SPE Abstract. Introduction

Transcription

1 SE 573 dcn Impvmn f Havy-Ol Rcvy by Usng Elcmagnc Hang.. azals ay. W. a R.. Jhns SE Unvsy f as a sn pygh 8 Scy f lm Engns hs pap as ppad f psnan a h 8 SE nnal chncal nfnc and Ehbn hld n nv lad US 4 Spmb 8. hs pap as slcd f psnan by an SE pgam cmm fllng v f nfman cnand n an absac sbmd by h ahs. nns f h pap hav n bn vd by h Scy f lm Engns and a sbjc ccn by h ahs. h maal ds n ncssaly flc any psn f h Scy f lm Engns s ffcs mmbs. Elcnc pdcn dsbn sag f any pa f hs pap h h n cnsn f h Scy f lm Engns s phbd. mssn pdc n pn s scd an absac f n m han 3 ds; llsans may n b cpd. h absac ms cnan cnspcs acnldgmn f SE cpygh. bsac Havy l s pdcd pmaly by dcng s vscsy sng ll-nn pcsss sch as sam njcn samsa and n s cmbsn. cn chn f cvy cnsss f ssvly hang h sv sng lccal ngy. Rssv hang can b paclaly bnfcal f svs n hch cnvnnal sam pans a ncnmc. Rssv hang s a spcal cas f a m gnal fm f hang basd n lcmagnc ngy E. E has h fllng advanags v sam njcn: can b sd cv mly havy hydcabn s n sscpbl ha lsss hgh a llb and s a mns a fa lss han f sam. mpad ssv hang E has hn h fman. hs f dnhl gnan lag ll spacng may b pssbl. lhgh s pnal as cgnzd n h la 7 s h a lavly f fld applcans f E hang and vn f ngnng sds. h pps f hs pap s amn h h pfmanc spns f E cmpas ssv hang. hs pap psns a mdl f sngl-phas fl calcla h mpa dsbn and h pdcvy mpvmn band hn an E hang sc an annna s placd n a ll. W cnsd bh cn-cn fl n hch h ll h h annna s als a pdc and c-cn fl h h fl s pps E ngy fl. Fl s ang plac cncnly h h addn f E ngy. Sady-sa slns f cn-cn fl shd a lav pdcvy nd I ncas f.5 -. ms cld l pdcn hn h np p as vad fm 5. pa mpvmn ccd hn h adspn cffcn as bn -3 and - m - hch ndcas ha h s an pmm adspn cffcn. Rssv hang s h spcal cas f an nfn adspn cffcn and h snc f an pmm sggss ha E hang can b m ffcv han ssv hang. F c-cn fl h mpvmn as vn ga f h sam np p. alclad ngy gans h a f pdcd njcd ngy n h 8 63 ang; sccssfl sam njcn pcsss hav gans f and. Indcn nvnnal hmal cvy pcsss sch as sam njcn sam sa and n s cmbsn njc n fld chang l pps n s ma fl as. hf h a cmplcans f gnang anspng hl avdng cssv ha lsss and dspsng h njcd fld. Elcmagnc hang E ds n a ha anspng fld hch can b paclaly bnfcal f dp svs and hn pay-zns h cnvnnal mhds a n cs-ffcv d cssv ha lss hgh h adjacn fmans hama and Jha 99. Fhm cnvnnal l fld and lccal pmn can b sd hch mas hs chn aacv h avalabl spac s lmd as ld b h cas n ffsh facls. h cmpnns f h pmn d f E hang has bn dscbd lsh Bdgs al. 985; Haagnsn 986; Sa al. and ll n b cvd n hs pap. Snc E has nsanansly fm hn hs mhd s ndpndn f h l hmal cndcvy f h l sand and s naffcd by pmably vaans hn h fman Km 987. Elccal hang applcans can b dvdd n cags basd n h fncy f h lccal cn sd by h annna: fncy cns a sd n lccal ssv hang ERH and a lss han 6 Hz s ha ssanc hang dmnas h pcss;

