZj PBZtI $t ejzs$bt wn1xd V ht I$R$t{$Bt $R 8sI YBb % FBYtRBt sti GBBIYBZR Rs Y st t$sj PB { I } tir Bt Y Rj$} I$Rst{ X sti tb Y {st$j % }BR$$Bt? qy I$& t{ A b t Y bb I$R}js{ 8 tr $R {szr I Ak Y js sj {Bts{ R$&t RR BP Y RZ Ps{ qy -} $8 tsj RZjR YBb % IB tb RYBb s js sj R$tZRB$Isj PB { qy$r $R A {szr $ $R {BZ}j I B Y js sj 8B$Bt BP Y V3 qb {s}z Y {BZ}j$t FBYtRBt sti GBBIYBZR 8BI j Y V3 js sj Ikts8${R sr s 8sRRTR} $ttisry}b RkR 8 qy JZs$Bt BP 8B$Bt BP Y {st$j % $} $R w W E[? L K?? L >?? ) B É 1$ R$t X q wnn(d yt sii$$bt B Y Ikts8${R BP Y V3 Y {st$j % $} 8ZR PBjjBb Y B8 ${ {BtR s$t A jbb >dh X )? b? b? X wnndd ne

37 θ θ v x s x c s x =vt x c x s b cx m k s k cx λ l 3$Z ntu V3 ]st$j % $t ]Bts{ BI FBYtRBt sti GBBIYBZR $t BIZ{ s tbtti$8 tr$btsj tbs$bt C ) Xb q )? b q X )? X b q )? X b q B ) B? bb É + )? 0 wnn1d ) q >? bb É X ) q > X bb É ) K?? b1>? =R$t Y {Bt% t$bt sab% ejzs$btr wnn(d sti wnndd s b $ tu R$tw1$CD ) [ L1 L = wnnnd C ) b b wdb X D R$tw1$CD wnn;d 7$8Zjst BZRjk RBj%$t ejzs$btr wnnnd sti wnn;d $% R s Zt$JZ s{ PB Y RZ Ps{ PB { $t $8 s{ 3$Z ntm $% R s k}${sj RZj BP Y 8BI j =ti RsAj {BtI$$BtR Y PB { PBjjBbR s R$tZRB$I Bs I sabz Y B $$t VR b$y BY 8BI jr Y$R PB { $R {B8}j jk {BtR %s$% _ $BI${jk YBb % Y {st$j % A {B8 R ZtRsAj sti Rts}R P B8 s Y$Y B s jbb s P ${$Bt PB { qy R ZtRsAj Rj$}R s $ % R$Aj sti sjrb {szr Is8} I BR{$jjs$Bt BP Y {st$j % sr $ {Bt$tZ R As{, Bt $R RsAj }sy k {BZ}j$t n

38 Nondimensional Friction Force Fc Nondimensional Piezoelectric Tube Displacement Xp 3$Z ntmu yjjzr s$% e-s8}j BP FBYtRBtTGBBIYBZR BI j Y V3 Ikts8${R B Y PB { I $% I P B8 Y $t s{$bt }B t$sj Y 8BI j $R saj B {s}z Y Rsj$ t P sz R BP Y -} $8 tsj RZjR y RYBbR ABY Y si$sas${ tsz BP Y t RZ Ps{ PB { sr b jj sr Y RsbTBBY RYs} %s $s$btr ne!y VB8${ 3 ${$Bt BI jr GY$j $ $R {j s Ys Y 8BI jr AsR I Bt Y $t Ps{$sj }B t$sj {s}z 8stk BP Y P sz R BP Y -} $8 tsj RZjR $ $R tb {j s by Y RB8 BP $t Ps{$sj $t s{$btr s t j { I yt }s ${Zjs Y 8BI jr sab% t j { stk I } ti t{ Bt Y {st$j % % jb{$k ned z jb{$k * } tist BI jr qy RBZ { R BP % jb{$k I } ti t P ${$Bt Ys% A t } B}BR I qy h R P ${$Bt RBZ { $R IZ B j { B8st ${ %s $s$btr A b t Y V3 {st$j % $} sti Y RZ Ps{ qy R {BtI $R IZ B st -{Yst BP j { BtR A b t Y bb ABI$ R qy jsr $R IZ B Y -{Yst BP }YBtBtR Vjj BP Y R 8BI jr s I $% I I$ {jk P B8 h R } $t{$}j R sti k$ ji P ${$Bt %sjz R Bt Y B I BP }${BW bbtr >dmh e-} $8 tsj RZjR RYBb Y nm

