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 Bouy vlu ol 9 Uul u-louvll ol 9 A y glzo of u-louvll ol A y glzo of h o Lg fuo Th l E / h glz o Lg uo 6 A l of y ohogol olyol 9 Iouo 9 A l of y ohogol olyol ug h u- Louvll ho MCO 9 A logu of o uo fly A glzo of ul y uo fly A loh w f o of ll ohogol olyol 5 o fuh o of MCO 5 6 ul Glz ulhl olyol GU 8 6 Dfo 8 6 Ru lo of o olyol 9 6 Ohogoly lo 9 6 Dffl uo 7 fh h of Chyhv olyol 8 o ul Glz H olyol GH 8 Il vo 8 El fo of o GH 8 Ru lo of o olyol 8 Ohogoly lo 85 Dffl uo 5 9 Th ul A f l of y ohogol olyol wh wgh fuo o 5 ouh ul A f l of y ohogol olyol wh wgh fuo / o 5 Il vo 7
El fo of olyol 7 Ru lo of o olyol 7 Ohogoly lo 7 5 Dffl uo 8 A uf oh fo MCO 8 How o f h f l of h wgh fuo of MCO gv? 8 How o f h f l of h u uo of MCO gv? 9 ll ohogol olyol Iouo f l of hygo ohogol olyol o f l of hygo ohogol olyol: If σ τ 5 A loh w Bl olyol Lgu olyol 7 Th f l Hygo ohogol olyol wh wgh fuo / o 9 5 Alo of f ohogol olyol fuo oo ul go 5 6 A oo w f f ll ohogol olyol 56 5 A glzo of u -uo fo h vwo of l fuo 59 5 Iouo 59 5 A glzo of h -uo 6 5 o ul u- of h glz uo 6 5 A y glzo of h -uo h λ λ / 6 5 A y glzo of h -uo h λ 67 6 A g olyol oluo fo h ffl uo of hygo y u of ll ohogol olyol l o 7 6 Iouo 7 6 A lg y 7 6 Th Tho 7 6 A l of h g o olyol 77 6 o fuh o of h g o olyol 78 6 A l hg of vl 78 6 A g h- u uo 78 6 A g foul fo h o u vlu of h olyol 79
65 l of h g o olyol ll ohogol olyol 8 65 Jo ohogol olyol 8 65 Lgu ohogol olyol 8 65 H ohogol olyol 8 65 ll ohogol olyol wh wgh fuo W o [ 8 655 ll ohogol olyol wh wgh fuo / W o [ 8 66 How o f h f l of h wgh fuo gv? 8 67 A g foul fo h vlu h ouy o of o ll ohogol olyol 85 67 Vlu of h ll ohogol olyol h ouy o 88 7 Alo of ol ll ohogol olyol fo l ouo of v Ll fo 9 7 Iouo 9 7 Evluo of v Ll fo ug ol ll ohogol olyol 9 7 Iv Ll fo ug ol Jo ohogol olyol 9 7 Iv Ll fo ug ol Lgu ohogol olyol L 95 7 l l of o 7 97 8 o fuh l fuo h lo 99 8 Iouo 99 8 Alo of zo gvlu fo olvg h ol h wv uo ug u of l fuo 99 8 Alo of f fuo h oluo of ol h wv uo hl oo 8 Two l of l fuo ug ou fo of f ll ohogol olyol 7 8 Evlug ol gl oju Bloghy 5
Ch Oul of o Th h lu 8 h Th h f how o glz h uul u-louvll ol wh y oluo o lg l I oh wo f h y u y Φ f uul u-louvll ol y λ ρ y > ρ > wh h ouy oo y y y y < < h u o f oo glz o o v ol y λ ρ E y wh h vul oo y θ y θ θ < < θ I houl o h h vg of h o h h glz oluo v h ohogoly oy I h y ug h ov ho h wll-ow y o Lg fuo hvg v lo hy gg glz how h h ohogoly vl h [-] Aoh o ou of h o of uul u-louvll ol wh y oluo gv h h I h h y ug h o h l of y ohogol olyol MCO wh fou f ou ll o uh g o o ffl uo of h fo / Φ Φ Φ ogh wh l olyol oluo h fo 5
[ / ] [ / ] [ / ] [ / ] g ohogoly lo g h u lo o o o Moov how h fou u-l of y ohogol olyol h glz ulhl olyol glz H olyol wo w u of f y ohogol olyol ll l u- of MCO I h wy wo hlf-goo u of MCO ou Bu uully h f ohogol olyol l ow u h lu I h ohv ou f ll ohogol olyol h f oluo of h wll-ow ffl uo of u-louvll y σ y τ y λ y whh σ τ λ gv I h h h u of hygo olyol whh fly ohogol wh o h v g glz-t uo fuo ou l h lo fuo oo ul go vg I g o ow h h wgh fuo of h h l of f ohogol olyol oo o glzo of T uo whh f w ow h o h hl h o h o h 5 llo o lg glzo of u -uo wh fou f ohv uo of hl o of h w uo vg fo l fuo o of vw I lo how h l o uul ol uo h glz -uo ovg o h ol uo g wh h u of l o fy I h h h - uo h lo loh wh h -uo glzo of h - uo lo ou how h lly ovg o h h-u uo h u of l o fy A h of h h o l of h glz uo u Bu w ov h ou uo h g olyol oluo Now ol o f g olyol oluo fo h ffl uo lly? Ch 6 l h uo l I h 6 how h h uo h g o olyol oluo wh y G 6
G / Th how h ll u of f f ll ohogol olyol h y h gl v foul o gl o of h foul uh h ffo of l hg of vl g h- u uo g foul fo h o u vlu of h olyol o o lo gv A h of h h l how o v g foul fo h vlu h ouy o of o ll ohogol olyol H g o ow h ll ohogol olyol hv u h l ouo of v Ll fo I oh wo f h Mou fo z R loy h u of ll ohogol olyol h h g ol ohogol olyol u o ou h v Ll fo ly wh o ol lulo fo fg h oo I h 7 y hvg h uo h l gv o lly o h v Ll fo lly h 8 ou o w u of l fuo h hv lo h oluo of ll ol h wv uo hl oo I oh wo ow h h oluo of u-louvll ol uully zo gvlu go Now f h fo gvlu o o zo o of h oluo wll -g Th oh u o w u of l fuo h oluo of h ll uo of ol h wv hl oo By og h o l of l fuo ou h f of h 8 l h o ll uo I h wy o l l gv A vully h o of l h wo w l of ohogol hygo fuo ou how h ug ou fo vl y hy fly ohogol wh o wo f fuo of G y Moov h h w hygo l f ol gl lly vlu h oju h h g of h gl y fly ohogol wh o h Ruj wgh fuo o h l l 7
8
Ch A y glzo of u - Louvll ol Iouo I h h w o oo u whh h uul u-louvll ol wh y oluo o lg l Th vg of h o h h oog oluo v h ohogoly oy A l w vg l of glz u-louvll ol o h ohogol oluo Th fo l glz h wll-ow o Lg fuo hvg v lo hy gg v h ohogoly vl [-] fo h glz fuo Bouy vlu ol Wh l ffl uo olv y h ho of o of vl lo h 8 o 8 h ol u o h oluo of oy ffl uo Th oluo of h uo y g ol of hl hy of l fuo I o o o uh oluo of h l ffl uo f w hv o o ol oo o h oluo uh h h ol wll hv uu oluo Th oo u l o oo o h oluo of h oy ffl uo hu o ouy vlu ol W h o f hv uvy o h oluo of ouy vlu ol y h ho of o of vl Uul u-louvll ol I h ov h h ho of o of vl vly l fo olvg l ffl uo of h fo wh * u * u ρ y z A B Lu Lu v y z gu y z u v Dvg of vo
A y glzo of u-louvll ol g j y z Th uo h ogo of vo uh log o ou wv f A * * B f o uh h * f o h ffuo of l u wh A B lly h oog - o f A * B [56 99] To hv uu oluo of uo whh oo o ul hyl ol o uly oo u o Th o yl oo l o ouy oo Th l oo fo uo uully h vlu of u y z u y z / whl h l ouy oo h fo u y z u y z η wh y z y z gv fuo h uf oug h o wh o olv u / η h vv h o of h ouw ol o Bu h ul oluo of u h ouy oo wll fou f o loo fo oluo of h fo u y z T v y z By uug o h uo o vly g * * A T B T λ T * * L v λ ρ v 5 wh λ o Clly olv fo yl ol hl hy Howv o olv 5 w houl u ouy oo h follow fo ly v y z v y z Th ol ow η ulol ouy vlu ol Nvhl lf o ool ol f 5 u o uo of h fo wh L y λ ρ y 6 y L y y > ρ > 6
