Coupled-Wave Theory for Biperiodic Diffraction Gratings
|
|
|
- Buddy Moore
- 5 years ago
- Views:
Transcription
1 Gatg Dato Cauato GD-Ca Cou-Wav Thoy o Bo Dato Gatg. Itouto... Pat : U R.... Notato:.... Gatg goty Et to... Pat : Thoy a Mtho ou ao o th toagt Th Maw Euato a hoogou-u outo S at S at tag O uato a o attog Th S at o a ouay ua.... Th S at o a hoogou tatu wthout ua.... Th S at o a ooat a Th S at o a o tatu Th S at o a uo tatu Chag o ŝ a to ata oazato oug Th S at o a hoogou tatu wth ua Th to a tao at... 6 A A. ou ao o th ttvty A B. Eota at outato A C. Dvato o th yty ato A D. Coutato o th th gatg R... 8 GD-Ca. vo 9/7/8
2 . Itouto GD-Ca out ato o a o gatg tutu og a oto a o-agt ota a. Pat o th out th a o ota got that a o wth GD-Ca th toagt haatt a ov a otua awo o th otwa u ta. Pat th ua agoth u th otwa o. Th gatg ato thoy vo Pat a o a gazato o th goou ou-wav RCW tho vw R.. Th ga o gatg thoy ha o ooaty wth th ou-o tho R. 4.g. th u o S-at R. a at ou atozato R. ; ut th gatg atv to a tagua ooat yt whh oy o o th gatg o vto ag to th ooat a. Pat : U R. Notato: goug ath at uto agut ut { } t ê ê ê ut a vto oto vto ata uy vto E E E E t vto H H H H agt vto o ttvty. Gatg goty gu how a o gatg tutu whh w u to utat th ty o gatg got that a o wth GD-Ca. Th a o ua-to a that a ta to o a aay o # tutu. Oy ou uh tutu a how ut th att t oay two o. Poto vto a ot wh ê ê a ê a othooa ut a vto. Th gatg tutu t a a ta o gatg tata ou y a o otat wth oua at GD-Ca. vo 9/7/8
3 < < tatu ;. L wh L th u o tata. Th w gay u a a tatu t. Th tata o ot ay t hyay tt ay wth t ata ooto. Tyay th gatg ay atto to tata o to aoat o-wa ay y taa o. Th gatg awh tw a utat u ow th gatg a a utat u.g. vauu aov th gatg. I aoa wth uato. th utat a utat a o to -t tata y < < th utat. L < < th utat. L Not that th ooat a towa th utat o th gatg a th tata a u o otto utat to to utat. It uato t o th utat. ê ê ê gu. Bo gatg tutu. Th gatg au to o oto o-agt ota a o t ota ot a uy haatz y t aa o ttvty whh a uto o. Th th atv ttvty ua to th ua o th o Statato o o-wa o hou u wth auto. Iag th u o tata ay ot ov a ay atuay ga auato auay u th u o ato o ao gaty a. Th tato o ou-wav thoy u R. St. VI.5. GD-Ca. vo 9/7/8
4 4 atv. a a aog to th au g ovto th agay at o o-gatv I.4 Th gatg haatz y two uata vto o a whh th ttvty uto taatoa yty haatt. Th vto a aa to th utat a hav th oowg ooat tato.5.6 Th vto a ay t g.7 Th ttvty vaat wth t to taatoa at y th vto o g.8.9 o a gu utat a a vw o th gu tutu howg th uata o a. u otat out o th gatg tutu wth a vau th u utat a th utat a t t o wth ah tatu. Th to ouay ooat o tatu o o th utat ot a o < <. u. u L. Th o that th gatg wa a ua to th utat wth ah tatu h th taa aoato. Ba o uato.8 a.9 at th oty oto GD-Ca. vo 9/7/8
5 5..4 ê ê ê gu. Gatg o. Eah tatu haatz y at ot two tatu- vto o a ot ay ta to a whh a aa to th utat a hav ooat tato a to uato.5 a.6. Th ut oot tatu a th o o tatu a ot a a. Th ttvty tatu vaat wth t to taatoa at y th o th vto.5.6 GD-Ca. vo 9/7/8
6 6 Th oty oto ay tog tha oto. a.4 whh ay to a tata. o a gu utat o a o tatu a a o tatu. a ou to tvy ua to a o a tata ut th goty to w a th toagt uato ay o t a a ho o that th o out ha th at o agtu.. th gatg ut y a hou ay hav a aa. Th aov to a to th ga a o a o tatu og a o gatg tutu. Th a two a a o tata that a tat ty tha th o a. t a uo tatu o a aa gatg tutu. Th ty o tatu haatz y a g o whh y ovto ho to ua to th gatg. I th a ty ua to a o t gth. So a hoogou tatu o a hoogou whh ot haatz y o. a a oth ty o t gth th a. Eah tatu ty o uo o hoogou a aoat o ay a t o th uata o a a ou tatu- hao h h h a h oog to tatu. Th hao a tg whh th tatu o a oow: o a o tatu th at o hao o-gua h h h h o tatu.7 a th tatu o a y h h h h.8 o a gu th oowg ato ho: ; o uvaty GD-Ca. vo 9/7/8
7 7.9 H th hao ot o th two tata a h h h h h h h h. o a uo tatu th hao aty th oowg oto h o h ; h a h uo tatu. a th o a oow: t out th ata uy uatt. h h a th. o a hoogou tatu th hao a a zo h h h h hoogou tatu.4 Th aov ato a otuay wh t o th gatg ata u. Th gatg ha two uata ata-uy vto a whh hav th ooat tato.5.6 a whh hav th oowg oa atoh to a GD-Ca. vo 9/7/8
8 8.7 Say ah tatu haatz y t ow ata-uy a vto a o tatu whh hav th a oa atoh to a.8.9. o a th tatu ty o uo a hoogou a tatu a u a a a oato.. hao o th gatg uata a u h h h h. By aaogy wth ytaogahy th a u t oa att vto a th hao a aaogou to M. o a o tatu a a o-zo a ay t; o a uo tatu o-zo a zo; a o a hoogou tatu a a oth zo. Th gatg tutu wth o tatu o tagua tutua o who wa a aa a ua to gu. Th tatu goty y t attog th tatu to t-gth t aa to a th attog ah t to o. o a gu utat th attog o tatu o th a o gu a. Mo oat gatg got a ao aoat a o-atto tutu. o a gu 4 utat a o tato o a ua tutu. Th g autoay ootot gag tatato ao a to o-attog o uvwa tutu uh a ua ot a ho. Iag th u o t ay ot ov auato auay u th u o ato o ao gaty a. GD-Ca. vo 9/7/8
9 9 Th t a u utay.g. t t t t. th o oog to th to. Th o wth ah t a u utay.g. o o t. wth th o o oog to th to. Eah o otay hoogou a th ttvty o o t tatu ot a o o o t tatu. Th w gay u a a t a w u a a tutua o. M t t t L o o L M tutua o gu. Statu attog goty. Th t ouay oto tatu a t o a t o aat L ; wh L th u o t o th tatu. Th vau hou aty th ato L L. GD-Ca. vo 9/7/8
10 Th ag ty t to ± y th oto L.4.g. th t-ha vau ato. t. A ay o th ooat og gu th to tt th oua o t at ot a. gu 4. Bo-atto ua tutu. Th o ouay oto t o tatu a t o a t o aat L L ; wh L th u o o o th t. Th vau hou aty th ato L L.5 Th a ag a ty t to ± y th oto L.6 L.7 GD-Ca. vo 9/7/8
11 L L L.8.g. th t-ha vau ato.5 t.th oua o o t tt th ta tw t a t at ot a. A hoogou t.g. t gu o ot u ay aat ato; t oy u a aat a a ttvty vau. A uo tatu t a a hoogou a a ag ua to t vto. A hoogou tatu o ot u ay o ato; t u oy a ttvty ato. A gatg ato ay ota u a ooat a og ata ht aat Δ a Δ whh ty taat tata atay y th at vto Δ Δ Δ.9 Th ooat a aoat wth a ata a at a atua hght th gatg. Th taatoa ht oy a to tata aov th ooat a a. Mut ooat a ay a th tota taato a to ay atua tatu th u o th Δ ht y a th ooat a ow th tatu. To ay a ata taato to ut a g tatu a ht o Δ a aty ow th tatu a a ht o Δ a aty aov th tatu. 4. Et to Th t E o a t E a t E t th utat a a tatt E th utat. Th t au to a g a wav E A π 4. wh A a otat vto a th t ata-uy vto 4. GD-Ca. vo 9/7/8
12 Th t E ot o a uoto o a-wav ou o E wth ata-uy vto whh a a y two ato o a E E E 4. A π 4.4 Th oot a ou ao a oot a two-oa ou ao. Th tatt ay ot o a-wav ou o t E wth ata-uy vto t E t E t E t 4.5 t t A π 4.6 Th at gatg-tagta ata u.. th a ê oto o a t o that o th t y tg ut o th gatg uata u t t ê 4.7 Th a wav gatg-oa ata u th t o th tagta u ê uy oto a u 4.8 u t t u t Th ua oot ah ho o that th ua oot agay at ogatv a th ua oot g uato 4.8- a ho o that th t oagat towa th gatg a th at oagat away o th GD-Ca. vo 9/7/8
13 gatg. Euato 4.7- a o th ata u a o a ato o a th gatg u. I ga th o a ag o to ut o outatoa aato oy a t u o o ta. Th ta o a y th t t whh t a whh t M M M M Th t t M a uto o. o a gu 5 utat a atua at tagta u at a ot. Th tg a t ato o a oy th a o a t to ta th th t t wou a oow M { } M { } M { } M { } M { } M { } Th t atu othogoa to E E t o t oto oto two ut vto a wh othogoa to ê a a a oth othogoa to GD-Ca. vo 9/7/8
14 4 g g g g 4.8 u / 4.9 Th t t a E E E 4. GD-Ca. vo 9/7/8 gu 5. Etoagt tagta ata u. a a vto a ay o th t a tatt o a th at atu a ot oto th a. o th t wav th oowg to ay ŝ ê ê
15 5 g g g g 4. u / 4.4 E E E 4.5 o th tatt wav th to a 4.6 t t t 4.7 t t t t t t 4.8 u / t t t 4.9 E E E t t t t t 4. t ua to uato 4.8 au a th t o th ght o uato 4 wou th a wth t. uttut o ato 4.7. Not th g ov o : Euato 4.9 a 4.9 u a u g wha uato 4.4 o ot. u to Th at a ay t o th t a th a 4. ot o o- t a tatt wav w t y to a ta t R a T o a R R R R R GD-Ca. vo 9/7/8
16 6 4. T T T T T I g th at th t a t atu a vauat at ot o th gatg to ua uato. a th tatt atu a vauat at ot o th gatg otto ua uato. L L E L E R R R R L E L E 4. L E L E T T T T E E t t 4.4 Th t ow P oagatg towa th gatg.. th wth a oa otat ê to R E E P 4.5 Say th t ow oagatg away o th gatg th to th o- t wav P ê R E E P 4.6 a th tatt ow oagatg away o th gatg th to th o- tatt wav P t ê R E E P t t t t 4.7 Th t a t atu a ty vauat at uato 4.5 a 4.6 a th tatt atu a vauat at uato 4.7. Th o- t a tatt ato a.. ato o at to t ow o ah at o a L η t η GD-Ca. vo 9/7/8