2 SE 573 Hgh fncy cns a sd n mcav hang W ad fncy RF hang. hs fncs may vay fm Hz Hz lvl and n hs md dlcc hang dmnas h pcss Km 987; Kma al. ; Sa al.. In hs pap E hang fs hang pdcd by h abspn f E ngy by h mlcls n h fman. W cnsd h n fncy ang f ngy. Sval ahs hav sdd h ffc f ERH n h l pdcn spns. Wanbag and cgal 988; Bayl and Wanbag 99. Hb al. 986 shd ha h s f mlpl lcds p ll as ll as h s f hznal lls as lcds cld b ffcv f hang havy-l fmans h l fncy lccal hang. Hv vy f paps hav appad f E hang. lhgh s pnal as cgnzd snc h la 97 s h a f fld applcans f E hang cmphnsv mdlng ffs. bnhy 976 dvd an pssn f h E p anan m la sdd by Fanch 99 ha alls calclang h mpa pfl f a sv ndgng E hang. In hs bnhy cpld E adspn and fld fl n a n-dmnsnal adal mdl f fl pfmanc. smplfy h ans f h mdl h nglcd ha cndcn and ha lsss adjacn fmans. dls ha accn f m physcal ffcs dvlpd la alhgh a ncasng cmply chsn al. 985; Fanch 99; cg and Vmln 996. Fld applcans f E hang a scac f hgh fncy hang. Kasvch al. 994 cndcd a pl sng a bhl ad fncy RF annna dmnsa h ably f E hang ha a cnfnd zn h hang h n sv and hby as h na llb mpa ncas l pdcn hs pap psns a mdl f sngl-phas fl calcla h mpa dsbn and h pdcvy mpvmn band hn an E hang sc an annna s placd n a ll hmal cnvcn and cndcn ncldd n h mdl. W cnsd bh cn-cn fl n hch h ll h h annna s als a pdc and ccn fl h h fl s pps E ngy fl. Fg. and Fg. sh a schmac v f h E pcss f h cass cnsdd. In all cass ndc E ngy dng fld fl. ahmacal dl h ngy balancs a dn n phass a s-calld "phn" phas ha ansp h E ngy and h cnvnnal "maal" phas h h sv and h l phas sd. h analycal an ha dscbs h hang f an l sv s basd n an ngy balanc ha alls ha ansf by cnvcn and cndcn and accns f h adad E p as a ha sc. Ha lss hgh h cnfnng lays s as y naccnd f. In ms f ha fls h ngy n h maal phas can b n n n dmnsn as d d d d h ms and n E. a h maal and E fls spcvly. h maal fl s gvn by: d d h h ms n h gh psn cnvnn fnc mpa f z and cndcn spcvly. Sbsn f h ha fl by cndcn as ll as h E fl n E. gvs In E. h vlmc fl a h al vlmc ha capacy h fld vlmc ha capacy and h hmal cndcvy a cnsans. h m s all f an abay cdna sysm as dscssd bl h s h dsanc cdna. h las m n h gh sd f E. s h gan n ha cnn bcas f h p appld hgh h "phn" phas as dscssd by Bd al.. h mahmacal pssn f hs m sls fm h sln f a sady-sa ngy balanc n h phn phas. h sady-sa sln s nn as amb's la f abspn dly sd n spcphmy 7 la sd by bnhy 9 f adal fl. I s dvd bl. h sady-sa n-dmnsnal ngy balanc f h phn phas s gvn by: d 3 d h s h css-scnal aa. E. 3 appls any cdna sysm.g. f cylndcal cdnas. E. 3 s alays a sady-sa bcas h mass f h phns s nglgbl. n mpan any n all f sls s h adspn cffcn. hs any s a sng fncn f h ans: avlngh f h E ngy h flds cnn and dny nam a f. W a as a cnsan h. Ingan f E. 3 gvs h fllng sln 4