A y glzo of u-louvll ol Th uo 6 houl o o o vl y wh ouy oo h fo y y 7 y y wh gv o ρ 6 6 o u ouou fo [ ] Th lf ouy vlu ol 6-7 ll gul u-lovll ol Moov f o of h ouy o gul o h ol wll fo o gul u-louvll ol I h o go ouy oo 7 o h ohogoly oy ly Now l y y wo oluo gfuo of uo 6 Aog o h u-louvll hoy [8 56] h fuo ohogol wh o h wgh fuo ρ o u h gv oo 7 ρ y y ρ y δ f f δ 8 f My o l fuo hol hl hy h oluo of gul o gul u-louvll ol h fy h ohogoly oo 8 o h o Lg fuo [8] Bl fuo [8 56] goo u l o ou ly [] Ulhl fuo [7 7] H fuo [7 7] o o ul oluo of o u-louvll ol ouly o of h o fuo hv h yy oy ly Φ Φ u of h hy hv fou vou lo hy gg g [8 56] fo o l Now f o h o l ylly v h ohogoly oy h o wll l o f o w lo hy gg h loglly h vou lo I h o y hvg h w glz o ll y ohogol fuo o h ohogoly oy A y glzo of u-louvll ol [] Whou lo of gly l y Φ u of y fuo h f h followg ffl uo A Φ B Φ C D E Φ λ 9 wh A B C D E fuo { λ } u of o Clly hoog E 9 uvl o h o-
A y glzo of u-louvll ol ol u-louvll uo 6 Φ y u y uug h yy oy Φ Φ o 9 o ly olu h A C D E v fuo whl B u o fuo Th o wll fuly u h o To ov h ohogoly oy of h u Φ f oh of uo 9 houl ull y h ov fuo B A B R A A A o o ov h fo of lf-jo ffl uo No h R v fuo u B o A v Thfo h lfjo fo of uo 9 o Φ A R λ C D R Φ E R Φ A R v fuo h ohogoly vl oog o uo houl o y y [ θ θ ] H y ug h θ oo of h fuo A R lyg h u-louvll ho o w hv [ A R Φ Φ Φ Φ ] λ λ θ θ C R Φ Φ θ θ θ θ E R Φ Φ Ovouly h lf-h of zo o o ov h ohogoly oy ough o how h h vlu θ θ E R Φ Φ lwy ul o zo fo vy glly o fo : Z o h uo fou houl If oh v o o h u w hv j j If o of h wo o vlu o h oh o v o ovly h θ j E R Φ Φ j θ
A y glzo of u-louvll ol Bu ov lo E R Φ v fuo Φ j o Thu h g of o fuo ouly j Th u lo hol fo h j j By og h ov o h ho of o h Tho [] Th y u Φ Φ f oluo of ffl uo 9 f h ohogoly lo wh θ θ * * W Φ Φ W Φ δ θ θ 5 * B A W C R C 6 A o h oog wgh fuo ov v fuo o [ θ θ ] I ow goo oo o oou l l h glz h wllow y o Lg fuo v h ohogoly oy A y glzo of h o Lg fuo [] Wh Ll uo u o Hlholz uo u λ u olv hl oo θ ϕ h followg ul [56] wh u u Δ Δ θ ϕu 7 u Δ u 7 u u Δθ ϕu θ θ θ θ θ ϕ 7 A w l h o y g u R Ψ θ Ω ϕ uug o Ll uo ol uo h followg oy ffl uo v R μ R Ω υ Ω 8 Ψ θ θ μ θ υ Ψ θ θ
A y glzo of u-louvll ol wh μ υ wo o vlu o oθ h l uo of 8 hg o Ψ Ψ υ μ Ψ 9 whh ll h o Lg ffl uo [8] oluo ully ow h o Lg fuo Th fuo ly y ol h hoy of ol I gl h h y of oluo fo uo 9 g o ff vlu of μ υ: If μ υ Z > h h oluo of 9 y Ψ U wh ow Ulhl olyol l of Jo olyol [7 7] fo I h wy h oluo f h ohogoly lo U U U δ δ! If μ υ Z 9 h oluo h fo ov y Lg Ψ wh o h Lg olyol [56] Moov og o [8] f h ohogoly lo! j δ j δ j! To o h h y of oluo l u f o h Jo olyol ffl uo [7 7] y y y y 5
A y glzo of u-louvll ol 5 uo / / A Af o ouo h h ffl uo A v ] [ A A A 6 Now uo 6 h u o h ffl uo A A A 7 Th oo < < y fo h ohogoly oy of h olyol u w u hv > Thfo y og μ < < υ 9 h l oluo h fo V Ψ 8 fyg h ohogoly lo V V V! δ δ 9 To h o Lg fuo ough 9 o hoo Ay A A B B C C D D E E υ λ μ ly h ho o lh h ohogoly oy o h vl [-] To o h l E Q υ Φ ow oluo of h ffl uo Φ Φ Φ E υ μ Aog o h ho w houl hv E Q E Q E Q δ υ υ υ
A y glzo of u-louvll ol 6 ov h h y fuo E v Th u Q υ E ow oluo of uo ow ohogol u h -g oo E E o ll h hoy of h o of fuo y ouy vlu ol of hl hy olv y ug h o of fuo of h gfuo of uul u-louvll ol H f w u f Q υ E h og o h oy h uow off fou y f Q υ E Q υ E Clly vou oo l fo E h ly l o h ohogol u Q υ E o l hoog h v fuo E gv o of h h of uul o Lg fuo fo A fuh l l wh E E / L u uy h h o l Th l If E E / u o h uo / h glz uo υ Φ Φ μ Φ 5 To o h oluo of h uo fo f vlu of μ υ o houl f o h glz ulhl olyol GU whh w f vg y Chh [7] O h oh h og o h ho f h gl uo 9 o hoo A A v fuo B A o fuo C D E λ A A A v v v fuo fuo fuo 6 h h y ffl uo
A y glzo of u-louvll ol 7 Φ Φ Φ 7 h glz ulhl uo hvg h o olyol oluo 8 ] / [ ] / [ ] / [ ] / [ ] / [ ] / [ U Th o GU ohogol wh o h wgh fuo o [-] f h followg ohogoly lo / / U U δ 9 Now y fg > > U G lg o uo 7 o g G G G If h ov uo o wh 5 h olu h Q G > gl oluo of fo υ μ / E Moov uug h vlu o og 9 yl 5/ Q Q δ π R Alhough o l fuo uh Bl fuo [8] ou goo u o o y fy ffl uo who off lvly v o ywy o o o h
A y glzo of u-louvll ol 8 hy o o fy h oo of h ho o f h g uo 9 w hoo A B C D E λ w g o h Bl ffl uo wh h y oluo Φ Φ Φ 5 Z 6 J J!! u h ohogoly vl of Bl fuo o y [ ] H ho o l fo J ul h f v fuo E fo uo 9 uh h h oog oluo h fy zo g [8 56] fo o l ly l o h of uul Bl fuo of o Thfo h oluo of h h uz follow: h uul u-louvll ol y λ ρ y > ρ > u h ouy oo y y y y o h followg ol < < y λ ρ E y wh h ouy oo y θ y θ θ < < θ ov h h oluo of l ffl uo h h yy oy y y
Ch A l of y ohogol olyol Iouo I h vou h w how o h uul u-louvll ol wh y oluo I h h y ug h u- Louvll ho fo y fuo w gog o ou l of y ohogol olyol MCO wh fou f o ll o uh g o o ffl uo ogh wh l olyol oluo g ohogoly lo g h u lo o o Th w how h lly fou u of y ohogol olyol fo h ou l Thy vly h glz ulhl olyol glz H olyol wo oh u of y olyol whh fly ohogol o h l l of h o l ly I h wy w lo ou wo hlf-goo u of ohogol olyol l u- of MCO A M Cl of y Ohogol olyol MCO ug h u-louvll ho [] By fg o h ho of h g ffl uo 9 hoo h followg oo A A v fuo B A o fuo C A v fuo D A v fuo E A v fuo wh l f λ Thfo o l wh o o ffl uo of h fo / Φ Φ Φ To o h olyol oluo of ov uo l u f uo h
A M Cl of y Ohogol olyol Φ Φ Φ Af og o lulo h o g h oluo of uo j j j wh lly f o h lf uo 5 Φ Φ Φ h h olyol oluo j j j 6 Couly og wh 6 gv ] / [ ] / [ ] / [ ] / [ 7 h o oo ou of ll y ohogol olyol wh fou f wh h oh vlu o oh vlu vh ogh H l u o ou h lo ll ow y ohogol olyol uh Lg olyol f o of Chyhv olyol ulhl olyol glz ulhl olyol GU H olyol glz H olyol GH l u- of 7 of ly Bu of h w ll h olyol Th o of ll ohogol olyol uho h wo oh y u of f ohogol olyol h l u- of gl o 7 w wll ou h h o 9 Th yol u oly u of yy oy howv o ho h oo h w wll how A ghfow ul fo 7 h 8 Moov h o y of ohogol olyol wh lg off of u w f
A M Cl of y Ohogol olyol ] / [ ] / [ 9 o f 5 9 w hv 5 7 5 7 5 5 5 5 5 9 Th l o of 9 hl u ow o h- u lo fo h olyol H f w u h hy fy h lo N C h f og of ouo h w o / C whh vl h l fo of O h oh h h u lo h lly f o h o u vlu of h olyol o u v' ho [7] y og h h ohogoly wh o wgh fuo Aog o h ho f } { f y C B A wh l C B A C > A fo h h wgh fuo W o h