17 7 R R E E E E P P η 4.8 R R t t t t t E E E E P P η 4.9 o a vat wav a o u u agay o t ato y zo. Pat : Thoy a Mtho 5. ou ao o th toagt Th tota toagt ot o th t whh ha th o y uato 4. o E a a a o o H a th at whh u th t a tatt a w a th wth th gatg. S th gatg vaat u taato y o uato.8 t a t that a taato o th t y w hav o t o th utg at oth tha to taat t y th a ot. A taato o th t y ha th a t a utyg th y a otat ato o π E E π 5. o uato 4.. Th at a t to hav a a o th t o th utg at w ao a y th a ato. H a taato o th at y ay uvat to ayg th aov ag ato a tho th aov ato a to th tota t u at E E π 5. GD-Ca. vo 9/7/8
18 8 ê S ha o oot uato.5 th a ato uato 5. oy o th oto o aa to th gatg ua ot a 5. E E π 5.4 Th th ut oot aa. Th that th tota v y π o wth o E / π E / π 5.5 Th a ty o oto ao ho o th gatg o uata o E / π E / π 5.6 Th at o a uato 5.5 a 5.6 a th ê a uato.5.6 o th ght-ha o th uato a t a a o ou a. Dotg th o- ou ot a E th oowg E - ou ao ota E E π 5.7 wh th gatg-tagta ata u a 5.8 Th uata gatg u a a y uato.5-7 a th oty oto 5.5 a 5.6 a v ty ug uato 5.7 a.7. Th ooat tato o 5.9 ê g g g g GD-Ca. vo 9/7/8
19 9 Th agt H t y a a ou ao H H π 5. Ba o th o t oto 4. a 4. th ao 5.7 a 5. a tuat a oow E E π 5. H M M M M H π Th Maw Euato a hoogou-u outo Th Maw Euato Gaua ut o a t-o toagt a a oto o-agt u a E π H 6. H E π 6. wh th wavgth vauu a th o ttvty. A t t-aa ato o π t / au. t t a th o ght vauu. Th u g th t ato I ato.4. Cog th a wh ua to a otat wth o ag 6. uttuto o uato 5.7 a a 6. y π E E π H π H π E H GD-Ca. vo 9/7/8
20 t th vatv wth t to. Patua outo o th uato a o th o E E A π 6.6 H H A π 6.7 wh E A H A a a ut otat. Dg 6.8 wth uato 6.4 a 6.5 u to A A E H 6. A A H E 6. Th ut vto ŝ y 6. g 6.4 g g g ŝ a o a othogoa t o a vto a otg uato 6. a 6. oto th a y A H 6.5 o th a ŝ ou ut a w a ay ut vto othogoa to ê. Dto 6.4 a th ho t o th ooat a ê a ê. GD-Ca. vo 9/7/8
21 A E A E A A H H A A E A E H 6.9 A H A E 6. By uttutg uato 6.7 a 6.8 o th ght o 6. a 6.9 th oowg oto ota / 6. Th oto t th o vau o ± 6. It au h that ozo athough th tato w at ov. E A Dg th ut vto ± H a A a t a E E E A A A H H A ± A A H Th tato autoatay at uato 6.5 a 6.6 a uato 6.7 a 6.8 u to A A 6.6 H E GD-Ca. vo 9/7/8
22 A A 6.7 H E Th ± g uato 6. a 6.5 a y to oat wth th g uato 6.. Th to u th g a a otatoa ov to a th uato yt wth t to vo o th ooat. Th vo hag th g o a vto ê oto.g. hag g. uato 6.8 a outy o 6. a 6.5 ao hag g. Noay th uato vovg o out wou oy va a ghtha ooat yt wha th ooat vo a th ooat yt t-ha. Howv th uato a v y hagg th g o a o out th t-ha yt. Th ± g uato 6. a th uato va u vo a th ± g uato 6.5 ty hag th g o H A H H u vo wthout hagg A o A o that uato 6. a 6. a va. A a wav a uy y t E au t H t y uato 6.6 a 6.7. Howv a atatv aoah that w o ovt th aay to oow to y th toagt t o th E a H E H E ŝ oto A a A a t th oto A H a A t ty o uato 6.6 a 6.7. Th aoah avatagou au otuty oto tw tata a a to th uatagta oto o E a H o whh th ŝ oto a a oot. Th ua-tagta oto ao u th oto oto vto whh a a ± ± 6.8 a ua-tagta ut vto othogoa to ŝ a a ± g aga u to a th to vaat u g vo. Ug th oowg ato 6.9 o uato 6. a 6.8 th oowg o o th ua-tagta a ota o uato E E A A 6. H A ± A H 6. GD-Ca. vo 9/7/8
23 H E A A E H A A Th aov a-wav uato a ha th ott o ga outo o uato 6.4 a 6.5. wtt a ± to at ty t o th ato o a th g ho uato ± ± ± ± ± ± uato a 6.. a a ay wtt a a ŝ ± ± 6.8 g g g g 6.9 ± ± ± ± ± ±. uato a 6.8. Ga outo o uato 6.4 a 6.5 o u a ow wav whh a t y a a GD-Ca. vo 9/7/8 E E E 6.4
24 4 GD-Ca. vo 9/7/8 H H H 6.4 wh E ± a H ± hav th utoa o A E E ± ± ± π 6.44 A H H ± ± ± π uato 6.6 a 6.7. Th uto a t t o th a oto ŝ E E E ± ± ± ± 6.46 H H H ± ± ± ± ± 6.47 A wth uato 6.5 th g uato 6.47 u a a otatoa ov to v vaa o o-out atoh u g vo. Th a oto aty th oowg atoh ± ŝ E H ± ± 6.48 E H ± ± uato 6.6 a 6.7; h oy th oto. Sua otuty oto tw tata ay to th oto oto a whh a a ŝ E E E 6.5 H H H 6.5
25 5 E H H H E E uato S at Athough th a-wav uato o to 6 oy ay a hoogou go thy a oay aot to ay thoughout th gatg tutu. W a uo that a tay th hoogou ay o ttvty to th gatg tutu at ay atua v. Th ay too th to gaty at th toagt out th ay ut wth th ay th o u a ow wav a aov. Th u/ow ooto ay a to ua tay o taty wh ± zo o o to zo o o atua o to 6.5 ut th oty a avo y g to hav a otv agay at. Th toagt taoato ao a a-ou go awh tw two hoogou ay t o a S at whh t th a atoh tw th tg a tg th go. S oot attg. Th utat otuay gu 6. I th gu t a ou vto that u a o th u-wav atu E a H a a ou vto ug a o th ow-wav atu E a H. Th og o th atu a w to 9. Th S at haatz a gatg tatu th tva < < a t a a ag tw at th tatu oua. Th tg th go u th u wav tg o th otto a th ow wav tg o th to ; a th tg th go u th ow wav at th otto a th u wav at th to. Th S at o uat S S S a S a th ag tw th tg a tg S S S S 7. GD-Ca. vo 9/7/8
26 6 gatg go gu 6. U a ow wav tg a tg a gatg go. Th gatg aay t a tatu ta a tay th hoogou ay ttou ay wth th ttvty otat to 6 ot a th ttou ay. Th ut oot ttou. Saat S at a out o a tata a o th utat a utat ouay ta. A tag agoth to 8 u to o th S at to a oot S at o th t gatg tutu.. wth a L uato 7. wh a a t o ow a aov tvy a th vau th gatg oua a uato. a.. Th tag o o otto to to. Th ta vau o th S at ow th gatg.. wth gv y th oto S S S I S 7. wh a zo at a I a tty at. Th tag oato ogvy ov u though th gatg ut L. At ah tag o th tag oato oy S a S to auat au zo at.. th o t tg th gatg o th utat. Th S at outato o a vua tatu owhat y tag avatag o th oowg yty ato GD-Ca. vo 9/7/8
27 7 S S S S o a tatu 7. Th a ou o th - o th ttvty wth th tatu a th ta ttvt aov a ow th tatu. Ao th oto o th agt g ovto t y th ± uato 6.5 a Rato 7. a ov A C. Th tag oato aov a u to ty out th at out th gatg ut th th gatg ut t a ghty t aoah out A D ay u. Th S-at o S S S a S a agoa o o-agoa o o tatu ty a to 9 out how th S at auato a tutu to ta avatag o th at aty. Sto though 6 v agoth o outg S at ay o ouay ua ooat a hoogou tata uo tata a o tata. 8. S at tag Th S-at ao two aat tva a ta to t a oot S at ovg oth tva a oow. Co a S at Sa ovg th tva o to a a S at S ovg th tva o to Sa Sa S S Sa Sa S S uato 7.. W wh to ota a oot S at ovg th o tva o to S S S S 8. Euato 8. a 8. a tat uvaty a GD-Ca. vo 9/7/8
28 8 8.4 Sa Sa Sa Sa I I 8.5 S S S S I I ± a at o th uato 8.6 S S S S S Sa Sa Sa Sa Sa I I I I Nt th og a outgog atu a aat o oot o th uato S S Sa Sa S Sa S Sa S Sa S Sa I I I I 8.7 Coag th wth uato 8. th o S at 4 S Sa S Sa S S Sa S Sa S S Sa S Sa Sa S Sa S Sa Sa S S Sa Sa S Sa S Sa S Sa S Sa S S S S I I I I I I I I 8.8 GD-Ca. vo 9/7/8 4 Sghty t ut uvat o o uato 8.8 a ota y ug th tt S Sa S S Sa S I I Sa S Sa Sa S Sa I I
29 9 A ot to 7 oy S a S to auat wh th S at tag o o otto to to. Not that uato 8.8 S a S o ot o Sa o Sa. Thu Sa a Sa ot a S a S a ot auat. I S a S a u thy a ty auat ug to-to-otto tag oato au S a S o ot o S o S. 9. O uato a o attog ± I th ou vto uato 7. ota a t u ± ± o t ug a o th wav atu E a H o ± ato o a agg o to. Eah t o oo to a tt P whh u th o a a oazato P whh a ta to o E a o H. I at th o a t to a t t a y oto 4. a 4.. utho th t o tt a ot atto to a u o ut whh w t ou o uh that th tg wav atu oog to ah ut oy o tg wav atu o th a ut. I oth wo th S-at o S S S a S o ou uat.. S S S a S a o-agoa o a a o-agoa y ayg a utato to th ow a ou a ah o oo to o o th ou uat ow a ou. Th t o a tt P u th auato w ogaz t o two uato : a o uato whh a th ou o a a aay whh uat th P tt wth ah o. Th ogazato y uato u u u uto a P P u a u a P u 9. a Th u o ou o a th u o P tt a wth o. Th oot o ± oog to o ± uato a aay w at a whh a E H ± u u u ± ± u u u P P 9. GD-Ca. vo 9/7/8
30 Th ou uat S w ay a wth a ut a uato 7. w tat a S S S S 9. o ou o o o ty a a S S S S ; 9.4 I ayg th tag oato uato 8.8 to o S at Sa a S to a g at S th ou o o Sa a S a g uh a way that a o o Sa tt a o o S th th uo o th two o u a g o o S.. Th S at o a ouay ua I g th S at o a ouay ua tw two hoogou go aty ow th ua a aty aov t uato 7.; gu 7. Th ta. Th ttvty ow th ua w ot a th ttvty aov th ua w ot. ouay ua gu 7. U a ow wav og a ouay ua. GD-Ca. vo 9/7/8
31 Th E a H ua-tagta oto a otuou ao th ouay ua. Th oto a y uato o ou o. I uato 6.5 a 6.5 ua to ow th ua a aov th ua. Ao th to o uato 6.5 o o th two oog vau w at a a... I th t ott th o th aov vau ay zo. Wth th otatoa uttuto th otuty oto a. E E E E.4 H H H H H H H H.5.6 E E E E Th oto a uvaty tat a oowg E E E E.7 GD-Ca. vo 9/7/8