39 P ${$Bt 8 srz 8 tr s Bt Y B I BP tstbw bbtr qy R % jb{$k I } tist 8BI jr Y PB I R{ $A $tr$t$h{st }s R BP Y RZ Ps{ B sr} $k $t s{$bt ne1!y BI jr qy 8BI jr sab% $% s BBI I R{ $}$Bt BP Y {Z t Rs BP Y j$ sz Bt Y js sj RZ Ps{ PB { $t Y V3U $t s{$btr PB s R$tj sr} $k Bt s }jsts RZ Ps{ qy$r YBb % $R Btjk s RZAR BP Y j$ sz Bt tstbr{sj $t s{$btr Z{Y s t$bt YsR A t $% t B hj8 I B JZsR$TI k RZ Ps{ R yt sii$$bt 8BI jr Ys% A t } B}BR I Ys $t{jzi 8Zj$}j sr} $$ R $t {Bts{ b$y s RZ Ps{ qy Rs sti s I } tist 8BI j I R{ $A R P ${$Bt PB s 8Zj$}j {Bts{ $t Ps{ >1xH *kts8${ P ${$Bt 8BI jr Ys {B% s b$i %s $ k BP j ty R{sj R Ys% sjrb A t } B}BR I >1EH y $R Ztj$, jk YBb % Ys RZ{Y 8BI jr b$jj jz{$is Y tsz BP RZ Ps{ $t s{$btr sr Y k s}}jk I$ {jk B Y V3 n

40 ]Ys} ; e-}str$bt BP FBYtRBtTGBBIYBZR BI j B qs}}$t BI ]Ys} n -}js$t I Y }YkR${sj tsz BP tb 8sj js sj RZ Ps{ sti P ${$Btsj PB { R ZR$t Y }s si$8ru {Bt$tZZ8 8 {Yst${R sb8${ }B t$sj PZt{$BtR sti h R } $t{$}j R y sjrb I R{ $A I s %s $ k BP {Bts{ 8BI js sj RZ Ps{ PB { 8BI jr!t 8BI j } B}BR I Ak FBYtRBt sti GBBIYBZR R 8 I }s ${Zjs jk } B8$R$t PB PZ Y Y B ${sj bb, qy$r {Ys} b$jj AZ$jI Z}Bt Y$R PBZtIs$Bt Ak -}sti$t Y FBYtRBtTGBBIYBZR {Bts{ 8BI j B s}}$t 8BI ;d is$btsj PB 7 j {$Bt BP FBYtRBtTGBBIYBZR ]Bts{ BI BI j!p sjj Y 8BI jr I R{ $A I $t ]Ys} n Y FBYtRBtTGBBIYBZR ]Bts{ BI BI j bsr 8BR RZ$sAj PB PZ Y stsjkr$r y YsI 8stk s s{$% P sz R 3$ R $R R$tZRB$Isj $t s{$bt }B t$sj $R s I Z}Bt Ak 8stk RBZ { R $t{jzi$t Bt R b$y h R } $t{$}j R k} I $%s$btr 7 {BtI Y 8BI j s R b$y s %sr }B $Bt BP Y -} $8 tsj RZjR y RYBbR Y R${,TRj$} tsz BP tstbr{sj RZ Ps{ PB { R sti } I${R s PB { Ys {st A {BtR %s$% NsRjk Y 8BI j {s}z R Y I } ti t{ BP Y$R PB { Bt Y V3 } B} $ R stk 8BI jr YsI Y R P sz R AZ tbt b sr b jj I % jb} I y $t{jzi I s {B8}j I R{ $}$Bt BP Y YB $9Btsj Ikts8${R BP Y V3 sti Y Bj Ys Y RZ Ps{ $t s{$btr }jsk $t $ NsRjk, k JZs$BtR sti }s s8 %sjz R b Rs I RZ{Y Ys ;(

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