A M Cl of y Ohogol olyol W W δ A C Moov f h ov oo A C > oly hol fo N h h ohogoly lo oly hol fo f u of Th l o wll hl u h o o o wo w u-l of h fly ohogol o h vl I l h h v ho lo vl fo h u lo whh A B C C uho h oo C > u lwy f f o o ly h v ho fo By og h uj h g fo of h ohogoly lo of MCO g W C W δ wh h wgh fuo y fg o 6 f W h vlu No h h fuo W u vh o o lh h ohogoly lo A logu of o uo fly [] Th ov fuo lo vg fo l o of vw I f h fuo logu of o uo fly hvg h gl fo ρ 5 fyg h f o ffl uo ρ ρ 5 Thfo w woul l o o ou h l o uo 5 h wgh fuo f f o ffl uo whh uvl o W W 6
A M Cl of y Ohogol olyol * W * W * * 6 o 6 o 6 u h W ly gl fuo lo ov fuo oly y fuo f u vll I gl h fou u-l of uo fly ouly u-oluo of uo 6 who l f vly follow / K W / / > > 7 K W / < < / > 8 9 K W / / < < > / < / > K W < < > / / Th vlu K ly h olzg o ol ov uo Moov ov h vlu of uo vh h fou W fo H l u ll h ov fuo Th ul y uo fly A glzo of ul y uo fly o o h f 6 h fo uo wll u o l u- of o ffl uo 5 H w hf uo h h l fo of 7 C W ll ow fuh f ly f y fg o h ohogoly lo o h w hv D C W W Clly hoog h fo gv h ul y uo fly Moov h h foo [6] Bolz-ho
A M Cl of y Ohogol olyol foo oy [8] wo o fo l o hoy h vg fo h glz uo A loh w f o of ll ohogol olyol O vfy h h lo w f of ll ohogol olyol lug Jo Lgu H olyol wll h f l of ohogol olyol h h l olyol 7 To f h loh w wh h followg ffl uo y y y Aog o [56] h o olyol oluo of how y Rogu-y foul ρ ρ wh ρ f h fo 5 Bu glly v fuo g v w gv y w y v v w wv w y v v v w w If u wh w houl hv v o v v ± Th oo lf h uo o ± ± ± w y y w y w y w Th uo lly l of Th h 5 ± ± ± w w K w
A M Cl of y Ohogol olyol 5 wh K h lg off of h lf-h olyol of lo 5 v o lg off of h gh-h olyol A w ov h ov lo h 5 f h lfh of 5 o o of h u -g o h o g h l fo of of v w lly o h uo f fo o 5 wo followg / w w w w w 6 / w w w w w w 7 uho f 8 l fo wo l lo w vly g / w w w w w 8 / w w w w w w 9 5 o fuh o of MCO Th lo 6-9 uful ool o g gg fuo fo MCO Uully gg fuo fo y of olyol z f y fuo l z G who o ow of h fo uffly ll h fo! z z G If z h h Rogu-y foul [56] Cuhy gl foul Ω u z u u f z f! π wh Ω lo oou uoug h o z u loy o o z G lly g [56 7] Th h y og h Roguy o fo lyg Cuhy gl ho o w hv
A M Cl of y Ohogol olyol 6 z z u z! ρ ρ z u wh : Now f z z uu o y og h lo 6-9 w o * / / / /! z z u z ρ ρ * wh : z u lly y ullyg oh of y z ug 8 w g * / / / /! z z z u z ρ ρ lly l u f ]! / [ / 5 / ] / [ * Thfo y og of gg fuo fo MCO v * * * / / / / / / / / z u z z u z z ρ ρ ρ ρ wh * u h fo Th l fo of olyol 7 lo l o o g hygo o fo h olyol u y ug o ly
A M Cl of y Ohogol olyol 7 h off of olyol 7 of h ohh yol: o w hv ] [ ] / [ ] / [ / ] / [ / / ] / [ 5 H f o lulo w vully f h / ] / [ / ] / [ 6 wh! γ γ o h hygo fuo of o [] uho 7 R R < > > z z z h gl o of MCO ly v y fg o 6 I h wy y lyg h Gu y [] 8 o lo h vlu of olyol f ouy o / To h h gol uff o u / 6 u 8 o g ] [ ] [ 9 No h o v h ov y h followg ul hv u ] [ ] [ ] [ ] [ ] [ Th o of MCO hv fou ow o goo oo o ou fou l u- of olyol 7 l
A M Cl of y Ohogol olyol 8 6 ul Glz ulhl olyol GU Th olyol w f vg y Chh l [ 7] H o h o of GU v lo w h Jo ohogol olyol Th yo hvo of fo olyol w lo u y Koolv [8] O h oh h Ch Il [] lo [5 ] ou h v o wl olyol o how h h glz ulhl olyol l of h Of ou h o oh glzo of ulhl olyol o Ay [9] ou wo l of ohogol olyol lg of h -Wlo olyol o [ ] wh h wgh fuo W W λ λ U T λ λ U T whh N f g T U vly h Chyhv olyol of h f o o glz GU fo λ o h λ h olyol w ou y Al-l Allwy Ay [5] lg of h -Ulhl olyol of Rog [6] Aywy w h o o how h GU ly of ouly ll o wll o o h uo oly ough o hv h l vo oog o h olyol l o h o of MCO 6 Dfo Choo h l vo uu o 7 o g [ / ] [ / ] [ / ] [ / ] [ ] [ / ] h l fo of o GU Moov h ulhl Ggu Lg Chyhv olyol of h f o ll l of GU hy of ly w hv Ulhl olyol: C! Lg olyol:
A M Cl of y Ohogol olyol 9!! Chyhv olyol of h f : T Chyhv olyol of h o : U 6 Ru lo of o olyol By lg h l vo o h l o C gv h u lo of o GU h fo N C wh og o C 6 Ohogoly lo Clly h wgh fuo of GU h uo 7 whou og olzg o Alo h fuo u v ov h oo l H h o wgh fuo lo o ] [ By og h o g lo fo h ohogoly lo of f u-l h fo C δ wh / / B
A M Cl of y Ohogol olyol o o olu h h o o h houl / > > No h B λ λ o h B gl [8] hvg vou fo h fo B λ λ π / λ λ λ o λ λ λ λ λ λ B λ λ λ λ λ λ 6 Dffl uo: Φ To v h ffl uo of GU ough o uu l vo o h ffl uo o g o 5 Φ Φ 7 fh h of Chyhv olyol [] Φ A w ow fou of goo ohogol olyol ow f o h fouh of Chyhv olyol hv vg h lu u o ow g [6 7 7 7] Th l fo of h vly π T o o θ oθ 6 π θ U o oθ 7 θ π o θ V o oθ 8 o θ π θ W o oθ 9 θ Now w woul l o h h h wo fuh of Hlf-goo ohogol olyol whh ul u- of hy g y ug h f o of Chyhv olyol hv h hlf-goo fo l u ll h h ffh h of Chyhv olyol To g h wo u w houl f o h o lo 8 Aog o h l vo of f Chyhv olyol : o f h vo l o 8 h w hv
A M Cl of y Ohogol olyol T 5 By of 5 h oy vo l of h of vo By ug h w vo f w f h hlfgoo olyol o o / f f X θ θ 5 wh θ o Aog o 5 X f h u lo N X X X C X X 5 whh C 5 Couly uug h oy vo -- o h g lo gv h ohogoly lo of h f of hlf-goo ohogol olyol W C X X W δ 5 O h oh h π B W 5 5 lf o C X X δ π 55 Clly hlf of olyol X ool w hv o X π 56 o f o f h oo of X oo h olyol wll f y lo ul ly uh Gu uu ul [7 7]
A M Cl of y Ohogol olyol lly h uj hol fo h l vo of h o Chyhv olyol Ag f h vo uu o 8 h U 5 57 uuly h oy vo o h fo 5 Now y ug h θ o l u f h olyol 5 o 5 / f f Y θ θ θ 58 fyg h u lo 5 N Y Y Y C Y Y 59 wh 5 C 59 hvg h ohogoly lo W C Y Y W 5 5 5 δ 6 wh 8 5 π B W 6 Th lo 6 lf 6 C Y Y 8 5 δ π 6 l o vou Y ool o Y π 6 H houl h h wo oh u of hlf-goo olyol h o ohogol u how of MCO Th u f
A M Cl of y Ohogol olyol f T f 6 f U f 65 Howv w hv W 66 W 67 hy o fll o h hlf-goo ohogol olyol goy Thu w glly o h followg l howg o o of h f o h of o Chyhv olyol ohogol o [ ] Tl : Ro of Chyhv olyol y Ty Noo Dfo Wgh K T o K U Th K V ouh K W fh K X h K Y 5 R Aog o h l vo of h o Chyhv olyol U If h vo l vy l of h- u lo wh C / v A y of o ohogol olyol h f h lo
A M Cl of y Ohogol olyol Z 68 h h oy l l > R 69 o log o h l N Th o olyol oog o h oo 69 uo of U Now 5 l C l C 7 h f olyol X Y log o h l N 8 o ul Glz H olyol GH Th GH w f ou y zgo who gv o o ffl uo fo h olyol [7 ol 5] lo h fo w wll gv h o Th olyol hz y ug loh w h Lgu ohogol olyol [7] Of ou h o oh oh fo h g [] Bu of h o oly o o h o of GH of h o o of 8 Il vo 7 8 El fo of o GH [ ] [ / ] [ / ] [ ] 8 Ru lo of o GH [ / ] 7 C N 7 wh C 7 8 Ohogoly lo 7 δ