32 H H H H.8 Th ouay ua o ot u ay oug tw ou o o tw oazato o; thu th S-at o S S S a S a a agoa a th z o th -th ou uat ua to o a. u u Wth uato 9.4 ta th o o uato.7 u o th a P a ta th o o uato.8 o th a u P S P P u u.9 u S P S u S P S S u S P S u S P... I th oato uato.9 zo th S hou ot ou u a a a-vau a ua. a t to zo. Th oto GD-Ca. vo 9/7/8
33 . Th S at o a hoogou tatu wthout ua Th S at o a hoogou tatu ug t ouay ua t o uato 6.44 a Th uato y E H ± ± ± φ E ± ± φ H ±.. wh th ha ht φ φ π. Th tatu oua a at a gu 8. y uato 6.5. Th tatu ttvty ot a uato 6.5. hoogou tatu gu 8. U a ow wav tavg a hoogou tatu. Euato. a. a uvaty tat a oow E E φ φ E E.4 H H φ φ H H.5 GD-Ca. vo 9/7/8
34 4 Th o atv oug o oazato oug wth th tatu o a u u uato 9.4; a wth a P u o th S at -th agoa t a S S S S φ.6.7 Th tatu S at y uato.6 a.7 a o wth th tatu ouay-ua S at uato.9- va tag uato 8.8. Th utg oot S at a ota ta wh a ou o gatg-oa uy zo th tatu o th o t oug ay. Howv th o a avo y g th ay t o a S at tg th toagt tato tw two ttou ay o ttvty oug th tatu. Th S at u th oug ua. S at o o tata a ay ato to ttou oug ay a to 6 v th S at o a hoogou ay a a azato o th o a.. Th S at o a ooat a A ooat a a a taatoa ot to th ooat at a atua hght th gatg ta. Th ooat a t y a S at a uato 7. wh t th hght aty ow th a a t th hght aty aov t. Th ta. Th ou vto ± uato 7. t uatt vauat at ow th a < a at aov th a > wh th ooat a y Δ Δ. Δ a Δ a th taatoa ot. o a gu 9 otuay utat a a a to th ooat wth ot Δ. Th ot vto Δ a uato.9 Δ Δ Δ. GD-Ca. vo 9/7/8
35 Th t tato E ow th a tao to th tato E aov th a wh E E. E Δ Suttutg th ou ao 5.7. a ug th oto o uato 5.9 th oowg atoh ota E π E π Δ.4 H th ooat taato u th oowg ha ht th ou ot E E φ.5 wh φ π Δ.6 5 Δ Δ ooat a gu 9. U a ow wav wth a ooat a. GD-Ca. vo 9/7/8
36 6 A a ha ht a to th H ot uato 5. a to ± ± th E a H uto y uato Th ha-ht ato a a oow E E H H φ φ φ E E φ H H.7.8 Th ha ht o ot u ay atv oug o oazato oug o a u u uato 9.4; a wth a P u o th S at -th agoa t a S S S φ S φ.9... Th S at o a o tatu A a ou o th gatg oty oto.5 a.6 th ttvty tatu uato. a t y a ou o th o π. Th tatu a u a a y uato.8- a th oty oto.5 a.6 a v ty ug uato. a.. A A th t o o th ou ot a o th gatg goty ato out to. Th tatu a u a a a oato o th gatg uata a u a GD-Ca. vo 9/7/8
37 7. h h h h.. uato.. Th ato o o ay atua ou o th toagt ao 5.7 a 5. a t a h h h h.4 wh a a tg y oo h h a a a tg th ag h h h h h < h h h < h h h h h h Th oo uto ou towa. Th tg a w t th a a w t uo oog to o tatu. Th t o a o a oog to a atua a a a ou o. Th t o a a a atyg ato.6 a.7 w uat a ot a o th -th a a th oog o w gat a th -th ou o. I uato 5.7 a 5. th atu E a H oog to o a uo w t a oow GD-Ca. vo 9/7/8
38 8 E E h H H h h h h h h h Th oowg gatg-tagta ata u a ao uato 5.8. Wth th to aog wth to 5.8 th ao 5.7 a 5. a t a E E π. H H π. I vog th S at o tatu th ê ê ooat otato ho o that ê aa to ;.4 Th S at to t o th ê ê ooat otato au th ± ± to o E a H t uato 6.46 a 6.47 ooatt. Thu th ho o ooat otato ha o t o th S at. Th ttvty ao. th ta th o o a o-oa ou th ooat aa to th gatg t π.5 wh ah ou ot a o-oa ou th t-tav ooat GD-Ca. vo 9/7/8
39 9 π.6 a a t o wth ah t a t o oth a wth ah tutua o. Th toagt ao. a. a ay t a t o-oa ao E E π.7 H H π.8 wh E E π H H π.9. Th ou ao uato.5.7 a.8 a uttut th Maw Euato 6. a 6. whh hav th t ooat tato E E H π. π H E E. E E H π. H H E π.4 π E H H.5 GD-Ca. vo 9/7/8
40 4 π E H H.6 wh ν t th vatv wth t to ν. I ag th uttuto Laut out u o ou hou oy a wh th out ato o ot hav out otut ; othw ovg o th ou w ouo a v ua tat ay ut R.. Th E a H ua-tagta oot a otuou ao ttvty otuty ua a th gatg wa tw tutua o wth ah t a aa to ê a ê ; h th ato E a E uato.4 a.5 a otuou wth a th o o ayg Laut u th uato. Th ato a E uato.6 w gay hav out otut; howv th t H a H o th t o th uato a otuou a h o a th tagta vatv H a H o Laut u a ay a y ovg th ato to th t o th uato H H π E.7 Th oa ttvty ato uato.7 t y a ou a to uato.5 π.8 Th oot oa. Suttutg uato a.8 uato.-5 a.7 a aatg ou o th oowg uato a ota E π E H π.9 π E E H π. E E H π. H E π. π H GD-Ca. vo 9/7/8
41 4 π E π. H H H H.4 E π Nt th ou ao uato.6.9 a. a uttut aov. O aga Laut u a to th out th uato tag a to avo ayg th u to out wth out otut. Th gatg wa tw t wth ah tatu a aa to ê a ê ; h th oot E E H a H a th aoat ou ot E H a E H a ao th vatv H a a otuou wth wha t aoat wth E a H gay a ot. Thu Laut u a ay a to uato. ut uato. a.4 ut o to ov th ttvty t to th o ah uato otag th otuou uatt. Th oato atat y ag th oowg to t.5 t.6 Th t oot a Totz at a oog oa at t a t a y th oto t t t t.7.8 Th at a t o wth ah t. Wth th to uato. a.4 a tat a o that uta o aato o Laut u GD-Ca. vo 9/7/8
42 4 π H H t.9 E π H t E π.4 H Euato.6 th ou ao wth t to o th ttvty t uato.. Th ttvty t uato.9 a.4 hav a ou ao whh a v o th oty oto.5 a.6. It oow o uato. a.4 that uato.5 a.6 a uvaty tat / / /.4.4 Th ttvty ou ao.5 oow o uato.4 a a o uato.5 a.4 th ou ot aty th oowg -oty oto / π π Eao.6 oow o oto.4. /.4 Ba o uato.4 th Totz at t y uato.5 at a a oty oto t t / π π /.44 a th oa Totz at t y oto.7 ha th a oty t / π t π /.45 GD-Ca. vo 9/7/8
43 4 H t a t y a ou ao a to uato.6.46 t t π Th at t y oto.8 a ay t a.47 t t π Suttutg uato a.47 uato.9-.9 a.4 a aatg ou o th oowg uato a ota H E E.48 H E E π π.49 H E E π π.5 E H H.5 E H H t π π.5 E t H H π π.5 Two oato w a th aov uato to at th uay tata o. Th t oato tuato tt th GD-Ca. vo 9/7/8
44 44 uato to a t ag a th o oato uato tat th uato ug at otato. Th t o o a ta th ao 5.7 a 5. y th t oto M M oto 4. a 4.. Th t atto to ou o oog to th a a uato.4 a th t o uo oog to o t y oto aaogou to 4. a 4. N.54 N.55 Th uato a uato.. a.7- w tt to th ag. Ao th uato.-4 a.7-4 w t to th ag N. Not that th ay a th to o t a t ty t o uato.7 a.8. Th a t a uato.5-5 a th ao t to N. Th uato a uth y ayg th uato 9. to th uo ah o u a ay a u u a u.56 u u wh a a o uato.4 u a u u h u u h h h u aoa wth.57 Th ttvty t uato.5-5 w t y Totz at a oow tt.58 tt t.59 GD-Ca. vo 9/7/8
45 45 tt t.6 Th oowg otatoa avato w u o th at tt tt tt tt tt u tt u u u u u u u u u u u Th at o a t. Sa hotha w u o th uatt uato.48-5 E ν E ν H ν H ν ν ν u u u u E ν ν u H u u u ;.64 ;.65. to.8 a.9 a uato.57. Th tagta uy t w t a ν u u ν ; ν.66 Wth th aov uttuto uato.48-5 y to E H E.67 π π E E H.68 E π E H π.69 H H tt E.7 GD-Ca. vo 9/7/8
46 46 tt π H H E π.7 H π H tt E π.7 A a otatoa ov th uy ato th aov uato w t a agoa at ν ν ; ν.7 Lavg out th a uato.67-7 a o oaty at o E H E.74 π π E E H.75 π E π E H.76 H H tt E tt.77 π H H E H π H tt π E π Th ttvty t uato.77 a.78 a ov to th oth o ah uato wh tt H H E.8 π H H tt E π.8 tt tt tt tt.8.8 GD-Ca. vo 9/7/8
47 47 Euato.74 a.8 a u to at E a H o uato a.79 E H tt H H π.84 E H tt H H π.85 tt E E E H π.86 tt E E E H π.87 Euato w tat t o th ŝ a oto a w th aat to u a ow wav atv to a ttou hoogou u o ttvty a to 6 uato Th u/ow ± aato vov th t uato 6.5 wth whh w az o o a oow ± ± ± u u.88 ± hou hav a otv agay at to u that. Th gatgtagta ŝ vto y uato 6.8 a 6.9 ay az o o u u.89 wh g g.9 g g GD-Ca. vo 9/7/8
48 48 Th ah o th to ay o to u oazato oug o uo gatg to 5 ut th oato ha o t o th ut th to. Th gatg-tagta vto uato 6.4 t a.9 u u ± ± ± ± Th oowg agoa at otato w u o a ± ν.9 ± ±.9 ; ν ν ν Euato a aat to th a oto a ao th oog u/ow oto ŝ E E E ± H H H ± ŝ E E E E E E.94 H H H H H H.95 H H E E E E.96 E E H H H H.97 Ug to.9 a.9 th uato a tat o oaty a GD-Ca. vo 9/7/8
49 49.98 E E E E E.99 H H H H H H H E E E.. E E H H H Th aov uato a u to tat ta uato t o th a oto ŝ H E π. H tt H E π. E E tt E E tt H π.4 E E E tt E E tt H π.5 Th uato a o th o.6 H H DEH E E.7 E E DHE H H wh GD-Ca. vo 9/7/8
50 5 DEH π I I tt.8 DHE π tt tt.9 Gv ta vau o th uatt at oto th tatu th vau at ay oth oto Δ th tatu a gv y E E H H Δ E Δ EE E Δ E Δ HE E H EH H H HH H.. wh th hav th o o a ota at EE HE EH DEH Δ HH DHE. I Δ t ua to th th at o th t o uato. w t a a atoh tw th uatt at a o whh th tatu S at a t. Howv th ota at outato a o uay uta wh Δ ag R. 5 o a atatv aoah w u. Δ t ua to th tatu th a y a ow o / Δ /. wh th ag ato ot ag ow ho o that th ota at a auat ug a atoa aoato. Dta o th auato a th ho o a out A B. Th ota at th ovt to a S at tg a tatu o th Δ a tag GD-Ca. vo 9/7/8