3 SE h s h cnsan E ha fl a h nn bnday. E. 4 can b als appld any cdna sysm by sbsng h cspndn and h dffnc a any dsanc h spcv nn bnday. hn f asan fl Δ f cylndcal fl Δ and Δ f sphcal fl. Sady-Sa Slns W sd sady-sa slns as a mans f: Valdang h ansn bhav bl and Esmang h mamm pdcvy mpvmn pssbl. a Fls. On f h advanags f E hang s ha ngy can b ansmd dp n h sv. F sady-sa fl n a asan cdna sysm E. bcms d d d d s ha and h fls a cnsan. h maal ngy fl s alays pps h phn fl h h cnsan s dmnd by h na f h fl as shn n Fg. 3. If h fl s cn-cn Fg. 3 pp; f s c-cn fl Fg. 3 l. h dph f pnan s nly gvnd by ; lag vals ndcang sh pnan dsancs. F ssv hang and h pnan dsanc s z hch mans ha h ngy ms b anspd nly hgh h maal phas ha s by cndcn. h ncasd dph f pnan f ngy ansp s a pnal mpvd ffcncy ha E has cmpad ssv hang. b mpa. F asan n-dmnsnal fl slvd E. analycally f sady sa cn-cn and c-cn fl h slns f h fm: 5 f cn-cn fl and 6 f c-cn fl. vans f E. 5 and E. 6 a n ppnd. Fg. 4 shs h sady-sa mpa pfls f bh cn and c-cn fl f lna n-dmnsnal fl f dffn vals f h adspn cffcn sng h 4 Hz and 95 Hz fncs an fm Ovalls. F n-dmnsnal adal fl E. as slvd assmng sady sa f cn cn fl banng h fllng sln 7

4 4 SE 573 h s h mpa a h llb dfnd as 8 dvan f E. 7 s als n ppnd. Fg. 5 shs h sady sa slns band f n-dmnsnal adal fl f cn and c-cn fl f h sam as abv. c dcvy Impvmn. Onc h mpa dsbn alng h mdm has bn dmnd h vscsy vaan a any dsanc fm h llb can b calclad sng any avalabl mpa-vscsy clan. H sd a vscsy-mpa lanshp f h fm: F / 9 h and F a mpcal cnsans dmnd fm h vscsy masd a nn mpas. In hs pap sd a val f 4.934E -5 ma-s and F 576. K dmnd fm vscsy vals f an I cd an fm Km 987. ppnd B gvs h fmlas sd calcla h sady-sa pdcvy ncas. ansn Slns Bcas f nsv cmply ansn slns ms b an nmcally. a mpas. nsan a. Sady-sa slns m an mpan fac n hmal l cvy namly h hmal mass f h c and flds. ncld hs ms ma a ansn sln. E. as slvd sng OSO lphyscs f bh asan and cylndcal cdnas f cn and c-cn fl. hs sfa alls sln f n m paal dffnal ans Es by fn lmns. F ansn fl sls ll dpnd n h bnday cndn a h ll. F cnsan fl a h mpa ncass h m nl achs h sady-sa sln. Fg. 6 shs h mpa pfl f a havy l sv I h 8% psy 9 m hcnss and a danag ads f 5 m af 3 days f hang f dffn fl as sng a sc f 63 W f adal cn-cn fl. Inal sv mpa as 3.97K F. valda h slns band fm OSO analycal slns f lna and adal fl dvlpd f h scv cas f n cndcn sng a smla pcd as psnd n a and cmpad h slns band sng OSO nd h sam assmpn. W als valdad h slns agans h sady-sa slns gvn abv. b mpas. nsan ss a h llb. F a cnsan pss dffnc E. as slvd h h cnny an sng OSO. F sngl-phas fl ndcng acy's la h fld fl cnsvan an can b n n gnal fm as φc Inally a cnsan a f a fn m sp s assmd. hs a s cnsand by h pss dp and h mpa-dpndn vscsy. hn E. s slvd g h n mpa dsbn s h vscsy pfl s pdad. Usng h n vscsy as an np f E. h n fl a can b calclad. hs a bng hld cnsan f h n m sp alls s calcla a n mpa dsbn. hs pcd s pad nl h ds al hang m s achd. Rsls W s fm Fg. 4 and Fg. 5 ha h mpa s n adal fl s lss han f lna fl. hs sl s bcas f