A M Cl of y Ohogol olyol 5 Th ov lo how h ohogoly vl fo / > 85 Dffl uo: Φ Φ Φ Φ 75 lly o h h lg off of H olyol H followg uly hol H h 76 9 Th ul A f l of y ohogol olyol wh wgh fuo o [] Aog o v ho f h oo C > hol oly fo f u of ov g fo N h h l olyol l woul fly ohogol Th o hl u o o w l of f y ohogol olyol whh l u- of y ly To v h f f u-l w houl f ou h logh vv of h wgh fuo W W W 77 If h ov fo o wh h logh vv of h wgh fuo W h w g 78 whh f h l vo oog o h f f u-l of y ohogol olyol H f 78 l 7 h l fo of olyol v 79 [ / ] [ ] [ ] [ / ] Rlg 78 h u lo lo gv 8 C wh N
A M Cl of y Ohogol olyol 6 C 8 Thfo h ohogoly lo / / C δ 8 vl ff / / > < > > Z C H goo oo o l how w h oo o lh h ohogoly oy 8 o h uo h g hu L u o h ffl uo of olyol 79 ug h l vo 78 uuly h uo 8 Φ Φ Φ If h ov uo w lf-jo fo h og o ho h followg u vh ] [ Φ Φ Φ Φ 8 O h oh h Φ olyol of g o g Φ Φ Φ Φ 8 Couly fo 8 8 w u hv 85 whh gv h followg ul > < / 86 I oh wo 8 hol f oly f / N whh } { N < / >
A M Cl of y Ohogol olyol 7 Coolly Th f olyol { wh o h wgh fuo N / < / > } N ohogol o f oly f W h h l hu lly l fo h f o u-l of GU GH ouh ul A f l of y ohogol olyol wh wgh fuo / o [] l o h f f u-l o ou h logh vv of h gv wgh fuo o g vly Il vo 87 El fo of olyol [ / ] [ / ] [ ] [ / ] 88 Ru lo of o olyol C N 89 wh C 89 Ohogoly lo 9 Bu 9 vl f o uvlly Φ Φ [ C Φ Φ ] δ 9 N N { } 9
A M Cl of y Ohogol olyol 8 Coolly Th f olyol { o h wgh fuo / } N 5 Dffl uo: Φ ohogol wh o f oly f N / Φ Φ Φ 9 A uf oh fo h lfo of MCO A w ov h vou o h fou ou u-l of y ohogol olyol w y ly w oly uff o o h l vo oog o h O h oh h l h h ohogoly vl of h u-l oh h f o GU ll f H lyg l foo y w v v h ohogoly vl o l f w v / w 7 h ohogoly vl wll o hg ouly o v l wh wgh fuo w v w v wll v o h vl Howv o o ow h h l wgh oo o h l of ohogol olyol w v / w Thfo oly y hvg h l vo w hv o ll oh o g uf oh fo h h y ou I oh wo f o o h y fg o h l uh gv h u lo gv wgh fuo o o h ll oh o wll v ghfowly H w o wo l u- of h oh How o f h f l of h wgh fuo W gv? By fg o h fouh ohogol u-l y o f ou h h wy fo vg o ou h logh vv W / W h u h wh Th followg l wll lfy h El Th wgh fuo W W 6 W 6 8 5 < < < < h ohogoly vl gv oh o uh l fo of olyol ohogoly lo To olv h ol oly uff o f h l vo oog o h gv wgh fuo o h uo f h logh vv of h f wgh ou h w hv
A M Cl of y Ohogol olyol 9 W W 6 6 8 6 H h l o olyol { 8 6 } No h h olyol ohogol wh o o [ ] fo vy o y o ow h hy h hf GU o [ ] u hy lly ly y Bu fo h wgh fuo W ff owh w hv * * W W W H h l ohogol olyol W W 5 5 W W 5 * W 8 6 * W 5 W Couly y og h ohogoly lo of h h u-l of MCO h f { 6 } ohogol wh o W o h u ou of h h o h oo N / fo 5 How o f h f l of h h u uo 8 gv? I gl h wo wy o h l of oog o gv h- u uo Th f wy o ly o h gv u uo wh Th l o y of olyol uo of h fou I [6] l ho l fo h f of ll ohogol olyol Th o wy o u h f fou of h wo u uo ogh whh l o olyol y wh uo uow vly Th followg l wll llu h ho El If h u uo 6 6 * *
A M Cl of y Ohogol olyol gv h f l olyol oluo ffl uo of olyol h l wgh fuo flly ohogoly lo of olyol oluo If h ov u uo ly o wh h uo uuly h o o h vlu H h l oluo of ov u uo h olyol hfo h ffl uo fou Φ Φ Φ Moov y lg h l vo h wgh fuo W o f ou h h l olyol ul of h fouh ou u-l H w hv C δ 5 o ho If h gv u lo oly fo 5 h u wh 9 h followg y wll v 9 9 6 8 5 5 5 5 7 olvg h y g ul h I oluo y ug h u-louvll ho fo y fuo l h o f g o o ffl uo hvg olyol oluo wh fou f Th oluo f g ohogoly lo who wgh fuo oo o logu of o uo I oh wo h fou l of h ul y uo fly h vly o h wgh fuo of fou ou u-l of MCO I h wy h followg l how h l fo of h o u-l of wll h wgh fuo of olyol f o f ohogoly vl flly o o h
A M Cl of y Ohogol olyol Tl : ou l u- of Dfo Wgh fuo ] Ivl & K [ If Co > / > > If N / < / > N lly w h ll wgh ov l v fuo h oo u lwy f y og h o of fo h ou wgh fuo Thfo hy lo o h fo / vly
A M Cl of y Ohogol olyol
Ch ll ohogol olyol Iouo I wll ow h h ll ohogol olyol of Jo Lgu H fly ohogol fy o o ffl uo of h fo A B C y D E y A D y whh A B C D E of I h h w o uy h oh u of hygo olyol l whh l oluo of ov uo fly ohogol wh o h f wgh fuo Th l hv vly lo wh h Jo Lgu olyol I ul h o l ly l o h glz Bl olyol ouly Lgu olyol L u wh h f f f l of hygo ohogol olyol Co h ffl uo of u-louvll y σ y τ y λ y wh σ A B C τ D E olyol of λ A D h gvlu g o Th Jo ohogol olyol fo σ τ Lgu fo σ τ flly H fo σ τ h ow y of olyol oluo of uo Bu h h oh y of olyol oluo h fly ohogol Th f f l f wh σ τ o uug h vlu gv h followg ffl uo y y y By lyg h ou ho l olyol oluo fo h uo wll v
ll ohogol olyol!! M Moov o ov h h olyol fly ohogol wh o h wgh fuo W o [ f oly f } { > > To ov h l o houl f w h lfjo fo of h uo M y y y y y Th ug h u-louvll ho o g 5 M M y y y y λ λ wh λ A w l h g } { y y y y o f > } { N N > h lf of 5 o zo w wll hv > > } { N N M M 6 Coolly Th f / } { } { < > > N N N M M u ohogol wh o h wgh fuo W o [ A h ffl uo how h olyol hv lo wh h Jo olyol H y fg o h Rogu o of Jo olyol [6] h Rogu foul of h f olyol M 7 O of h vg of ov o o lul h o u vlu of h olyol o h uo f 7 l h o lo M M 8 h go y yl
ll ohogol olyol 5!! M! 9 O h oh h o w hv!!! M!!!! Th fo lo how h > y oo fo h ohogoly of h olyol M Thfo Coolly Ohogoly lo!!! M M δ! f oly f N < > o h olyol { M } {! } fly ohogol wh o h wgh fuo W o [! M M δ o f l of hygo ohogol olyol: If σ τ Th o ly l o h glz Bl olyol Th Bl olyol fo σ τ w f u y [5] 99 Thy lh h ol ohogoly of Bl olyol o h u l h l ohogolzg wgh of h olyol hv ly gv [5] Th 97 h glz Bl olyol w vw y [8] Thy l oluo of uo fo σ τ y B wh B o h o Bl olyol Now whou lo of gly l u o h followg ffl uo
ll ohogol olyol 6 y y y By lyg h ou ho o how h N! 5 olyol oluo of Clly h olyol l o h glz Bl olyol! B N 6 If h uo w lf-jo fo 7 / / / / M y y y y y h ullyg y y y 7 vly ug h w g N N y y y y λ λ 8 wh λ Ag g } { y y y y h oo } { N N > u h lf of 8 o o zo hfo > } { N N N N 9 Coolly Th f / } { } { < > N N N N N u ohogol o wh o h wgh fuo / W o [ o h olyol } { N u fly ohogol wh o h wgh fuo / W o [ Bu h Rogu o of ll ohogol olyol o y W W C wh W wgh fuo C o vlu o olyol o f C W / uo h o foul h