51 5 oato a o ah o oug th th to ota th S at o a tatu o th. Th ot uato.6.7. a. ato out o th ota at o that th at a-vau o a yt o-aog tatu.. I I DEH I DHE I EE I EH I HE I HH.4 I o a a ooat taato a a a to to ov th ooat og to th yty a o that th oto ho. Euato.98- a u to tat uato. a. t o th u/ow atu E ± a H ±. Dg ± E H ± ±.5 uato. a. taat to wh Δ Δ.6 ± ± I ± I I EE I HE / / ± EH ± HH I I.7 I uato.7 th ± g u a oat a th ± g a oat. Th t guaat to o-gua ha a o-zo agay at uato.88. GD-Ca. vo 9/7/8
52 5 Euato.6 a aag a oow wth th wav tg th tatu o th ght o th uato a th tg wav o th t I Δ I Δ.8 Th uato a ov o th tg wav to t th S at wh S Δ S S S Δ.9 S S S S I I. It ot ay to out th t S at. Ba o th yty ato 7. S S S S oy S a S t. Tag avatag o th yty th oowg tag oato tvy ou Δ S S I S S S S S S I S S Δ Δ. o uato 7. a 8.8 wth Sa S S. Th oato at t to u u th u S at o a tatu o th Δ. uato.. 4. Th S at o a uo tatu A uo tatu a tat a a a a o a o tatu ug ut a w azato o oato o th uato to. I uato. th ag o t to { } π 4. Euato.4 u to GD-Ca. vo 9/7/8
53 5 h h 4. a uato.5 a wth th oowg to o I I h h < h h : : oo / h oo / h 4. h a h aot oth zo; oto.. Rato.6 a.7 a a y a g ato otag ut o o th a o I I h h < h h : : / h / h < < 4.4 S th oth a uota th a t u o a a a aoat ou o. But at th o tuato oto 4. a 4. w at a ut a t u o o. A ag uato otag a o aog to th tto. I atua uato.5 a.8 u to th ooat otato y uato.4 a th tatu ttvty t o. Th oty oto.4 a.4 a a wth a g oto / Suttutg uato.4 a uato. y H 4.9 GD-Ca. vo 9/7/8
54 54 Thu wth th ho o ooat otato y uato.4 a o th ata u ha th a ê oot. I th oot w a zo; a ayg to.66 th oowg oto ota 4. Ba o to.9 t ao oow that th w zo wth th o to o th a g a. Sto 5 a o to o that a u to avo th toa oto ug that o a wh. I o a th ta uato.6 a.7 aat to ou TE Tav Et a TM Tav Magt wh E DEH TE H TM TM E DEH H H DHE E H DHE TE E 4. TE DEH π I 4. tt TE DHE π 4. tt TM DEH π I 4.4 TE TM DHE TM tt π 4.5 I th a th at DEH a DHE uato.8 a.9 hav th oowg o DEH DEH TM DEH TE 4.6 DHE DHE TE DHE TM 4.7 GD-Ca. vo 9/7/8
55 55 Souto to uato 4. a o th o E Δ EE TE E EH TE H 4.8 H Δ HE TE E HH TE H 4.9 E Δ EE TM E EH TM H 4. H Δ HE TM E HH TM H 4. wh EE HE TE TE EH HH TE TE DHE TE DEH TE Δ 4. EE HE TM TM EH HH TM TM DHE TM DEH TM Δ 4. Δ a uato. wth th ag ato o a a tag oato a uuty a to ov th ag ato. Wth oazato oug th o oog to a a to t to two ou o oth oog to th a a a ut oog to t oazato TE o TM. Wth th aato ah o ha oazato P u uato 9. that a a ta o TE o o TM P u o TE o TM 4.4 Dto.5 o a oow o wth oazato oug ± E H ± ± o TE o TM 4.5 Th u/ow atu ± a y uato.98-. Ba o th to uato 4.8- taat to a uato havg th a o a uato.6 wh GD-Ca. vo 9/7/8
56 56 ± ± EE ± ± TE EH TE TE TE ± HE HH TM TM EE / ± EH TM TM HE / ± HH o TE o TM 4.6 Th S at th a uato.. 5. Chag o ŝ a to ata oazato oug A ot to 4 th w zo o a wth th o to o th a uato.9 a oto 4.. Howv th o ah oto uato.9 a o to avo th toa oto ug oazato oug o a ato o th -th o wh. Th o ah oto o to a othogoa to th tatu a uy vto ath tha th gatg a uy g 5. Wth th ooat otato t uato.4 th 5. zo o that zo. t uato No o th ut o to o 4 at y th aoto o to 5. u o.9; howv th S at o a tata ut o to vt to th oo to.9 o tag th to o th gatg uuatv S at. Th ŝ a to a t t oay y a S at y th ou out ow. No o tha o o th tagta u to 5.8 a zo au th gatg a u a a ay t. GD-Ca. vo 9/7/8
57 57 uato.5-7. W au that zo o atua o 5. Th ootato o th ut that th o oagato to ua to th utat. Th toagt tato o ato o w ± a o a oto u at a atua v th gatg a w a o a ± oto at v tay aov. a a to t th a hag to th awo o a S at a to 7. O o th two a vto ŝ o y th o ah oto uato 6.9 wth ; a th oth ay ut wth g uttut o a uato 5.. ± a ± a aog to uato 6.4. Th toagt utho t t o u a ow wav a ttou u o ttvty. Ba o uato wth th ŝ a hag y th oowg ato whh a avato o E H E E H H E H E H E H E E H H Th uato at otuty o th gatg-tagta oto o E a H tw a. Th t y uato 6.5 a 5. GD-Ca. vo 9/7/8
58 a th a t hav th ooat oto y uato 6.8 a 6.4. Mag th uttuto uato 5. a 5.4 a tat a / / / / / / / / H E H E H E H E 5.6 I th -th o o ato o th uato 5.6 a ovt to uato 9. wh 5.7 ± ± ± H E 5.8 S / S 5.9 / S S GD-Ca. vo 9/7/8
59 59 Th v S at taoato ha th a o a uato 5.8- ut wth a thag. Swag S a S uvat to vtg th S at taoato. I tg th gatg tag oato th S at aov ut a to ovt o th ŝ a y uato.9 to that o uato 5.; th th uo tatu S at wth TE a TM ou a; a th th v o th aov S at a to vt a to th a o uato Th S at o a hoogou tatu wth ua A hoogou tatu a a a o a o tatu whh th ag o a uato. a oth t to {}. Dotg th tatu ttvty a uato. u to 6. I th a th o atv oug tw th ou o o ah ou o aoat wth a g ou o. utho th o oazato oug o th uato to 9 a to a t to th ag {} ;.. a 6.. uato 9. a.56. Th oazato ± uato 9. a a P u a wav atu P u E H ± ± ± o TE o TM o TE o TM Th at tt tt a tt that aa uato.8 a.9 a whh a uato.6.8 a.8 y to -y- at tt / tt GD-Ca. vo 9/7/8
60 6 tt 6.7 Dta uato.6 a.7 aat to ou TE a TM E E DEH DEH TE TM H H H H DHE DHE TE TM E E TE TM 6.8 wh TE π DEH 6.9 DHE DEH TE TM π π π π TM π DHE 6. wth ± a ± ± 6. I th a th at DEH a DHE uato.8 a.9 a -y- at havg th oowg o DEH DEH TM DEH TE 6.4 DHE DHE TE DHE TM 6.5 Souto to uato 6.8 a o th o GD-Ca. vo 9/7/8
61 6 6.6 TE TE H EH E EE E Δ 6.7 TE TE H HH E HE H Δ 6.8 TM TM H EH E EE E Δ 6.9 TM TM H HH E HE H Δ wh 6. Δ TE TE TE TE TE TE DHE DEH HH HE EH EE 6. Δ TM TM TM TM TM TM DHE DEH HH HE EH EE Th ota at a vauat o o Δ Δ Δ Δ o o TE TE TE TE HH HE EH EE π π π π 6. Δ Δ Δ Δ o o TM TM TM TM HH HE EH EE π π π π 6. Euato taat to a uato havg th a o a uato.6 wh GD-Ca. vo 9/7/8
62 6 ± ± ± ± ± ± ± TM o / / TE o TM TM TM TM TE TE TE TE HH HE EH EE HH HE EH EE 6.4 Suttutg o uato 6. a 6. uato 6.4 u to th oowg Δ ± Δ ± Δ ± Δ ± ± o o TE : o π π π π 6.5 Δ ± Δ ± Δ ± Δ ± ± o o TM : o π π π π 6.6 Th S at th a uato.. Not that a zo uato 6.5 a 6.6 ut th ato u to / Δ π Δ π wh aoah zo 5. I zo th uato ota t ut th oty u y g to hav a o-zo agay at. GD-Ca. vo 9/7/8 5 o ua aato th ato hou a y / Δ π Δ π wh δ π 6 < Δ wh δ th u o.. th at vau uh that a δ a uay tguha.
63 6 7. Th to a tao at Th uato 9. oog to th t E w ot a E E ; a th oog to th t H w ay ot a H H : u u u E E E E P E E H H H H P H H u u u Tag th S at uato 9.4 to t th uuatv S at o th t gatg ta th oy o-zo t o th ght o th uato a tho oog to th t S S S S E E H H E H E E H H 7. Th a vau th uato t th ooat ow a aov th gatg tvy 7.4 L 7.5. uato. a.. Ayg uato 9. uato 7. u to th oowg two uato GD-Ca. vo 9/7/8
64 H H H S S E E E S S E E P H H E E I u u u u u 7.7 H H H S S E E E S S H H P H H E E I u u u u u Th H - atu a at to th ± H E - atu y uato 6.48 ± E u E H 7.8 u E H 7.9 u E H 7. GD-Ca. vo 9/7/8
65 65 wh a a th utat a utat ttvt uato... Th uatt th aov uato a gat a oow uato 4. a 4.4 u u 7. E E 7. E E 7. E E 7.4 E E 7.5 E E t 7.6 E E t Mag th uttuto uato 7.6 a 7.7 a oag wth uato 4. a 4.4 w ota th oowg I u u u u u u u u u u u u u u u E E R R T T H H E S S E E E S S E E P E H E H E E t 7.7 GD-Ca. vo 9/7/8
66 66 / / / I u u u u u u u u u u u u u u u u u E E R R T T H H E S S E E E S S E E P H H H H H E H E t 7.8 H th to a tao at a a oow H H S S R T E E S S R T P E H E H E E I u u u u u u u u u u u 7.9 GD-Ca. vo 9/7/8
67 67 I P T R T R u u u u u u u u u / / u u u / S S S u H H H E H E S H H E E H H 7. A A. ou ao o th ttvty Th oowg to o th ttvty tuto tatu au a ooat otato wth ê aa to uato.4. Th tatu t o a o tatu a aa to th o vto.g. gu a othogoa to uato.; o th t a aa to ê ; o A. gu utat th atoh tw th tatu o vto t a uy vto a th ooat a ê a. ê o a uo tatu aa to uato.4 y ; uo uato.; h A. I th a othogoa to th t otato; o th t a ao aa to o th uo a. ê Wth tatu th gatg ttvty t o a th a o a hoogou tatu otat; h th ttvty ha th utoa o GD-Ca. vo 9/7/8
68 68 o tatu hoogou tatu o < < L A. wh th tatu oua a at uato. a.. ; a th u o tata L tutua o ê ê gu. Statu o vto a uy vto a ooat a. A o tatu atto to t. Th ttvty wth ah t t o a th a o a uo tatu otat GD-Ca. vo 9/7/8
69 69 o o tatu uo tatu tw a A.4 wh th t oua a at. Th ouay oto ay ot th ag o ag o. Eah t o a o tatu th hoogou o atto to hoogou tutua o o tw a A.5 wh th o oua a at. uato.. Th t oua a t o th o aat whh aty ato. a.4: L L A.6 A.7 Th o oua wth ah hoogou t a t o th o aat whh aty ato.5-7: L L L L A.8 A.9 A. A o tatu o A. o uato.6 a A.; h th ttvty ha a ou ao o th o GD-Ca. vo 9/7/8
70 7 A. π wh A. /. uato.5. Euato A.4 that o th o a tw o A.4 wh A.5 π Euato A.5 uttut o th t o uato A.5 a th ou vo oua a to t th ou ot L L π π π A.6 wh th uto a 6 A.7 / o a uo tatu uato A.5 y 6 o ua aato th oowg tato o th uto ov to A.7 o to avo v ou-o o o a : < δ δ 6 6 / GD-Ca. vo 9/7/8 wh δ th u o.. th at vau uh that a δ a uay tguha.