5 SE dln f h E ngy a casd by h pandng css-scnal aa f adal fl. h dln ld b vn lag f sphcal fl. a gvn psn cn-cn fl alays sls n a small han ds c-cn fl f adal fl. Evdnly ha gnad n h sv s nd h ll n sch fl; h hgh h fl a h m ha s pdcd. hs ffc s vdn als n ha h ncas n c-cn fl pnas dp n h fman. h ffc f a lag E adspn s cas a lag na h gnal llb. h ffc f ncasng adspvy s dscssd fh bl. h s n all cass a ad-ff bn a lag pnan dsanc and a lag a h llb. mpas n h na llb zn as ll as h advanc f h had fn n h fman a als affcd by h pdcn a f cn-cn fl. s h amn f l pdcd ncass m f h ha gnad by E s acd fm h fman. hs dcass h mpa s n h fman and mv h ffcvnss f E hang bcas h E ngy s cnsanly hang h na llb aa nsad f ppagang h had fn n h sv. S Fg. 6 ndcn has an mpan ffc n h slns. Fg. 7 shs h ffc f cndcn n h mpa dsbn f asan cn-cn fl. F adal fl Fg. 8 shs a lag ffc hn cndcn s cnsdd ncasng h mpa nly ab 8K cmpad a 9K ncmn hn hs ffc s nglcd f h 4Hz fncy val f h adspn cffcn. cnsan a f 3 BO as assmd and h adspn cffcn f a 4 Hz fncy. m - and a 95 Hz fncy. m - sd vala h ffc f cndcn a dffn fncs. h mpa na h sc ncass ab 7K hn cndcn s nglcd b h s s nly ab 8K hn s cnsdd f lna fl f h l val f h adspn cffcn. Usng h hgh adspn cffcn val alhgh a hgh mpa na h E sc s achvd hn nglcng cndcn dclns shaply hn m fm ha hl gs fh n h sv hn h s cndcn. sh h ffc f h adspn cffcn n sady-sa slns sd a val f 4 BO f an I cd. Fg. 9 shs a I f cn-cn lna fl f ab.5 ms f a p np f W. h I ncass as h p n h sc ncass. F an np p f 5 W h I mpvmn as ab. F all h vals sd f h np p h pa n h I ccd hn h ang f -3 and - m - hch ndcas h snc f an pmm adspn cffcn. Whn h ncass bynd hs pn a cnsdabl dcn n h I ccs. lag psns ssv hang; vdnly E hang can pfm ssv hang n hs slns. F lna c-cn fl h I as vn ga f h sam vals f np p han n cn-cn fl. Fg. shs a mamm I f ab 4 ms f a p f 5 W. hs s m han h ms h val band f h cn-cn fl cas. Hv hn ncass bynd - m - pdcn dclns bac h nal pdcn a. F adal cn-cn fl h mamm I ncas as ab 4.6 ms h cld pdcn f an np p f 5 W. hs s appmaly n hd f h mpvmn band f lna fl hch shs ha h ffc f cndcn s m mpan n adal han s n lna fl dcng h s n mpa n h na llb zn and hf h I. Fg. shs h I f adal cn-cn fl f dffn vals f np p. Unl lna fl h mamm pdcn ccd hn h ang f - and m -. ansn slns f adal cn-cn fl sh h mpa ncass h adan m and h had zn nds fh n h sv appach sady-sa slns. nsnly h I ncass as m pgsss. Hv h m ach sady sa changs sgnfcanly fm n n yas dpndng n hh h ll s pdcng a a cnsan a a a cnsan pss. Whn h pss dp s fd and h a ncass pgssvly m f h ha s hdan fm h sv and a sady sa mpa as lng b achd cmpad h cnsan a cas. Fg. shs h h mpa pfl vas h m f adal cn-cn fl. h m achv sady sa s lss han a ya f a lavly small pdcn a. I as lng achv sady sa f ccn fl vn pdcng a h sam a S Fg. 3. hs s bcas h E ngy ms avl a lng dsanc cas h s n mpa ncssay mv h l na h pdcng ll h h ad f a anspng fld. Hv h I f c-cn fl s hgh han f cn-cn fl f a cnsan pss dp hn hy a cmpad a h sam m bcas n c-cn fl ms f h E ngy mans n h sv hl pdcng as ppsd cn-cn fl. scssn hs sdy psns a sngl-phas mdl calcla h mpa dsbn and h pdcvy mpvmn f havy-l cvy hn sng E hang. Rsls shd h snc f a mamm I f ha hav calld an pmm adspn cffcn hf an acca dmnan f hs paam f h sccssfl applcan f hs chn s mpan. Whn h val sd f h adspn cffcn s small by sng h ng fncy n ngh ha s gnad hn h fman. Snc fld fl s ang plac cncnly hs ha s acd fm h fman bf ass h fman mpa ngh cas a sgnfcan dcn n h l vscsy mpv l pdcn. On h h hand a vy lag adspn cffcn psns ha h E ngy s absbd alms nsanansly n h fman s h had zn ds n nd n h sv. Rssv hang s a spcal cas f E hang h l fncy s cmmnly sd. lhgh lcc cn fm l fncy ls pnas dp n h sv han hgh fncy h s n mpa f h had zn