ll ohogol olyol 7 / N To ol h ohogoly lo of N o u h ov foul ou h o u vlu of h olyol Aogly f l h lo N N h go y yl!!! N H o houl o h f > h W Thfo lf!!!!! w flly g!! N 5 Coolly Ohogoly Rlo!! < N N N δ A loh w Bl olyol Lgu olyol [8] I g o ow h h loh w Bl olyol Lgu olyol To f h lo w f o h glz Bl uo y y y 6 uo h / y Thfo / y 6 fo o
ll ohogol olyol 8 7 Now f 7 ± 7 h hg o ± 7 O h oh h ow h h gl oluo of g g g 8 y h oflu hygo fuo []! g 8 o y og h uo 7 8 olu h h fuo y ± 9 f h uo 6 f oly f uuly h o Bl olyol l of h Lgu olyol w hv!!! L B I h wy N lo y h Lgu olyol o h! L N Th l lo uful o g w f gl fo h Lgu olyol u uug o 5 yl!! L
ll ohogol olyol 9 Th f l: Cll hygo ohogol olyol wh wgh fuo o [9] A w u o ow fo h uo A B C y D E y A D y Z o f f u of ll ohogol olyol I h w uy h l f l of hygo olyol whh fly ohogol wh o h wll-hv wgh fuo / o Th fo fuo o o l uo oo u y hvg l o o glz h T lg uo ov h o h Nol uo ju l T- u uo Of ou h h vo o h uj wh o l Howv fo uyg h l f w houl ou l u- of h uo fo σ τ how h h olyol g fo h fly ohogol wh o h ov u ρ o h l vl H l o vou w h h ffl uo y y y h olyol oluo h fo [] [ / ] I! By fog u-louvll uo lyg h hu h w l fo h f o of f ll ohogol olyol w v I I O h oh h [] > N N { } 5 I 6 w flly g Coolly 5 Ohogoly Rlo
ll ohogol olyol 5! π ρ I I δ / If oly f N < / ρ I o o o ou h h wgh fuo of ov ohogoly lo oo o h uul T u uo o h w hv / T ρ < < N π / 7 Now w h wh o y h o h of h oy of olyol I h h uh o v olyol l whh fly ohogol o glz h u I o h uo f w o h followg olyol J 8 uh h > Af og o ouo o 8 h followg ffl uo wll v fo h olyol 9 y y y O h oh h h uo 9 w of h ffl uo of hygo fuo [56] o f lyg o hg of vl o wll h h ul h J / whh / Th foul l o fo h f olyol 8 uho h olyol hv o l oy Ug h Rogu o 8 o ly u f w v o 8 h
ll ohogol olyol 5 / w v w v J w v w v w v w v w v w v w v w v w w v w J o f v w h J J Now l u o h ffl uo 9 h fo of lf-jo uo y y ly h u-louvll ho fo o o h J J y y y y ] [ λ λ wh λ g y y y y vl f h oo R > N N } { / hol h lf of o zo ouly > > } { / N N J J R I ju o ou h o u vlu of h olyol To ou h o l u f l h Rogu o 8 J J 5
ll ohogol olyol 5 Th y og h J h h ohogoly oy go y fo 5 yl! J 6 Now uo h gh h of 6 Th lf 7 o / / π π θ θ θ θ Thfo h ohogoly oy of f olyol : Coolly 6 If W h wgh fuo of h olyol J h w hv & / olyf If o! / / > < N J J W R δ θ θ θ π π θ 8 No h 8 wll lf o f o ul u u ow h θ θ θ θ o lylly gl f N H y owg h θ θ θ θ θ θ θ θ o & o 9 w hv 5 o / / π π π π θ θ θ θ Th uly 5 l h 5
ll ohogol olyol 5 π / θ π oθ θ θ h π / 5 π / π / oθ θ θ θ π oh Thu f ul u 8 h o u vlu of h olyol wll lly o N o g J!! [ ] / π π 5 H goo oo o oou ol l of h ov ohogoly 6 5 oy uo h f { J } gv Th ohogol 6 6 wh o h u W o f h ohogoly lo 5 J 6 f oly f 5 6 J 6 5!!hπ δ 5 5 5 Alo of f olyol fuo oo ul go Uully h f of ohogol olyol l o h ohogol olyol h h ouou I oh wo h ff uo h fo σ Δ y τ Δ y λ y 5 wh Δ y y y y y y σ A B C τ D E λ A D h o ll ohogol olyol of vl [57] o Hh olyol [] Q N N N 5
ll ohogol olyol 5 fly ohogol wh h ow oo > o N < N < fy N N! N Q Q δ 5 N N N! Th Kwhou olyol [57] Rh olyol [57] Dul Hh olyol [] o fuh h hv lf h goy of f hygo ohogol olyol Aog o ohogol olyol hoy ovou h y y fuo f of h o olyol ov h f f h Dhl oo Now w woul l o o ou h h f olyol N { J } N < / lly l fo og h fuo f o h uo ough o o h followg f oo N f C J N < / R > 5 Aog o Coolly 6 C! π / π / oθ θ J θ θ f 55 No h h g N < / h u o g of h oo 5 o l h olyol { J } h u o g o Th followg l lf h y lyg h G-h ohogolzo o [6] El L u ou J fo Thfo { J } {6 6 7} f ohogol olyol wh o h wgh fuo W Ag o π!7!h J J δ 7 6 o l y fg o h h lo gv
ll ohogol olyol 55 π h Now y og h ov ohogoly lo og h of o o h g olyol fo f f whh vully yl 88h 85 9 π 6 6 f 69 6 f 6 f f 6 7 f 6 7 7 Th oo fo y y olyol fuo of g o Moov o h h o olyol o y lyg h G-h ohogolzo o f h o of wgh fuo W o I h w hv B B C C B Af lulg h off B C fo h o ohogol wll v 7 { } 6 O of h oh vg of f olyol o y of f gl ug Gu go hoy By loyg h zo of olyol J h olo o h Lgg olo o o h gl f wh h o g N Th uj lf y h followg l
ll ohogol olyol 56 El By lg h zo of J h Lgg olo wo-o oo wll v h fo 8 π f h 5 69 85 f 5 85 5 85 f 5 85 Th oo fo f y l oo of h l Aywy houl o h h u o g of h ul oo f : N { < } o l f 79] h w hv N 5 lo [6] [7] h g [6] l fo h wgh fuo of olyol I [7] fo h wgh fuo of N 6 A oo w f f ll ohogol olyol Th Rogu o of h f ll ohogol olyol uful ool o f o l lo w J H olyol lo w M Lgu olyol vly o h uo h followg l houl f o lw l 56 l H w hv 57 W l J l / W H lly h hu l o v l lo w M Lgu olyol I h w hv M Now g l l M / 58 yl! L 59
ll ohogol olyol 57 A h of h h w uz h glly h u of ll ohogol olyol h g y h ffl uo Alo h A B C D E oog o h uo of o u h h Th followg l how h Tl K Noo A B C D E If - If L w w If H w v / w w v M w / v w v w v 5 N w w w 6 J * * * * * wh * * * * * Moov h followg l how h gl o of h l uh hf ohogol olyol h wgh fuo of olyol o If ohogoly vl h uo oog o h wgh fuo flly h oo of : hf olyol v H w w * I w v Tl Wgh fuo K Ivl Duo oo v w If Nol w v R < w v T lg w v R W < / Glz T w v R R w [ G w > > w v [ < / lg > w > v > [ < / w Iv g w > If [ ] > > B J L w w M v 5 N w 6
ll ohogol olyol 58
Ch 5 A Glzo of u -uo fo h Vwo of l uo 5 Iouo u -uo h fou vou lo hl O of h o of h -uo o ovg o h ol uo h u of l o fy I h h y ug Cuhy gl w ou glzo of h -uo fuo wh fou f how h ovg o h ol uo g W ov ohv of hl o of h w uo Moov h h -uo h lo loh wh h -uo w lo ou glzo of h -uo ov h ovg o h h-u uo h u of l o fy H w ou uo g wh h o ffl uo wh l fo oo wh 5 : W W 5 whh ly o wh ll ohogol olyol f h wgh fuo W [56] Th oluo of uo 5 W W 5 wh ll l Th vl l u- of 5 O of h h B uo whh uully y h gl wh L L l fuo C L L 5 ol u C o oou [6] Th Eul Cuhy gl [8] wo o ul of B y gl whh of u l h Th Eul gl gv y 5 R > R > > >