71 7 uo A.8 Euato A.6 a at a o that t o th ooat otato y ug th oowg tty ê ê A.9 o uato A.8 A. a.. Dg γ A. uato A.6 to L γ π π A. o a uo tatu ty o t agtu a ua to o γ zo. Th oty oto.5 a to th ght o uato A. y th -oty oto.4 o A. / / π π wh A. / GD-Ca. vo 9/7/8
72 7 A.4 / gu utat th got atoh y oto.4 A. A. A. a A.4;. gu a uato.. Th ou ao.6 o ota o uato A. π A.5 Suttutg o uato A.4 th ou ot a ota L L π π π A.6 Euato A.6 a at a o that t o th ooat otato y ug th oowg tt ê ê A.7 A.8 o uato A.6.4 a.. Wth th uttuto uato A.6 to L γ π γ π A.9 GD-Ca. vo 9/7/8
73 7 Th Totz at t to.5 a t v t t to.7 hav th oowg o o uato A.4 a tw o t t A. a tw o t t A. wh t A. A. t t Th a th aov uato a t to th t aoa wth oto.54. N t a t y ou ao.46 A.4 t t π wh th ou ot a t o uato A. L L t t t π π π A.5 Wth uttuto A.7 a A.8 th to GD-Ca. vo 9/7/8
74 74 t L t π γ π γ A.6 Th oa ttvty ot a A.7 Mot o th aov uato vovg uato A ao ay wth th yo uttuto o o. uato.8 a.47. A B. Eota at outato Th ota o a at R. 6 A A/ A a out ug a a-a-ua tho B. wh th ght-ha ota vauat ug a Paé aoato a th ow vauat y uag th ota t. But a at to at uato. th a-a-ua agoth w a y a aa-ta tho whh th ota A / ovt ty to a S at whh th ta wth t t to u u a tatu u S at. Th tag oato a o uay ta tha at uag. I th ott o uato. th at A o th o A Q P B. wh P DEH Q DHE B. B.4 GD-Ca. vo 9/7/8
75 75 A ha a a o th ott o uato 4. a 4.. Th zo o uato B. a ot to ov outatoa y two way: t th ag ow o ot to a ag a t wou hav to wthout th zo o. A o th u o oato th Paé aoato a u y g oato that uty zo. I aoa wth R. 6 to th ag ow a ho o that A / < / B.5 wh ot th ty-o.. th au aout ow u A/ a A / B.6 It vt o Eato B.6 a B. that A / a P / Q / B.7 Howv a aty taoato a a to th ght-ha ota uato B. to ota Q P I I Q / P I I / B.7 o ay o-zo. Ug th o o th ota t u to hoo o that a P / Q / / < / B.8 a ho to z th t o uato B.8. Th zato oto P / Q / P B.9 Q whh u uato B.8 to P Q / < / B. Th ag ow y uato B. tyay gaty tha that y uato B.5. At t g to aty uato B. th ag ato a to A GD-Ca. vo 9/7/8
76 76 A A/ P P / Q Q / B. T h ota o A th out ug a 66 Paé aoato A 6 A 6 A B. wh th ot a! 6! B.!! 6! Th ot ua vau a } { } B { 6 Suttutg uato B. uato B. o Q P B B B B B B B B B.5 wh B I I 4 I 6 PQ PQ PQ B.6 B I Q I 4 I 6 PQ PQ P B.7 B I I 5 PQ PQ P B.8 B Q I I 5 PQ PQ B.9 Not th oo uo th aov uato. A a ou o th ooaty th oowg atoh ho B B B B B B B B B. B. o whh t oow that uato B.5 a uvaty tat GD-Ca. vo 9/7/8
77 77 Q B B P B B B B B B B B B B B B B. A o th a o o P uato. a 4. a y uato.8 a 4. a ot to otz th auato o B B B B. A C. Dvato o th yty ato 7. Th tatu yty ato 7. ay gay wh th S at haatz a gatg go that vaat u a ooat taoato that a to a to. uato 7.. Th yty a otat ty o th S at otuto ou out to a oow. Th ota at uato. at th oowg oto EE HE EH EE HH HE EH I HH I C. Th a ut o th zo o th ota agut EE EH I EE EH I HE HH I HE HH I I DEH I Δ I DHE I I DEH I Δ I DHE I DEH EE EH Δ DHE HE HH C. Euato.7 ha th o A EE A ± EH B ± B HE A ± HH B C. ± ± wh GD-Ca. vo 9/7/8
78 78 GD-Ca. vo 9/7/8 C.4 C.5 h t g oato uato C. y th oowg o / A I I B T B B A A HH HE EH EE B A B A C.6 Th atoh a vt to ota B A B A B B A A HH HE EH EE C.7 uttuto o uato C.7 C. y C.8 h t two o th o a C.9 C. h two tt y th oowg C. C. oag uato C. a C. wth uato. th yty ato 7. a S I I T I T C ota.
79 79 A D. Coutato o th th gatg Th toagt th gatg a t y ayg uato 8. a 8. wh a a th ooat at th otto a to o th gatg L ;. uato. a.. th v at whh th to t a Sa a S a th uuatv S at o th oto o th gatg ow a aov tvy. Th t ow th gatg zo o uato 8. u to Sa Sa D. I th tatt ou out a u uato D. to t th at Sa Sa. Howv th o ou uay uta o a th ow oto o th gatg oau o that Sa a a oth zo. Th uty a avo y tg o uato 8. S S D. T h t uato D. t th t a th t a t y uttutg uato D. D. I SaS Thu th ta ha th oowg o SaS D. S S D.4 wh S I SaS SaS D.5 S S S S D.6 Th outato ou y uato D.5 a D.6 oy o Sa S a S. Sa a out ty ug otto-u tag au th ta g uato 8.8 S o ot o Sa Sa o Sa ; GD-Ca. vo 9/7/8
80 8 a S a S a out ty y ug to- ow tag au uato 8.8 S a S o ot o S o S. At tg a th gatg-tagta toagt oto a t o uato I th gatg hoogou at th tota toagt a th t y ayg uato 6.48 a Th uato t th at o oto. I th gatg hoogou at th th vato t o ay. Euato whh a uvat to uato t th tagta oto; a th gatg-oa oto H a E a t y uato.74 a.8. R. Mh Nvè Evgy Poov Lght Poagato Po Ma MaD I. Nw Yo.. L. L ouato a oao o two uv at agoth o og ay ato gatg J. Ot. So. A. A L. L U o ou th aay o otuou o tutu J. Ot. So. A. A L. L Nw ouato o th ou oa tho o o ua- gatg J. Ot. So. A. A L. L Mutay oa tho o ato gatg o atay o th a ttvty J. Ot. So. A. A C. Mo a C. Va Loa Nt Duou Way to Cout th Eota o a Mat Twty-v Ya Lat SIAM Rvw Vo. 45 No GD-Ca. vo 9/7/8
CONSTRUCTION DOCUMENTS
//0 :: 0 0 OV Y T TY O YTO: TY O YTO W # : U.. O OVTO 00 WT V V, OO OTUTO OUT U 0, 0 UTO U U \\d\ayton rojects\ayton nternational irport\.00 Y ustoms acility\\rchitecture\ rocessing enovation_entral.rvt
Noise in electronic components.
No lto opot5098, JDS No lto opot Th PN juto Th ut thouh a PN juto ha fou opot t: two ffuo ut (hol fo th paa to th aa a lto th oppot to) a thal at oty ha a (hol fo th aa to th paa a lto th oppot to, laka
Nonlinear System Identification Using Takagi-Sugeno-Kang Type Interval-valued Fuzzy Systems via Stable Learning Mechanism
IANG Itatoa Joua of Cout S 8: IJCS_8 9 Noa St Idtfato Ug aag-sugo-kag Itva-vaud uzz St va Stab Lag ha Chg-Hug L ad Y-Ha L Abtat I th a w oo a tab ag ha fo ov aag-sugo-kag t tva-vaud ua fuzz t wth at fuzz
Handout 30. Optical Processes in Solids and the Dielectric Constant
Haut Otal Sl a th Dlt Ctat I th ltu yu wll la: La ut Ka-Kg lat Dlt tat l Itba a Itaba tbut t th lt tat l C 47 Sg 9 Faha Raa Cll Uty Chag Dl, Dl Mt, a lazat Dty A hag l t a gat a a t hag aat by ta: Q Q
9.6 Spherical Wave Solutions of the Scalar. Chapter 9: Radiating Systems, Multipole Fields and Radiation
Cha 9: Raag Syss, Muo Fs a Raao A Ovvw of Chas o EM Wavs :(ov hs ous sou wav quao bouay Ch. 7 o a wav sa o wo s- sas saa by h - y a Ch. 8 o oug was - Ch. 9 J, ~ ougog g wav o sb, as a aa - Ch. J, ~ ougog
Lecture 7 Diffusion. Our fluid equations that we developed before are: v t v mn t
Cla ot fo EE6318/Phy 6383 Spg 001 Th doumt fo tutoal u oly ad may ot b opd o dtbutd outd of EE6318/Phy 6383 tu 7 Dffuo Ou flud quato that w dvlopd bfo a: f ( )+ v v m + v v M m v f P+ q E+ v B 13 1 4 34
Three Phase Asymmetrical Load Flow for Four-Wire Distribution Networks
T Aytl Lo Flow o Fou-W Dtuto Ntwo M. Mo *, A. M. Dy. M. A Dtt o Eltl E, A Uvty o Toloy Hz Av., T 59, I * El: o8@yoo.o Att-- Mjoty o tuto two ul u to ul lo, yty to l two l ut. T tt o tuto yt ult y o ovt
Analytical Evaluation of Multicenter Nuclear Attraction Integrals for Slater-Type Orbitals Using Guseinov Rotation-Angular Function
I. J. Cop. Mh. S Vo. 5 o. 7 39-3 Ay Evuo of Mu u Ao Ig fo S-yp O Ug Guov Roo-Agu uo Rz Y M Ag Dp of Mh uy of uo fo g A-Khj Uvy Kgo of Su A Dp of Mh uy of S o B Auh Uvy Kgo of Su A A. Ug h Guov oo-gu fuo
GAPH YBO A P5.0 PPG GATO XXX- " A YT V ABBVATO OA PP Z ( H) AOU YBO () () () () () HT " QUPT GATO G PP BAK TAA BAK KY OT AWG TT TOP TT BOTTO TT A: /8" = '-0" A O OO PA, TO O TA TA O. A HT O. P.0 AA O AG
AH CURRITUCK RESERVE LLC
TULL K OA,.. 22 W T VTY MAP OT TO AL OTH A (20) G OTH LG FMA ZO X UV TABL FMA ZO HA X FMA ZO X AH UTUK V LL POJT: PAL B HAYWOO & YTHA J WA XMPT UB MOYOK UTUK OUTY OTH AOLA GHT--WAY-AMPU V L TABL FMA ZO
fo=^i^oj=i mlto=i `ljjrf`^qflp=i o^i=lqp YOL TO H T xx xx xx xx L UO/UL UTO, OUT T +7'-0" O 6" LOW H L, WHH LOW. UT U T TO L T. L UL TO UTO, OUT T +7'-0" O 6" LOW H L, WHH LOW. UT U T TO L T. L UO/UL UTO,
Homework 1: Solutions
Howo : Solutos No-a Fals supposto tst but passs scal tst lthouh -f th ta as slowss [S /V] vs t th appaac of laty alty th path alo whch slowss s to b tat to obta tavl ts ps o th ol paat S o V as a cosquc
A New Dynamic Random Fuzzy DEA Model to Predict Performance of Decision Making Units
Jo o Ozo I Egg 6 75-9 A w D Ro Fzz DEA Mo o P Po o Do Mg U A gho * Mgho A Azoh S Sgh A Poo D o I Egg F o Egg P--oo U Th I Poo D o I Mg Ah T U Th I A Poo D o I Egg F o Egg P--oo U Th I R Oo 4; R 3 J 5;
Control Systems. Lecture 8 Root Locus. Root Locus. Plant. Controller. Sensor
Cotol Syt ctu 8 Root ocu Clacal Cotol Pof. Eugo Schut hgh Uvty Root ocu Cotoll Plat R E C U Y - H C D So Y C C R C H Wtg th loo ga a w a ttd tackg th clod-loo ol a ga va Clacal Cotol Pof. Eugo Schut hgh
SUNWAY UNIVERSITY BUSINESS SCHOOL SAMPLE FINAL EXAMINATION FOR FIN 3024 INVESTMENT MANAGEMENT
UNWA UNIVRIT BUIN HOOL AMPL FINAL AMINATION FOR FIN 34 INVTMNT MANAGMNT TION A A ALL qto th cto. Qto tha kg facg fo a ca. Th local bak ha ag to gv hm a loa fo 9% of th cot of th ca h ll pay th t cah a
11/8/2002 CS 258 HW 2
/8/ CS 58 HW. G o a a qc of aa h < fo a I o goa o co a C cc c F ch ha F fo a I A If cc - c a co h aoa coo o ho o choo h o qc? I o g o -coa o o-coa? W ca choo h o qc o h a a h aa a. Tha f o o a h o h a:.