6 6 SE 573 s n as hgh as can b hn sng hgh fncy E hang. ng ssv hang ngy s mmdaly absbd n h fman s h mpa s s small cmpad E hang. s a cnsnc s pssbl g b l pdcn as hn E hang s sd. nh mpan nsgh pvdd fm hs sdy s ha E hang f c-cn fl gvs a b pdcvy mpvmn han cn-cn fl. nclsns W dvlpd a sngl-phas mdl calcla h mpa dsbn and h pdcvy mpvmn band hn an E hang sc s placd n a ll. Rsls lad h fllng cnclsns:. Usng h sady-sa mpa dsbns calclad h mamm I mpvmn band fm E hang. na fl cn-cn slns shd an mpvmn f p hl h c-cn fl p 36 f h sam val f p sd. F adal fl h I as ab n hd f h val band f lna fl. lhgh hs sls band f h spcfc sv and l pps sd hy cnfm E hang as a pmsng chn f havy-l cvy.. h I mpvmn shd a mamm val a a fn adspn cffcn. hs fndng sggss ha E hang can b m ffcn han ssv hang. 3. Whn hmal cndcn s sgnfcan a small mpa s n h na llb zn ccs cmpad hn cndcn s nglcd. hs ffc s m mpan f adal han f lna fl. hf ha ansf by cndcn shld n b nglcd hn calclang h mpa dsbn f E hang. 4. ansn slns shd ha hn h pdcn a s fd sady sa s achvd al cmpad hn h a s alld ncas by fng h pss dp. 5. -cn fl ylds b l pdcn as han cn-cn fl. ansn slns shd ha as h had fn advancs n h fman m ngy s allcad hn h sv casng h l a ncas m apdly han f cn-cn pdcn. Hv af yas f pdcn h chang n mpa s dcd hch mnmzs h chang n h l a. cnldgmns ay W. a hlds h W.. ny ncf nnnal ha a h Unvsy f as. Nmncla ss scnal aa c al sv cmpssbly /F mpcal cnsan f vscsy clan / F mpcal cnsan f vscsy clan h hcnss J pdcvy nd 4 / pmably hmal cndcvy / 3 lngh vlmc ha capacy / pss / p np / 3 l pdcn a 3 / E ha fl / 3 E ha fl a nn bnday / 3 ads llb ads mpa m fld vlcy / G alphabs