A glzo of u -uo 6 whl h Cuhy gl y h foul π 55 whh R > R > R > No h oh lo 5 55 o h G fuo Th lo 55 ul ool o ou o ff loog f gl o h uo w u h lo R 56 whh w h ol lf h of h l gh h Couly w hv 57 Now f 57 uu h h gl 55 hg ow 58 π Th ov gl ly y ol o ou glzo of h -uo 5 A glzo of h -uo [] Th u -uo [69 7] hvg h oly y fuo f / T < < N 59 π / h o of h o o uo h lg ol of ol oulo Aog o ho hl f X vly h vlu v of oh l wh h z of ol oulo hvg h vlu μ v σ h h o X μ vl T h h oly y fuo 59 wh g of / fo [7] Th ho u h of hyoh vl o hoy wh h z of h l ll fo l h
A glzo of u -uo 6 Now y ug 58 o h f of h -uo To o h w uu 58 o g π 5 h gh h of 5 v fuo wh o h vl w l oo g ogly 5 λ λ λ λ π Th ov gl u o glz 59 5 T λλ λ λ λ λ π wh < < N ol u λ λ No h λ λ y oo fo 5 u h oly y fuo u lwy ov Alo o h h olzg o λ λ π / of 5 l u h oog g l fuo o I l h fo 5 h uul -uo v Moov fo h olzg o of uo 5 ul o h olzg o of h -uo Th f ov y lyg h Lg ulo foul [8] z z π z 5 z Bu og o o of h ho lg hoy T ovg o h f of h ol uo N [6 7] h l T N 5
A glzo of u -uo 6 H w o how h h lo vl fo h glz uo T λ λ To ov h l w u h o ovg ho DCT [] o h l u of fuo λ λ λ λ 55 o vy N o fful o h π R 56 λ λ λ λ O h oh h w hv 57 l λ λ λ λ h o ovg ho h f fo ouou gl fuo g w hv f g h l f l f 58 y og h l lo 57 w o 59 l T λ λ λ λ / λ λ / λ λ λ λ l / / / l / / / π N R Tg h l o oh of 5 yo lo o fo h G fuo h followg y y 5 π l To ou h vlu of h uo gv y h f 5 uff o o h f gl
A glzo of u -uo 6 π 5 whh gv h vlu of 5 λ λ E [ T] λ λ 5 O h oh h E [ T / ] ly ou f o lulo w g fo h v u of 5 λ λ V [ T ] E [ T ] E [ T ] 5 λ λ I vlul o o ou h 5 5 gv h vlu v of h uul -uo vly Bu ow h h -uo h lo loh wh h h - uo [56] f y f 5 / / / N < < / / wh 5 I oh wo w hv T 55 By fg o h ov lo h f h h -uo w glz y lo 5 ow ul o glz h f of h -uo 5 follow 56 λ λ B λ λ wh λ λ 56 B o 56 h uul -uo f 5 Aog o h followg ho h glz fuo 56 ovg o l of h G uo [7] f y G > < < 57
A glzo of u -uo 6 Tho If h G uo gv y 57 h w hv l λ λ G χ wh χ o h f of h h-u uo oof L u f h u λ λ λ λ I y o how h π λ λ λ λ [ N 58 λ λ λ λ l / 59 Thfo og o h DCT w hv 5 l λ λ G l / λ λ / / l λ λ / Moov o fful o how h λ λ T λ λ 5 5 o ul u- of h glz uo I h o w o uy o y y u- of h glz uo 5 56 5 A y glzo of h -uo h λ λ / If h l λ λ / o 5 h 5 T T o π y glzo of h oy -uo whh
A glzo of u -uo 65 Th uul f of h -uo ovouly v y 5 No h og o h Lg ulo foul w wll h h olzg o of h -uo f o 5 I oh wo w hv / π / 5 π / Alo o h h h glz uo 5 u log o [-] u h oly y fuo u lwy ov hfo π π w ough o hv o / O h oh h fo θ w hv oθ hfo o ov o / uff o how h π π [ ] R N 5 o h uo l u f h u U o g 55 π π U / > [ U U ] [ U U ] [ ] π π Now f w h u U o log o [ ] l h w u hv whh ov 5 Th followg fgu lfy h fo [ ] [ ] h vl - gu : / gu : g how h f T / wh olzg o 5 / 8 g 5/ how h o-ov fuo T / π / o / h vl A h ov fgu how h glz uo 5 y T T R 56
A glzo of u -uo 66 Moov og o 5 5 h vlu v of uo 5 h fo E [ ] V[ ] 57 Clly h lo gv h vlu v of h - uo Tho T ovg o N oof If h u o o h o how h o R 58 Couly w hv o / / l T l o / / l o / / / l o / / / N 59 By fg o 56 w ow f h glz -uo oog o h f gv u- follow 5 B o wh o B π / / θ o θ o θ θ 5 Tho ovg o h h-u uo oof W f h u o o g [ N < 5
A glzo of u -uo 67 H og o DCT w f ou h / l l G 5 / / / I o fful o vfy h h glz uo T l o h oh follow T 5 R H goo oo o u o vou h h h wgh fuo of ohogol olyol M oo o h oy - uo uh h f o h gl v h oo o h uo 5 A y glzo of h -uo h λ Ag l u o o h h o h wgh fuo of f ohogol olyol J 5 W < < wh ll l Th fuo u- of h o uo 5 u h logh vv of 5 ol fuo o ov f N l 5 h W N R 55 O h oh h w hv π / π / θ π / θ θ o θ 56 o θ θ π / π π! / 57 Thfo y glzo of h -uo y f
A glzo of u -uo 68 TA K < < N R 58 wh K /! π π 58 Th uo 58 wh olzg o gv y 58 w f [] o h ul oh Bu w ll ofy lfy To o h w λ 5 o g TA π 59 whh l o fo h y uo 58 o h l uo w lly hv TA TA 59 Th yy of uo 58 o 59 how y g fo f vlu of gu : gu : Aog o 58 58 h l fo of h wo o fgu hv vly h fo 5 5 g : TA 6 oh π / 5 g : TA h π / Now h followg A o A5 oll h o of h y uo 58 o 59
A glzo of u -uo 69 A Th vlu v of 59 vly y E [ ] V[ ] 55 h lo gv h vlu v of h -uo A T A ovg o N Th oof l o h f f o hoo λ λ h f u λ λ A By h fo 56 og h λ w f λ D 55 R N < < wh 55 π / / θ o D θ θ θ A ovg o h h-u uo Th oof l o h oof of Tho wh λ λ A5 Th uo l o h oh y T A T 55 A R Th oh y glzo of h -uo wh w λ λ 5 I f gv 55 T λ λ T λ λ oh π Thfo h of h h w f o h h followg ul u- of h gl uo 5: λ λ / y λ y λ λ y
A glzo of u -uo 7
Ch 6 A g olyol oluo fo h ffl uo of hygo y u of ohogol olyol l o 6 Iouo I h h w wll g foul fo h olyol oluo of h wll-ow ffl uo of hygo y y y y how h ll h h f ll ohogol olyol fl wll h f ohogol olyol fl vg h f l of h v olyol u [] W wll lo o gl o of h o u o h uo w houl o h ffl uo σ y τ y λ y 6 whh fo σ olyol of g o τ olyol of g λ h gvlu g o uo h h olyol oluo of 6 o y o f v h h o o uo 6 olyol oluo I 99 Boh [] lf h olyol oluo of 6 how h h oly olyol y u o l hg of vl g gfuo of h ffl uo 6 lo [] Jo olyol { } { } Lgu olyol L } { } { { H } H olyol Bl olyol { B } { } Th 988 Nfoov Uvov [56] gv o gl o of uh gg fuo fo h olyol Cuhy gl o
A g olyol oluo fo h hygo ffl uo 7 o o of h gv σ τ Of ou h oh o h Rogu o of h olyol o l fo h h w wll o h h o oh oh h g [ 7] Bu fo vg g oluo fo 6 w houl ou lg y whh y o ov u o 6 A lg y If C l u h C C C 6 o f w! C uh h h w g 6 wh! o h glz hygo fuo of o g [] Ch No h o ou h lo 6 w hv glly u h wo R Z 6 A g l fo 6 wh I h w hv 65 whh og o Gu y ou h foul 8
A g olyol oluo fo h hygo ffl uo 7 lf o 66 Th f y of 66 fou [] 56 h o y 66 l of [] 57 fo g u Now goo oo o oou h ho of fg g olyol oluo fo uo 6 6 Th Tho Th o olyol oluo of h ffl uo y y y Z 67 gv y h foul G y 68 wh G / o h uly y l oo gv 68 h fo G G l whh vl fo lg o lly fo 68 fo o l
A g olyol oluo fo h hygo ffl uo 7 oof Co h ffl uo 67 uo h wll hg o H y y y 69 If / u 69 h ± 6 Thfo 69 lf y ± y y 6 O h oh h uo 6 l of h Gu hygo ffl uo g [] 6: y y γ y 6 ± fo / γ vly o y og -g oluo of 67 og h lo 6 6 w u hv 6 / ± K ± ± 6 lo w of h vl o h w hv 6 K / ± ± o 6 wo followg u- olu 65 K * /
A g olyol oluo fo h hygo ffl uo 75 / ** K No h oh ov lo oly ff y u g h gu of h o foul whh o o ff o h ffl uo 67 I oh wo f w o h w wll h h o foul of 65 Thfo oly h foul u o h oluo To ou ** K uff o o h lg off of oog o foul whh gv y / /! ** K 66 Bu og o y 6 67 o y og h oluo 65 ug 68 67 hg o 69 / / lfyg h lo uug ** K y 66 flly gv h o