I N A C O M P L E X W O R L D
IS L A M I C E C O N O M I C S I N A C O M P L E X W O R L D E x p l o r a t i o n s i n A g-b eanste d S i m u l a t i o n S a m i A l-s u w a i l e m 1 4 2 9 H 2 0 0 8 I s l a m i c D e v e l o p m e
Adaptive Fuzzy-Neural Control for a class of Nonlinear Time-Delay Systems using a State Observer
o 7(6, Oct 7, PP 6-6 Aaptv Fuzzy-Nua Coto o a ca o Noa m-day Sytm ug a Stat Ov Sm FRIKHA, oham DJEE a Na DERBE Cm-a, Natoa Schoo o Eg, Uvty o Sa, ua *Copog Autho' E-ma: mha@yahoo Atact I th pap, a ov-a
GRAPHS IN SCIENCE. drawn correctly, the. other is not. Which. Best Fit Line # one is which?
5 9 Bt Ft L # 8 7 6 5 GRAPH IN CIENCE O of th thg ot oft a rto of a xrt a grah of o k. A grah a vual rrtato of ural ata ollt fro a xrt. o of th ty of grah you ll f ar bar a grah. Th o u ot oft a l grah,
Neural Networks The ADALINE
Lat Lctu Summay Intouction to ua to Bioogica uon Atificia uon McCuoch an itt LU Ronbatt cton Aan Bnaino, a@i.it.ut.t Machin Laning, 9/ ua to h ADALI M A C H I L A R I G 9 / cton Limitation cton aning u
Fredholm Type Integral Equations with Aleph-Function. and General Polynomials
Iteto Mthetc Fou Vo. 8 3 o. 989-999 HIKI Ltd.-h.co Fedho Te Iteg uto th eh-fucto d Gee Poo u J K.J. o Ittute o Mgeet tude & eech Mu Id u5@g.co Kt e K.J. o Ittute o Mgeet tude & eech Mu Id dehuh_3@hoo.co
Java Applets / Flash Java Applet vs. Flash
ava Alet / Flah ava Alet v. Flah oltal oblem wth Mooft hhl otable moe dfflt develomet ot a oblem le o exellet val develomet tool Alet / Flah ood fo tato volv omlex e t whee XTML t elemet ae ot adeqate
Wedge clamp, double-acting for dies with tapered clamping edge
Wg c, ou-ctg or th tr cg g Acto: cg o th tr cg g or cg o o r or cg o jcto oug ch A B Hr g cg rt Buhg Dg: Dou-ctg g c or cg o r or or or cg jcto oug ch. Th g c cot o hyruc oc cyr to gu houg. Th cg ot ro
Cylon BACnet Unitary Controller (CBT) Range
ATASHEET Cyo BAC y Coo (CBT) Rg Th Cyo BAC y Coo (CBT) Rg g o BTL L BAC Av Appo Coo wh p 8 op, y o oog g o p. Th v h g ow o o, po ppo o g VAV ppo. BAC MS/TP F Sppo h oowg og BAC oj: A/B/AO/BO/AV/BV, A,
An Example file... log.txt
# ' ' Start of fie & %$ " 1 - : 5? ;., B - ( * * B - ( * * F I / 0. )- +, * ( ) 8 8 7 /. 6 )- +, 5 5 3 2( 7 7 +, 6 6 9( 3 5( ) 7-0 +, => - +< ( ) )- +, 7 / +, 5 9 (. 6 )- 0 * D>. C )- +, (A :, C 0 )- +,
An Interactive Intuitionistic Fuzzy Non-Linear Fractional Programming Problem
o ou of pp gg R SSN - Voum Num pp - R uo p:wwwpuoom v uo uzz No- o ogmmg om zz m pm of Mm u of S w v o gp O : --- T pp vop w v mo fo ovg o fo pogmmg pom o uo fuzz o v mo f o m M pf g of - v m-m pom ov
THIS PAGE DECLASSIFIED IAW E
THS PAGE DECLASSFED AW E0 2958 BL K THS PAGE DECLASSFED AW E0 2958 THS PAGE DECLASSFED AW E0 2958 B L K THS PAGE DECLASSFED AW E0 2958 THS PAGE DECLASSFED AW EO 2958 THS PAGE DECLASSFED AW EO 2958 THS
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
K E L LY T H O M P S O N
K E L LY T H O M P S O N S E A O LO G Y C R E ATO R, F O U N D E R, A N D PA R T N E R K e l l y T h o m p s o n i s t h e c r e a t o r, f o u n d e r, a n d p a r t n e r o f S e a o l o g y, a n e x
H STO RY OF TH E SA NT
O RY OF E N G L R R VER ritten for the entennial of th e Foundin g of t lair oun t y on ay 8 82 Y EEL N E JEN K RP O N! R ENJ F ] jun E 3 1 92! Ph in t ed b y h e t l a i r R ep u b l i c a n O 4 1922
X-ray Diffraction from Materials
X-ay ffato fo Matal 8 Spg St Lt; Yag Mo Koo Moday ad Wdday :5~6: . X-ay ff Sattg. Thal ff Sattg d to to Vbato. Odg ad ff Sattg d to Stat plat Howo . X-ay ff Sattg ffato of x-ay: pod aay of ato Ba podty
Creative Office / R&D Space
Ga 7th A t St t S V Nss A issi St Gui Stt Doos St Noiga St Noiga St a Csa Chaz St Tava St Tava St 887 itt R Buig, CA 9400 a to Po St B i Co t Au St B Juipo Sa B sb A Siv Si A 3 i St t ssi St othhoo Wa
Neutrosophic Hyperideals of Semihyperrings
Nuooph m Vol. 06 05 Uv o Nw Mo Nuooph Hpl o mhpg D Ml Dpm o Mhm j P Moh Collg Up Hooghl-758 mljumh@gml.om A. h pp w hv ou uooph hpl o mhpg o om opo o hm o u oo pop. Kwo: C Pou Compoo l o Nuooph mhpmg.
INSTITUTIONAL DEVELOPMENT PLAN & LAWRENCE PUBLIC LIBRARY EXPANSON 707 VERMONT STREET LAWRENCE, KS SITE PLAN FOR LOCATION MAP SP-1
OTIO -1 ITITUTIO VOT & IT O UI IY XO 0 VOT TT, -2 0 VOT TT, UI IY XO O ITITUTIO VOT & IT IT TI IITIO - ITITUTIO VOT & IT O UI IY XO 0 VOT TT, V '0" + 1' '0" '0" O " I YO IT TI, 20, V 2 '0" O, I U, I OTIU
CHARACTERIZATION FROM EXPONENTIATED GAMMA DISTRIBUTION BASED ON RECORD VALUES
CHARACTERIZATION RO EPONENTIATED GAA DISTRIBUTION BASED ON RECORD VAUES A I Sh * R A Bo Gr Cog o Euo PO Bo 55 Jh 5 Su Ar Gr Cog o Euo Dr o h PO Bo 69 Jh 9 Su Ar ABSTRACT I h r u h or ror u ro o g ruo r
Chapter 2: Descriptive Statistics
Chapte : Decptve Stattc Peequte: Chapte. Revew of Uvaate Stattc The cetal teecy of a oe o le yetc tbuto of a et of teval, o hghe, cale coe, ofte uaze by the athetc ea, whch efe a We ca ue the ea to ceate
Posterior analysis of the compound truncated Weibull under different loss functions for censored data.
INRNAIONA JOURNA OF MAHMAIC AND COMUR IN IMUAION Vou 6 oso yss of h oou u Wu u ff oss fuos fo so. Khw BOUDJRDA Ass CHADI Ho FAG. As I hs h Bys yss of gh u Wu suo s os u y II so. Bys sos osog ss hv v usg
Diffraction of Elastic PP-, SV- and SH- Waves on the Arbitrary Deep-founded Cavities in the Anisotropic Rock Massif
Dffcto of Etc PP- SV- S- W o th ty D-fou Ct th otoc oc Mf Lyzzt B tyty Zhu K Mo Bt E Yy tct Th ot to ch th yc t-t ho of ttoc f wth fw ct fou fo th ufc C of oto ffcto of tc PP- SV- S-w co ytc oou tho y
Kummer Beta -Weibull Geometric Distribution. A New Generalization of Beta -Weibull Geometric Distribution
ttol Jol of Ss: Bs Al Rsh JSBAR SSN 37-453 Pt & Ol htt://gss.og/.h?joljolofbsaal ---------------------------------------------------------------------------------------------------------------------------
RAKE Receiver with Adaptive Interference Cancellers for a DS-CDMA System in Multipath Fading Channels
AKE v wh Apv f Cs fo DS-CDMA Ss Muph Fg Chs JooHu Y Su M EEE JHog M EEE Shoo of E Egg Sou o Uvs Sh-og Gw-gu Sou 5-74 Ko E-: ohu@su As hs pp pv AKE v wh vs og s popos fo DS-CDMA ss uph fg hs h popos pv
BEM with Linear Boundary Elements for Solving the Problem of the 3D Compressible Fluid Flow around Obstacles
EM wth L ou Elts o olvg th Pol o th D opssl Flu Flow ou Ostls Lut Gu o Vlsu stt hs pp psts soluto o th sgul ou tgl quto o th D opssl lu low ou ostl whh uss sopt l ou lts o Lgg tp. h sgul ou tgl quto oult
/99 $10.00 (c) 1999 IEEE
P t Hw Itt C Syt S 999 P t Hw Itt C Syt S - 999 A Nw Atv C At At Cu M Syt Y ZHANG Ittut Py P S, Uvty Tuu, I 0-87, J Att I t, w tv t t u yt x wt y tty, t wt tv w (LBSB) t. T w t t x t tty t uy ; tt, t x
NORTHLAKE APARTMENTS
PRT RW RVTO VTY P PROT RPTO TR # UR P PROPRTY.. /..T..... T. R. V..W.P.. '. OT......... R...U..O. O. O. OT. OOR. PT..T..Y...... P. V.. R... W....... V.. Q. QUP..W.. XT.....O.................. OR OT R OTO
CBSE SAMPLE PAPER SOLUTIONS CLASS-XII MATHS SET-2 CBSE , ˆj. cos. SECTION A 1. Given that a 2iˆ ˆj. We need to find
BSE SMLE ER SOLUTONS LSS-X MTHS SET- BSE SETON Gv tht d W d to fd 7 7 Hc, 7 7 7 Lt, W ow tht Thus, osd th vcto quto of th pl z - + z = - + z = Thus th ts quto of th pl s - + z = Lt d th dstc tw th pot,,
A Simple Representation of the Weighted Non-Central Chi-Square Distribution
SSN: 9-875 raoa Joura o ovav Rarch Scc grg a Tchoogy (A S 97: 7 Cr rgaao) Vo u 9 Sbr A S Rrao o h Wgh No-Cra Ch-Squar Drbuo Dr ay A hry Dr Sahar A brah Dr Ya Y Aba Proor D o Mahaca Sac u o Saca Su a Rarch
School of Aerospace Engineering Origins of Quantum Theory. Measurements of emission of light (EM radiation) from (H) atoms found discrete lines
Ogs of Quatu Thoy Masuts of sso of lght (EM adato) fo (H) atos foud dsct ls 5 4 Abl to ft to followg ss psso ν R λ c λwavlgth, νfqucy, cspd lght RRydbg Costat (~09,7677.58c - ),,, +, +,..g.,,.6, 0.6, (Lya
NORTHING 2" INS. COPPER COMM. CABLE 6" D.I. WATER LINE 52 12" D.I. WATER LINE 645, ,162, CURVE DATA US 40 ALT.