7 SE adspn cffcn / φ psy facn fld vscsy / Sbscps c cld h had l al Rfncs bnhy E.R dcn Incas f Havy Ol by Elcmagnc Hang. J. dn.. ch 5 3: a. and a.w.. spcs Rlvans Sb Flj d Flds Baj alnamn Elcmagnéc. VS-Invp IN Bayl B.. and Wanbag R Impvd alclan f Ol dcn Rspns Elccal Rssanc Hang ERH. ap SE 48 psnd a h 85h SE nnal chncal nfnc and Ehbn N Olans sana 3-6 Spmb. Bdgs J.E Ssy G. Spnc H.. and Wanbag R Elcmagnc Smlan f Havy-Ol Wlls. ap psnd a h hd Innanal nfnc n Havy d and a Sands. ng Bach alfna. Bd R.B. Sad W.E. and ghf E.N.. ansp hnmna N Y y: Jhn Wly & Sns Inc. alla R.. 7. Elcmagnc Hang f Ol. Emgng and phal chnlgs hap. lm Engnng Handb Vl 6. hama. and Jha K.N. 99. Havy Ol Rcvy Fm hn ay Zns by Elcmagnc Hang. ap SE 487 psnd a h 87h SE nnal chncal nfnc and Ehbn Washngn 4-7 Ocb. OSO B. 7. OSO lphyscs dlng Gd Fanch J.R. 99. Fasbly f Rsv Hang by Elcmagnc Iadan. ap SE 483 psnd a h 65h SE nnal chncal nfnc and Ehbn N Olans sana 3-6 Spmb. Haagnsn Ol Wll cav ls. US an N Hb.. Vmln F.E. h F.S. and apjac.e Nmcal Smlan Rsls f h Elccal Hang f abasca Ol-Sand Fmans. SERE : Islam.R. Wadada S.S. and Bansal. 99. Enhancd Ol Rcvy f Ugn a Sands f lasa sng Elcmagnc Hang Wh Hznal Wlls. ap SE 77 psnd a h Innanal cc chnlgy nfnc nchag lasa 9-3 ay. Kasvch R.S. c S.. Fas.. and Fnan.F l sng f a Rad Fncy Hang Sysm f Enhancd Ol Rcvy Fm amacs Eah. ap SE 483 psnd a h 69h SE nnal chncal nfnc and Ehbn N Olans sana 5-8 Spmb. Km E.S Rsv Smlan f n s Elcmagnc Hang f Havy Ols. h dssan as & U. llg San as. cg B..W. and Vmln F.E Elccal Hang h Hznal Wlls h Ha ansf blm. ap SE 377 psnd a h 996 SE Innanal nfnc n Hznal Wll chnlgy algay anada 8- Nvmb. chsn R.G. h F.S. and Vmln F.E Rcvy f abasca Bmn h h Elcmagnc Fld css. J. dn.. ch 4 : Ovalls. Fnsca. aa. al.. Oppns f nhl lcc Hang n Vnzla: h as Sds Invlvng dm Havy and Ea-Havy d Ol Rsvs. ap SE 7898 psnd a h SE Innanal hmal Opans and Havy Ol Sympsm algay lba anada 4-7 Nvmb. Sahn. Kma. Knapp R.B. and vm.. Elcmagnc Hang hds f Havy Ol Rsvs. ap SE 655 psnd a h SE/G Wsn Rgnal ng ng Bach alfna 9-3 Jn. Sa R. pahy B. Bdgs J.E. and Fa l S... msng gss n Fld pplcan f Rsv Elccal Hang hds. ap SE 6979 psnd a h SE Innanal hmal Opans and Havy Ol Sympsm agaa Vnzla -4 ach. Wanbag R.. and cgal F.W Ol dcn Rspns n s Elccal Rssanc Hang. J. dn.. ch 7 6: 45-5.