A g olyol oluo fo h hygo ffl uo 76 olyol oluo of uo 67 h fo 68 H h f of h ho ov To u h lg wh o houl u h l lo l h followg y 6 whh l of y 6 fo! C H w woul l o o ou h h gl foul G ul ool o ou h off of fo y f g y If fo l h off of h g olyol h ough o lul h G Δ Δ Δ Δ Δ Δ Δ Δ Δ Δ 6 whh Δ No h h ov lf lo ll f o y vlu lug zo y o f ou h h oh vlu o oh vlu 68 vh ogh Af lfyg G fo w vully g 6 Th ov lo l h 6 Moov 6 how fo l h f h 6
A g olyol oluo fo h hygo ffl uo 77 6 A l of h g olyol 68 I h ul l u ly h Gu y g u h 68 Th uo l h If h followg l fo h g olyol 68 v 6 / / / / / / / / / / / uho f o o o h Nfoov Uvov oh o h ffl uo 67 lf-jo fo h og o h h Rogu o of gv y 6 ρ ρ wh ρ Now f w uo h lo f o 6 w g 6
A g olyol oluo fo h hygo ffl uo 78 / / / / 6 o fuh o of h olyol 68 6 A l hg of vl Ug h o 6 o v l hg of vl fo h o olyol lly Aug w v h o lo hg o 65 w w wv w v v ρ w v w v ρ w v O h oh h ρ w v lf ρ w v w v w v w v v ρ w Thfo 65 fo o w v w v w v w v 66 w v w w v w 67 w v w v v whh how h ff of l hg of vl o h olyol 68 o f w v 67 h w hv 68 6 A g h- u uo Th o foul of 65 ul lo o ou h u uo of h g olyol 68 I oh wo l log wh vou
A g olyol oluo fo h hygo ffl uo 79 of h Gu hygo fuo fo gg u lo o l h followg y hol fo h fuo [8] 69 By ug h foul 65 off 66 f o u 69 h 69 h f o ouo o flly g 6 whh o h o olyol of 68 h l vlu gv o oh oh o 6 [5] [5] 6 A g foul fo h o u vlu of h olyol L ] [ U L ohogoly vl whh fo f fl of ou o of h zo of σ o ± By ug h Rogu o of h olyol 68 w hv / U L U L ρ ρ 6 Couly gg y fo gh h of 6 yl! U L 6
A g olyol oluo fo h hygo ffl uo 8 65 l of h g olyol 68 ll ohogol olyol A w o h fo h uo 6 o l u of ohogol olyol o h l l Jo Lgu H olyol h of h whh fly ohogol h oh o fly ohogol fo o vlu of I h o w o u h vou g foul o h o of h of h u 65 Jo ohogol olyol If l 68 h!! 6 h Jo ohogol olyol wh wgh fuo ρ 6 ohogoly lo 65! δ Th olyol lo 66 whh o of h ow hygo o fo h Jo olyol g [] [7] h Ggu ulhl Lg Chyhv olyol of h f o ll l u- of h Jo olyol h followg o ghfowly olu fo h Ggu olyol: 67 /!! C λ λ λ λ λ λ Lg olyol:
A g olyol oluo fo h hygo ffl uo 8!!!! 68 Chyhv olyol of f : / T 69 Chyhv olyol of o : / U 6 65 Lgu ohogol olyol If o u 68 h L!! 6 h Lgu ohogol olyol wh wgh fuo ρ 6 ohogoly lo!! L L δ 6 65 H ohogol olyol If l 68 h H 6 h H ohogol olyol wh wgh fuo ρ 65 ohogoly lo! H H δ π 66
A g olyol oluo fo h hygo ffl uo 8 65 ll ohogol olyol wh wgh fuo W o [ Aog o h oh l h o f o ou h W logh vv of h gv wgh h y fg o W h o ffl uo o vly g 67 I [5] h fly of h y of olyol ll Roov-Jo olyol lo [65 5] I [] h l olyol o y M fo whh w g 68 M N Alo w how h o h f { M } ohogol wh o h wgh fuo W o [ f oly f > > N L u h o ou h o u vlu of h olyol o lo u h gl lo 6 Aog o h fo lo w hv! Thu og 68 yl 69 M!!!! 65 655 ll ohogol olyol wh wgh fuo / W o [ W If h fo g h h v W 65 I [5] h olyol of h y ll Roov-Bl olyol I [] h olyol o y N fo whh w hv
A g olyol oluo fo h hygo ffl uo 8 N 65 Moov h o w how h h f N N } { ohogol wh o h wgh fuo W o [ f oly f > N Nvhl ug h gl lo 6 hl u o h o u vlu of h olyol follow! 65 Couly h ol ohogoly lo h fo 65 fo!! < N N N δ 656 ll ohogol olyol wh wgh fuo D C B A D C B A D C B A W o l o h wo vou y oug W W w g h CD AB BC AD C A D B CD AB C A 655 I [5] h olyol of h y ll Roov-uo-Jo olyol I [9] h l olyol o y D C B A J fo whh w hv C A D B C A BC AD C A BC AD CD AB D B CD AB C A CD AB BC AD C A C A D C B A J 656 66 How o f h f l of h wgh fuo gv?
A g olyol oluo fo h hygo ffl uo 8 l o h h o y o f ou h h wy fo fg o ou h logh vv W / W h ρ h wh L u lfy h uj y o ρ l gv low El Co h wgh fuo W < < If h logh vv of h wgh fuo ou h w g W W Couly h l o ohogol olyol No h h olyol ohogol wh o h gv wgh fuo o [] fo vy vlu Thfo o y o ow h h olyol h hf Jo olyol o h vl [] hy lly y h g olyol 68 El Th wgh fuo W < < gv Thu W 8 8 W h l o ohogol olyol 8 8 Th olyol fly ohogol fo 9 u og o h 9 w u hv N { } < / H h f { 8 8 } ohogol wh o h wgh fuo o El Co h wgh fuo W θ < < θ R Th w hv W θ θ W θ whh gv h l o ohogol olyol fo vy vlu El o h wgh fuo W 8 < < whh l of h o of h B uo w hv W W 5 6
A g olyol oluo fo h hygo ffl uo 85 6 Thfo h o ohogol olyol fo u og o 6 h < 8 / Th h h f { 6 } ohogol wh o h wgh fuo 8 / o [ 67 A g foul fo h vlu h ouy o of o ll ohogol olyol [] I h vou o of h h w fou g foul fo h olyol oluo fl of h wll-ow ffl uo 6 Now h o 68 w o o oh uh foul whh l u o g foul fo h vlu of o ll ohogol olyol h ouy o of fo o h gol w houl g u h gl fo of h Rogu o of h olyol 6 ll oog wgh fuo ρ Whou lo of gly l u uo h θ θ whh θ θ 657 I h gl θ θ 657 h ouy o of h ulyg vl fo h oog ll ohogol olyol Th h f θ θ f ul h olyol of h Bl y f oh θ θ f u ff fo h oh h olyol of h Jo y wh f o of h vlu o ± h olyol of h Lgu y flly f oh vlu ± h h olyol of h H y Th lo 657 l h h wgh fuo lf wh R o ρ R θ A θ B 658 A B 659 No h h lo 658 follow u h logh vv of h fuo * A B W θ θ ul h logh vv of h wgh fuo
A g olyol oluo fo h hygo ffl uo 86 u v u Rv 66 u v o 658 vl O h oh h og o 6 h Rogu o of W W o f 658 l o h ov o h R θ θ θ θ A B A B R θ θ 66 A B θ θ / θ θ A B Bu og o h Lz ul f g f g 66 w hv 66 θ θ A B A B A B θ θ H 66 lf 66 / Th f oh gl o fo h olyol oluo of uo 67 Cog 68 66 w g ghfowly 665
A g olyol oluo fo h hygo ffl uo 87 Δ Δ Δ Δ Δ / Δ Δ Δ / wh g Δ Rlo 66 lo of h hygo fo 666 θ Δ Δ θ / θ Δ wh θ θ f y 657 Of ou h hygo o ll lf To lfy 666 w u h hygo y 667 whh w u ly 67 wh h ff fo If w hoo ul 668 θ θ h y 667 lo 666 669 B A Δ B θ / B A O h oh h ug Gu y 669 fuh lf / 67 /
A g olyol oluo fo h hygo ffl uo 88 whh h fo h f foul of 65 uho h y λ λ λ 67 λ λ λ lo vl fo λ h lo 67 ough h fo of h o foul of 65 oo 67 Vlu of h ll ohogol olyol h ouy o Ug h l o fo h o ll ohogol olyol w ow ou h g vlu of h olyol h ouy o of fo θ θ vly If w h o foul of 65 h θ θ 67 67 vly Thfo w g / / θ 67 / / / θ / 675 o l y og h o 65 fo h o Jo ohogol olyol w hv Couly 67 675 yl 676 677 Moov y og h o 65 fo h o Lgu olyol L wh w hv Thfo ju o oo θ θ v y oug h oog l o g