OU ' ' ' ' QUY O HO O. UY OHG G O UY O UF O GG HO M H M H O H. O...8. OM Y U -. + O. + OY K HOU O. MH + - H - ' YM F ' ' ' O HGO ' G ' 8.% H- ' U U. - M. c 8'. OY. K HOU O.... OMY & / OGOO Y 8 --> K GG
Some New Classes of Orthogonal Polynomials and Special Functions: A Symmetric Generalization of Sturm-Liouville Problems and its Consequences
o Nw Cl of Ohogol olyol l uo: A y Glzo of u-louvll ol Cou y Moh MAJED-JAMEI Uvy of Kl D of Mh Kl Gy My 6 hd h uv y ofo Wolf KOE D of Mh Uvy of Kl Kl Gy Co Oul of o 5 A y glzo of u - Louvll ol 9 Iouo 9
Control system of unmanned aerial vehicle used for endurance autonomous monitoring
WSES NSIONS o SYSES ONOL oo-o h, s Nco osttsc, h oto sst o vhc s o c tooos oto EODO - IOEL EL, D vst othc o chst o Sc c, St. Ghoh o, o., 6,Scto, chst, ONI too.ch@.o htt:wwww.-cs.o SILE NIOLE ONSNINES,
Simplified Model for Penetration Depth Analysis of Extra-Large Concrete Caissons During Construction
Joua o Cv Egg ad Scc Ju 5, Vo. 4 I., PP. 6-7 Spd Mod o Ptato Dpt Aay o Eta-Lag Coct Cao Dug Cotucto Wag Hog-Xa, Sau W. Cug Scoo o Nava Actctu ad Oca Egg ad cv gg, Saga Jao Tog Uvty, Saga 3, P.. Ca Scoo
Journal of Physics: Conference Series. Related content. Recent citations. To cite this article: A Suparmi et al 2013 J. Phys.: Conf. Ser.
Jou of Phyc: Cofc S Aot Souto Of Schog Euto o Eckt Pott Cob Wth Tgootc Poch-T No-Ct Pott Ug oovk Poyo To ct th tc: A Su t J. Phy.: Cof. S. 9 w th tc o fo ut hct. t cott - Souto of Schog uto fo Th o Hoc
THE COAST ADVERTISER
K O :5G G O V OFF»* xf Y 5 8 FOK OU O Q K F O G 0 O JY 6 959 U G G O F U OV F K G G 7 G K J J q x G J G J G V O O ; V V ; G ; ; O K G J ; ; G G V 0 " q j V V G x q 27 8:30 j ; ; G J ; : J z G Y : $20000
176 5 t h Fl oo r. 337 P o ly me r Ma te ri al s
A g la di ou s F. L. 462 E l ec tr on ic D ev el op me nt A i ng er A.W.S. 371 C. A. M. A l ex an de r 236 A d mi ni st ra ti on R. H. (M rs ) A n dr ew s P. V. 326 O p ti ca l Tr an sm is si on A p ps
Overview. Splay trees. Balanced binary search trees. Inge Li Gørtz. Self-adjusting BST (Sleator-Tarjan 1983).
Ovrvw B r rh r: R-k r -3-4 r 00 Ig L Gør Amor Dm rogrmmg Nwork fow Srg mhg Srg g Comuo gomr Irouo o NP-om Rom gorhm B r rh r -3-4 r Aow,, or 3 k r o Prf Evr h from roo o f h m gh mr h E w E R E R rgr h
CONTENTS. Hugo Reitzel, the pickles enthusiast CERTIFICATIONS JARS POUCHES & CANS SALAD DRESSING MINI-TUBES
v4. APRIL 2018. Hugo Rz, h pk hu Th of h uhd gu g ou Hugo Rz. I 1909, Ag, Sw vg, h uhd h ow op wh vo: o p up h wod of od! Ad fo ov o hudd ow, w hoo h hg b ug ou xp o o ov ou bu od o bo THE od p. W ufu
Easy Steps to build a part number... Tri-Start Series III CF P
ulti-l i Oti iul ( oto) ow to O ol os sy ts to uil t u... i-tt is 1. 2 3 4. 5. 6. oto y til iis ll tyl ll iz- st t ott y & y/ ywy ositio 50 9 0 17-08 ol ulti-l i oti otos o us wit ulti-o sil o tii o y
2 tel
Us. Timeless, sophisticated wall decor that is classic yet modern. Our style has no limitations; from traditional to contemporar y, with global design inspiration. The attention to detail and hand- craf
SYSTEMS OF NON-LINEAR EQUATIONS. Introduction Graphical Methods Close Methods Open Methods Polynomial Roots System of Multivariable Equations
SYSTEMS OF NON-LINEAR EQUATIONS Itoduto Gaphal Method Cloe Method Ope Method Polomal Root Stem o Multvaale Equato Chapte Stem o No-Lea Equato /. Itoduto Polem volvg o-lea equato egeeg lude optmato olvg
The tight-binding method
Th tight-idig thod Wa ottial aoach: tat lcto a a ga of aly f coductio lcto. ow aout iulato? ow aout d-lcto? d Tight-idig thod: gad a olid a a collctio of wa itactig utal ato. Ovla of atoic wav fuctio i
Anouncements. Conjugate Gradients. Steepest Descent. Outline. Steepest Descent. Steepest Descent
oucms Couga Gas Mchal Kazha (6.657) Ifomao abou h Sma (6.757) hav b pos ol: hp://www.cs.hu.u/~msha Tch Spcs: o M o Tusay afoo. o Two paps scuss ach w. o Vos fo w s caa paps u by Thusay vg. Oul Rvw of Sps
Priority Search Trees - Part I
.S. 252 Pro. Rorto Taassa oputatoal otry S., 1992 1993 Ltur 9 at: ar 8, 1993 Sr: a Q ol aro Prorty Sar Trs - Part 1 trouto t last ltur, w loo at trval trs. or trval pot losur prols, ty us lar spa a optal
ON THE EXTENSION OF WEAK ARMENDARIZ RINGS RELATIVE TO A MONOID
wwweo/voue/vo9iue/ijas_9 9f ON THE EXTENSION OF WEAK AENDAIZ INGS ELATIVE TO A ONOID Eye A & Ayou Eoy Dee of e Nowe No Uvey Lzou 77 C Dee of e Uvey of Kou Ou Su E-: eye76@o; you975@yooo ABSTACT Fo oo we
T T V e g em D e j ) a S D } a o "m ek j g ed b m "d mq m [ d, )
. ) 6 3 ; 6 ;, G E E W T S W X D ^ L J R Y [ _ ` E ) '" " " -, 7 4-4 4-4 ; ; 7 4 4 4 4 4 ;= : " B C CA BA " ) 3D H E V U T T V e g em D e j ) a S D } a o "m ek j g ed b m "d mq m [ d, ) W X 6 G.. 6 [ X
Structure and Features
Thust l Roll ans Thust Roll ans Stutu an atus Thust ans onsst of a psly ma a an olls. Thy hav hh ty an hh loa apats an an b us n small spas. Thust l Roll ans nopoat nl olls, whl Thust Roll ans nopoat ylnal
SCHEMATIC SYMBOLS AMP METER MASTER RESCUE ASSISTANCE INTERCOM SYSTEM STATION CIRCUIT BREAKER CIRCUIT BREAKER (GFI) GFI CONTACT (N.C.) CONTACT (N.O.
YO & VITIO I YO ITO (I) OTO OO O TTO O IT TTO O OTO T TTO I T IT ITO YT TTIO O I IT TTIO OTOIZ OTO OTT Y O TTO O TTO (T) T TTO I 000 TI YO T IIT IIT (I) OTT (..) OTT (.O.) OTT (OT,..) OTT (OT,.O.) IOT
Winnie flies again. Winnie s Song. hat. A big tall hat Ten long toes A black magic wand A long red nose. nose. She s Winnie Winnie the Witch.
Wnn f gn ht Wnn Song A g t ht Tn ong to A k g wnd A ong d no. no Sh Wnn Wnn th Wth. y t d to A ong k t Bg gn y H go wth Wnn Whn h f. wnd ootk H Wu Wu th t. Ptu Dtony oo hopt oon okt hng gd ho y ktod nh
Simulation of Natural Convection in a Complicated Enclosure with Two Wavy Vertical Walls
A Mtt S, V. 6, 2012,. 57, 2833-2842 Sut Ntu Cvt Ct Eu wt Tw Wvy Vt W P S Dtt Mtt, Futy S K K Uvty, K K 40002, T Ct E Mtt CHE, S Ayutty R., B 10400, T y 129@t. Sut Wtyu 1 Dtt Mtt, Futy S K K Uvty, K K 40002,
In the name of Allah Proton Electromagnetic Form Factors
I th a of Allah Poto Elctoagtc o actos By : Maj Hazav Pof A.A.Rajab Shahoo Uvsty of Tchology Atoc o acto: W cos th tactos of lcto bas wth atos assu to b th gou stats. Th ct lcto ay gt scatt lastcally wth
Previous knowlegde required. Spherical harmonics and some of their properties. Angular momentum. References. Angular momentum operators
// vious owg ui phica haoics a so o thi poptis Goup thoy Quatu chaics pctoscopy H. Haga 8 phica haoics Rcs Bia. iv «Iucib Tso thos A Itouctio o chists» Acaic ss D.A. c Quai.D. io «hii hysiu Appoch oécuai»
Power Spectrum Estimation of Stochastic Stationary Signals
ag of 6 or Spctru stato of Stochastc Statoary Sgas Lt s cosr a obsrvato of a stochastc procss (). Ay obsrvato s a ft rcor of th ra procss. Thrfor, ca say:
The Real Hydrogen Atom
T Ra Hydog Ato ov ad i fist od gt iddt of :.6V a us tubatio toy to dti: agti ffts si-obit ad yfi -A ativisti otios Aso av ab sift du to to sfitatio. Nd QD Dia q. ad dds o H wavfutio at sou of ti fid. Vy
Handout on. Crystal Symmetries and Energy Bands
dou o Csl s d g Bds I hs lu ou wll l: Th loshp bw ss d g bds h bs of sp-ob ouplg Th loshp bw ss d g bds h ps of sp-ob ouplg C 7 pg 9 Fh Coll Uvs d g Bds gll hs oh Th sl pol ss ddo o h l slo s: Fo pl h
P a g e 5 1 of R e p o r t P B 4 / 0 9
P a g e 5 1 of R e p o r t P B 4 / 0 9 J A R T a l s o c o n c l u d e d t h a t a l t h o u g h t h e i n t e n t o f N e l s o n s r e h a b i l i t a t i o n p l a n i s t o e n h a n c e c o n n e
Fun and Fascinating Bible Reference for Kids Ages 8 to 12. starts on page 3! starts on page 163!
