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1 Sury Lee 4

2 ecll hve h Give ul vere SU let K 2 2 H zt t z 2 t & d h XFSC dete he he hve 4 here ± FSCZ dete Hy V tepered H dtributi r 9 t c c l tr Hilrt y t uderd prcipl vlue p/9yyldy K 3 tr Hilrt Actully t he t dd 52 2 ddp ti iprtt terl & ulr Furier ultiplier t r d ydytp D eibrhd vlue cpute thruh ple tht ee ll M tz perr eed FD ly e ztkt X eple i t Whe i eve tz t zt t ple dperr ce 2 CD Hcdt tzczttzy cpute t e H Cdt r d rhytdt eed ll d pt

3 e chrcterizti Firt 96 ur d Ludi & Hel SHNDCSZ k ud th µlh ] et d h Hel { C GSCZ P ke A r Firt he [ tuiti Firt de tice Z µ ; h ply re F i crdte eve y e S eed ly r Prjecti dee plr e FK iplie dee ^C eve A u zt Veriy Fl h Fl ee detere ll 3 ie e Hver hle \{ eelr deed z h $ l r d ll dieretible t tht y deed \{ C lldeed F tht eed FS tht derivtive cpute F try heree deree 9^ eve heree [ h hrd dee P t 5 d ut uice t reble t t ct N 2 ^ k d 5 2 tht te e FC Q p l prve de r h hve d 2 l Ludi 2 Sr c d plyil heeu tdrd 2 t cditi et rl l r Cider i eve i Fc d t rpidly decre t µ dep hr hece ply ctt

4 i 3 le l 9 Fc 4 deed 2F i h hr FC Write th prve c z l e l e F t t Z 4 t 2 Fr e M lt e cli true 2 e el / el he? uiciet e ie de el prcliej j e F l k Pe ive upti h ply hve 9 r ply de e k d hr d h Ji F FF 4 4 h r 5 c l d h < h j ; c 5 z d bhd revble c ulrity t d puctured ucti C p2 et tht h H ce d buded re buded d p derivtive Fc deed eit ] 25 d ctuu hy [itl ] hve hich 2 h upti here kµr Prt 25 k d &µrl cb 9 d d [ Cli tphkkkcld t de lek/kiet9ld retild ] [ Let ld derivtive ll ply 2 tpt 6 l vecr e ce ce 3 ttr ; ; ^ d ll it derivtive

5 here Skj F { ki heree % pplied he ply ducti Apply j kj 2 uld el l t reduce idj vlid cli < c e hl t Suppe ey[ pr de heeu perr cli 324eticYCejFtjllSkjiD3qd7hcDKt@h eplicitly pr he pplied c CCPC h { C CZ ply A e chr X r i Mrever A c h ctructed tht prve Supprt lter 49 bve l ; cpctly upprted Whe zld rc upprt dh et ± tercept Xl he de CPC uppe relie h Sh tep etr th l it rite c yu ce { le t e ± r/rlddh@t9ti9djypcddh ply c dep / z d Al 3 h Let it P he P hrd t Xl ee ill it ± G re ue Fr CFC Pick e c dee h X X it ter t X S WS qly d XFC W S dh l dep X ive hr Aue dh t l c Z S Xl ul t 9 i de y d he tht d hr d 2 & yet ply X y de

6 eed h Fr h 2 Fr Al Ltly h ht d {r h it t C GC h / he he d S every dh i HSC Suppe UCC q upti d hich hl h dep tie hve ut 9 here hlt S hl d ith t ul Xl tht h t t upti upprte ive cuter eple tie u %liy cpct d r bve d CDdi CPC li dh X reve htt S X WZA d r Let Al iplie h hld det h± re deed / jectivity S S uiquee 9 dh tht h py y et re re Xl By K it previu eed he h X here previu Flly cue dh re & heree cditi dep Z dltd previu ± 9 ± tht vhe W tie d cditi et rhl dep ctully h he SC 9 hllddyzul7z@hlc3dbyupti Fr dh AC crd plr i e Hver tie 3 d 9 7d l M WS dep hd r / t t d hl ul MCW tht Nte hi ce i li dh X 542 huld hich e dep ctrdicti cue S t he 9 t 5 X X re W che XS ul c l che ul ct rbitrrily true d rdil

7 Ar chr X SH re e u eted c Fr X r Bert due Fritz Jh X PP 2 \{ dee X ll l ltte dt tteydt tf tt z h X eteded Fr 5 X h Frlly tt X LHS dee rx etei it Mrever i Jh l l \{ p_ ketch [ By et tlr re prjecti th k jl HS d k it j X th ue re it y re ^ 97 z y tile d M re zer y h ll h 7 FC 7 dee d c de cd ly itely y Nte CZ eq lr re heeu r?ctteddtrt2i2jttdtrzqctddt t pitive hve ± Xte X tht y X t here d rjc eed et l At eed e i 27 h irt th deiti prbletic h h lce de irt eted directil iplie eir [ 4k jqe hich y it c it derivtive N rdiet trivil u t tile y Jh prllel directi perpediculr veriy 7 equti hich ht 8

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