8 8 SE 573 Spply nfnng ay Ovbdn Fld Fl Fld Fl h hcnss nfnng ay Undbdn E fl nnna Fg. Schmac v f E hang f cn-cn fl. Spply dc nfnng ay Ovbdn h hcnss Fld Fl E fl nnna nfnng ay Undbdn Fg. Schmac v f E hang f c-cn fl.

9 SE Engy fl W/m. E fl Ha f l sanc fm nl m.4. Ha fl Engy fl W/m E fl sanc fm nl m Fg. 3 Schmac cmpasn f ngy fls f cn-cn fl p and c-cn fl bm.

10 SE mpa K W 4 BO n-cn alpha.3m- n-cn alpha. -cn alpha.3 -cn alpha. mpa K n-cn alpha.3m- n-cn alpha. -cn alpha.3 -cn alpha. 63 W 4 BO sanc fm nl m sanc fm llb m Fg. 4 Sady-sa mpa pfl f cncn and c-cn asan fl f dffn vals f h E adspn cffcn. Fg. 5 Sady-sa mpa pfl f cncn and c-cn adal fl f dffn vals f h E adspn cffcn BO cndcn alpha.m- / cndcn alpha. cndcn alpha.3 / cndcn alpha.3 6 mpa K 36 Fg. 6 Effc f cndcn ha ansf n h sady sa mpa pfl f lna cn-cn 63 W fl f dffn vals f h adspn cffcn.3. m - 34 mpa K W 3 BO sanc fm llb m Fg. 6 Effc f h l fl a n h mpa pfl f cn-cn adal fl af 3 days sanc fm nl m Fg. 7 Effc f cndcn ha ansf n h a sady sa mpa pfl f asan cn-cn fl f dffn vals f h adspn cffcn.

11 SE cndcn alpha.3m- / cndcn alpha.3 cndcn alpha. / cndcn alpha mpa K 4 I sanc fm llb m Fg. 8 Effc f cndcn ha ansf n h adal sady sa mpa pfl f adal cncn fl f dffn vals f h adspn cffcn...e-6.e-4.e-.e.e /m Fg. 9 Rlav pdcvy nd I f asan cn-cn fl as a fncn f h adspn cffcn f dffn np p vals I I E-6.E-4.E-.E.E /m Fg. Rlav pdcvy nd I f asan ccn fl as a fncn f h adspn cffcn f dffn np p vals...e-6.e-4.e-.e.e.e4 /m Fg. Rlav pdcvy nd I f adal ccn fl as a fncn f h adspn cffcn f dffn np p vals.

12 SE days days days Sady-sa 6 55 mpa K mpa K ya ya 6 yas 9 yas Sady-sa sanc fm llb m sanc fm llb m Fg. mpa pfl vaan h m f adal cn-cn fl a a cnsan l pdcn a. Fg. 3 mpa pfl vaan h m f adal c-cn fl a a cnsan l pdcn a. ppnd dald dvan f h analycal slns f h mpa dsbn f cn and c-cn lna and adal fl s psnd. hs slns sd valda h sls band fm OSO lphyscs. a Sady-Sa mpa. na Fl nsdng sady sa SS E. f asan fl dcs : c d d d - d d d s d a vaabl chang smplfy h sln ang h n-dmnsnal ngy fl s: d - d Sbsn f E. - n E. - ylds: d d -3 d d h bnday cndns psnd by E. -4 and E. -5 dscb h assmpn f cnsan mpa a h bnday and h symmy f fl a h nn bnday -4 d d h m ha psns h E sc n E. - can b pssd n a smla fm bnhy's p anan -5

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