F a Faa R K 8 12 a a 3! a a 163! 2013 a P, I. ISN 978-1-62416-216-9. N a a a a a, a,. C a a a a P, a 500 a a aa a. W, : F G: K Fa a Q &, a P, I. U. L aa a a a Fa a Q & a. C a 2 (M) Ta H P M (K) Wa P a
Order Statistics from Exponentiated Gamma. Distribution and Associated Inference
It J otm Mth Scc Vo 4 9 o 7-9 Od Stttc fom Eottd Gmm Dtto d Aoctd Ifc A I Shw * d R A Bo G og of Edcto PO Bo 369 Jddh 438 Sd A G og of Edcto Dtmt of mthmtc PO Bo 469 Jddh 49 Sd A Atct Od tttc fom ottd
Statics. Consider the free body diagram of link i, which is connected to link i-1 and link i+1 by joint i and joint i-1, respectively. = r r r.
Statcs Th cotact btw a mapulato ad ts vomt sults tactv ocs ad momts at th mapulato/vomt tac. Statcs ams at aalyzg th latoshp btw th actuato dv tous ad th sultat oc ad momt appld at th mapulato dpot wh
OH BOY! Story. N a r r a t iv e a n d o bj e c t s th ea t e r Fo r a l l a g e s, fr o m th e a ge of 9
OH BOY! O h Boy!, was or igin a lly cr eat ed in F r en ch an d was a m a jor s u cc ess on t h e Fr en ch st a ge f or young au di enc es. It h a s b een s een by ap pr ox i ma t ely 175,000 sp ect at
Executive Committee and Officers ( )
Gifted and Talented International V o l u m e 2 4, N u m b e r 2, D e c e m b e r, 2 0 0 9. G i f t e d a n d T a l e n t e d I n t e r n a t i o n a2 l 4 ( 2), D e c e m b e r, 2 0 0 9. 1 T h e W o r
Central County Fire & Rescue - Station #5
A CL UT CHUL G : HT T : PLA AK. L UB V CU TYP. UPPLY ALW (C) TT BTU/H CLG CAPACTY HATG CAPACTY LCTC A BTU/H B T A WB BTU/H T A B VLT/PH CA CP U (dba) WGHT (lbs) CU-1 AK XZQ07 BUK 117 Cassette 320 6325
Planar convex hulls (I)
Covx Hu Covxty Gv st P o ots 2D, tr ovx u s t sst ovx oyo tt ots ots o P A oyo P s ovx or y, P, t st s try P. Pr ovx us (I) Coutto Gotry [s 3250] Lur To Bowo Co ovx o-ovx 1 2 3 Covx Hu Covx Hu Covx Hu
Today s topics. How did we solve the H atom problem? CMF Office Hours
CMF Offc ous Wd. Nov. 4 oo-p Mo. Nov. 9 oo-p Mo. Nov. 6-3p Wd. Nov. 8 :30-3:30 p Wd. Dc. 5 oo-p F. Dc. 7 4:30-5:30 Mo. Dc. 0 oo-p Wd. Dc. 4:30-5:30 p ouly xa o Th. Dc. 3 Today s topcs Bf vw of slctd sults
Klour Q» m i o r L l V I* , tr a d itim i rvpf tr.j UiC lin» tv'ilit* m in 's *** O.hi nf Iiir i * ii, B.lly Q t " '
/ # g < ) / h h #
T h e C S E T I P r o j e c t
T h e P r o j e c t T H E P R O J E C T T A B L E O F C O N T E N T S A r t i c l e P a g e C o m p r e h e n s i v e A s s es s m e n t o f t h e U F O / E T I P h e n o m e n o n M a y 1 9 9 1 1 E T
I M P O R T A N T S A F E T Y I N S T R U C T I O N S W h e n u s i n g t h i s e l e c t r o n i c d e v i c e, b a s i c p r e c a u t i o n s s h o
I M P O R T A N T S A F E T Y I N S T R U C T I O N S W h e n u s i n g t h i s e l e c t r o n i c d e v i c e, b a s i c p r e c a u t i o n s s h o u l d a l w a y s b e t a k e n, i n c l u d f o l
CBSE , ˆj. cos CBSE_2015_SET-1. SECTION A 1. Given that a 2iˆ ˆj. We need to find. 3. Consider the vector equation of the plane.
CBSE CBSE SET- SECTION. Gv tht d W d to fd 7 7 Hc, 7 7 7. Lt,. W ow tht.. Thus,. Cosd th vcto quto of th pl.. z. - + z = - + z = Thus th Cts quto of th pl s - + z = Lt d th dstc tw th pot,, - to th pl.
STATE OF NORTH CAROLINA DIVISION OF HIGHWAYS LOCATION: GREENSBORO EASTERN LOOP FROM NORTH OF US 70 RELOCATION TO US 29 NORTH OF GREENSBORO
j M HU M : // $$$$UAM$$$$ A: J: ee heet -A or nex of heets ee heet - or onentional lan heet ymols ee heet - an - or urey ontrol heets J Hicone % % enoer H G H uffine Mill Ae ompany -- A + G -- A + - /
A o odatio List Asoke campus
A o odatio List Asoke campus Thi gs ou should k o. The fi st pa e t ust e do e o ou a i al da. Stude ts ha e to p epa e o e i Thai Baht to pa fo the pa e t.. The fi st pa e t i ludes the deposit o ths,
Bayesian Estimation of the parameters of the Weibull-Weibull Length-Biased mixture distributions using time censored data
Bys Eso of h s of h Wull-Wull gh-bs xu suos usg so S. A. Sh N Bouss I.S.S. Co Uvsy I.N.P.S. Algs Uvsy shsh@yhoo.o ou005@yhoo.o As I hs h s of h Wull-Wull lgh s xu suos s usg h Gs slg hqu u y I sog sh.
A NEW GENERALIZATION OF KUMARASWAMY LINDLEY DISTRIBUTION
ou of Sttt: dv Thoy d ppto Vou 4 Nu 5 Pg 69-5 v t http://tfdv.o. DOI: http://d.do.og/.864/t_754 NW GNRLIZTION OF KUMRSWMY LINDLY DISTRIBUTION M. MHMOUD M. M. NSSR d M.. F Dptt of Mtht Futy of S Sh Uvty
Valley Forge Middle School Fencing Project Facilities Committee Meeting February 2016
Valley Forge iddle chool Fencing roject Facilities ommittee eeting February 2016 ummer of 2014 Installation of Fencing at all five istrict lementary chools October 2014 Facilities ommittee and
A Review of Dynamic Models Used in Simulation of Gear Transmissions
ANALELE UNIVERSITĂłII ETIMIE MURGU REŞIłA ANUL XXI NR. ISSN 5-797 Zol-Ios Ko Io-ol Mulu A Rvw o ls Us Sulo o G Tsssos Th vsgo o lv s lu gg g olg l us o sov sg u o pps g svl s oug o h ps. Th pupos o h ols
SER/ES 2OOBE FRP DOUBLE DOOR
I / l h LI AIU OOR, I AU T, RATO, L 6 OOR Tlpho () 6676 t lc ' o * * c : < Tz : A c (:» ) R/ OO R OUL OOR OUTI "IAT" " A OA RA ITH U U / / < a;, / >a zo Ol a : U x: < w " cw O I * v a It_ RAL OT ll z I
Born-Oppenheimer Approximation. Kaito Takahashi
o-oppehee ppoato Kato Takahah toc Ut Fo quatu yte uch a ecto ad olecule t eae to ue ut that ft the=tomc UNT Ue a of ecto (ot kg) Ue chage of ecto (ot coulob) Ue hba fo agula oetu (ot kg - ) Ue 4pe 0 fo
Analysis of Collaborative Learning Behaviors and the Roles of Collaborative Learning Agent
A v L Bhv h v L A Ik L (Sj Uv, S. K, @j..k) J H L (Uv Ih, S. K, jh@h..k) Sh J (S N Uv, S. K, v712@..k) E M S (S N Uv, S. K, 04@..k) K A M (E T h I, S. K, k@..k) H J S (E T h I, S. K, hjh@..k) A: v h h
BUDA TOWN CENTER CLICK FOR DRONE VIDEO. PJ KAMINER
CICK FO DONE VIDEO UDA TON CENTE PJ KAMINE 5.485.0888 pkm@oo. ANCE MOIS 5.485.0888 mo@oo. INTODUCTION T Coo p o p foowg oppouy o pu 00%, mu- vm u, Tx. u 00, ubj popy w-ou, fg,,397 SF bug ow-o by m Sup.
-Z ONGRE::IONAL ACTION ON FY 1987 SUPPLEMENTAL 1/1
-Z-433 6 --OGRE::OA ATO O FY 987 SUPPEMETA / APPR)PRATO RfQUEST PAY AD PROGRAM(U) DE ARTMET OF DEES AS O' D 9J8,:A:SF ED DEFS! WA-H ODM U 7 / A 25 MRGOPf RESOUTO TEST HART / / AD-A 83 96 (~Go w - %A uj
BUDA TOWN CENTER CLICK FOR DRONE VIDEO. PJ KAMINER
CICK FO DONE VIDEO UDA TON CENTE PJ KAMINE 5.485.0888 pkm@oo. ANCE MOIS 5.485.0888 mo@oo. INTODUCTION T Coo p o p foowg oppouy o pu 00%, mu- vm u, Tx. u 00, ubj popy w-ou, fg,,39 SF bug ow-o by m Sup.
Characteristic of the Pepper CaRGA2 Gene in Defense Responses against Phytophthora capsici Leonian
J o 2013, 14, 8985-9004; o:103390/jm14058985 O o Jou o ou 1422-0067 wwwmom/jou/jm h o h 2 o hyohho o - Zh 1,2,, - J 1,, - 1,2, Ju- 1,2, -Xu 1,2 Zh-u o 1,2, * 1 2 o o ouu, ohw & Uy, 712100, hx, h; -: zy41982@126om
Integrated Optical Waveguides
Su Opls Faha Raa Cll Uvs Chap 8 Ia Opal Wavus 7 Dl Slab Wavus 7 Iu: A va f ff a pal wavus a us f a u lh a hp Th s bas pal wavu s a slab wavus shw blw Th suu s uf h - Lh s u s h b al al fl a h -la fas Cla
Bayesian Credibility for Excess of Loss Reinsurance Rating. By Mark Cockroft 1 Lane Clark & Peacock LLP
By Cly o c o Lo Rc Rg By M Coco L Cl & Pcoc LLP GIRO coc 4 Ac Th pp c how o v cly wgh w po- pc-v o c o lo c. Th po co o Poo-Po ol ch wh po G o. Kywo c o lo c g By cly Poo Po G po Acowlg cl I wol l o h