A g olyol oluo fo h hygo ffl uo 89 L 678 uho h H olyol w of h Lgu olyol g [] lo 5 w lo olu h H! 679 /! lly fo h Bl olyol B wh w hv o f oug h oog l o o h B 68
A g olyol oluo fo h hygo ffl uo 9
Ch 7 Alo of ol ll ohogol olyol fo l ouo of v Ll fo 7 Iouo I h h 6 w how h fo h hygo ffl uo f f l of ohogol olyol oul I h h w f ly h Mou fo z R fo h o uo o g h ll ohogol olyol wh gv ow Th w how h h g ol ohogol olyol vy ul ool o ou h v Ll fo ly wh o ol lulo fo fg h oo I h wy y lyg f f ol ll ohogol olyol w fo l h o of o o lly o h v Ll fo To o h w houl g o h hygo ffl uo y y y 7 uo h hg o z R Thfo h uo 7 vully l l y l l l y l l y 7 l wh l l l l l l ov g Ovouly o of h oluo of uo 7 ol gv ow l l olyol l h o h l l l l l l l l vly Aog o h u-louvll ho o f wgh fuo oog o h ffl uo 7 l l l l l l W l l l l l l l 7 Now u h [ L U ] ohogoly vl o w houl hv
El ouo of v Ll fo ug ol ll ohogol olyol 9 U L A l l l l l l l l l l l l l l l W δ 7 wh U L l l l l l l l l l l W A 75 o h o u vlu Th oog o h uo 7 h ohogol fo o f vlu of l l l l l A h oo w uo 7 7 Mou fo z fo ff vlu of o l f o h h ol Jo olyol f 76 o h fo vly gv 77 h ohogoly lo of Jo olyol ow h ohogoly lo of wll lo ow 78!!!! > > δ Moov h ffl uo of y l of h uo 7 fo l l l l l w hv y y y 79 lly o o h Mou fo of oh fv l of ol ll ohogol olyol H o o l of h h ju w o h ll ffl uo of h fo u howv h l of 7 o h ol Lgu ohogol olyol L L f
El ouo of v Ll fo ug ol ll ohogol olyol 9 y y y 7 wll h ol H ohogol olyol H H f y y y 7 7 Evluo of Iv Ll Tfo ug ol ll ohogol olyol [8] I wll ow h h Ll fo ov owful ho fo lyzg h l y Howv y hyl ol l o Ll fo who v o ly of ul fuo Bu of h ol v h hv o o h lo u o ow o l Ch llh [] hv ou v Ll fo of l of o-ol fol fuo Ev Chug [] hv o Ll fo vo ug ol oou h ol l lo [7] Il [] h loo o gg h ou ho fo ouo of Ll fo vo Th ol of v wo- Ll fo fo oly y fuo h y Tgl 998 [7] uho h ol of ul vo of Ll fo h u y vl uho o l Cuh Vloh [9] hv v ho fo h ul vo of Ll fo I [6] Dog h ou gulzo ho fo h uo I [] Cu h u ou oo lo [9] whl Mll Guy [55] hv u Jo olyol [68] h l wow fuo fo Ll fo vo lly wo [6] goo loghy h g h o f o Bu wh h v Ll fo u fo y vlu of h vl ov o o h v o of of lly fuo ou o h lul y olvg y of uo whh u o gul y f o hoo o u ohogol olyol uh ho ug ohogol olyol gv o vluo of h vo gl ug Gu uu h ol l [66 58 59 67] Of ou h hf vg of h ho h y of fg ll oo l ol of olyol of hgh g of h lulo of of ol Choffl u [7 9] H w wh h o h h ohogol olyol wh gv ow u ul ool o ou h v Ll fo whou y ffo fo fg h oo of ohogol olyol To hv h gol w houl u h ohogoly o of ol ll ohogol olyol ou o 7 I h wy w h o fo l ouo of Ll fo vo 7 Iv Ll fo ug ol Jo ohogol olyol L u o h Ll fo ogh wh v 7
El ouo of v Ll fo ug ol ll ohogol olyol 9 ] [ ] [ > L f f f L λ λ π By fg o h vou o w f l oluo of h ov gl uo ov h ow l y og 78 w lly hv!!!! δ 7 Now l fy h Dhl oo A C 7 By lyg h oy 7 h o 7 h off C fou!!!! C 75 O h oh h g h v Ll fo fo h uly 7 yl ] [ ] [ L C L f 76 Moov og o h fo 76 w hv! ] [ ] [ L L δ 77 whh L f ε ε δ uh h > ε ε ε ε f / h D fuo Couly h l 78!!!!!!!! f δ δ
El ouo of v Ll fo ug ol ll ohogol olyol 95 oluo fo h gl uo 7 No h h fo oluo vl f oly f f gl ovg 7 l fuo u h Dhl oo Th fuo h gh h of 78 ly f wgh uo ol fo ouo of f gl 78 o [ H f h uo hg oh oluo wll Th o wll fy h uj 7 Iv Ll fo ug ol Lgu ohogol olyol L l u f h u L L! 79 h f h ohogoly lo L L!! δ 7 If h o A L C 7 o h y lyg 7 7 h off C wll v!! L C 7 Thfo w lly hv ] [ ] [ L L C L f 7 O h oh h L L L ] [! ] [ 7 o vully h l!!!!! L f δ δ 75 oluo fo h Ll fo vo Ag w o h 75 vl oly f f gl ovg h fuo l
El ouo of v Ll fo ug ol ll ohogol olyol 96 u h Dhl oo I lo 75 h fuo / f wgh uo o [ Bu y og h o 7 f ol ll ohogol olyol lo l fo o ouo of v Ll fo u h fuo y h fly oly o l oo o o h o l f w f h u M M! 76 h f h ohogoly lo M M!!!! δ 77 wh } { M N N > > h y og h oo < N A M C N N 78 lyg 77 o 78 w g!!!! M C 79 Thfo N M L C L f ] [ ] [ 7 whh L M L ] [! ] [ 7 H 7 N M f!!!!!!!!! δ δ o oluo fo h gl uo ] [ f L H w h h vo ol lo oou fo h gv ow olyol
El ouo of v Ll fo ug ol ll ohogol olyol 97 J H N lly I ow goo oo o wo l l h wy 7 l l of o 7 El L u o l of ol Jo olyol fo / Th f y o o T 7 ll h ol Chyhv olyol of h f [7] By og h o 78 l u lo uo h fo Th l h h gl of 78 lf / / /!!!! / / π π Thfo h v Ll fo fo h gv h fo! /! /!!!! L δ π π δ Clly h ov lo vl f El o h l w u h ly o 75 o h uo f L ] [ π To v h oluo of h gl uo f w hv o vlu h f gl oog o 75 H w hv 5/ / 8 5/ 5/! 5 7 L π π π π
El ouo of v Ll fo ug ol ll ohogol olyol 98 No h fo h l gl w hv u g h wll-ow Gu y Couly h o 75 fo o!! 5/ / 8 5/ L δ δ π π Th ov lo hol f oly f > Z
Ch 8 o fuh l fuo h lo 8 Iouo I h h w wll ou o w l of l fuo uy h lo h ll uo of l hy 8 Alo of zo gvlu fo olvg h ol h wv uo ug u of l fuo [5] I h oluo of ouy vlu ol uully zo gvlu go Th lo h lulg h gvlu of o h w woul of l o f h ozo oluo of h l y A X λ X wh λ Bu o h oh h λ l h A fo X h h of A u l o g Th oh fo h ouy vlu ol lly I oh wo f l o of h g of uo l o h ol o zo h o of h oluo wll f v By ug h o w ou l of l fuo ly fo h ol h wv uo hl oo H l u f f h followg u z z C z z oh l z 8 z z z z h l z wh z ol o l fuo ov g u I o fful o vfy h oh of f u fy uu o o ffl uo h fo z z z z y z z z y y 8 ov h z z Couly w l wh oly o l of l fuo whh f h oluo of uo 8 Th fuo C z z z z hv vl o u- h uful o uy u- h Chyhv olyol f o hoo z o z 8 u h wll-ow Eul y I h h followg u wll
o fuh l fuo h lo C z o z o o z T z z o z A o z z U z 8 wh T z & U z o h f o of Chyhv olyol Moov f h l z l 8 h ffl uo of h f of Chyhv olyol v z y z y y 8 Th o l h ol Chyhv fuo h g y z o z Thu fo h l w hv C z o z o o z z o z o z 85 I h wy lg h l z 8 yl o z z z z z o z z z z z z z o z z o z z 86 Thfo h fuo 85 vully fy z y z z y y 87 I houl o h h l fo of h l fuo C z o z z o z 85 oul v y h Mov foul I oh wo l u uu θ o h Mov foul o g o o o 88 Couly w hv [ / ] C o / T [ / ] o / * U * 89
o fuh l fuo h lo * * I how h h ov ol Chyhv fuo T U ohogol wh o h wgh fuo W o fy h followg ohogoly o vly f * * T T π f π f 8 * * U U f π f H wohy o o ou h J Boy 987 [] l h ol fuo * / / T / o h vl [ l ho w houl h o h h fuo oul v oly y lg z o z 8 Bu o f h vg h h Lg o Ao Lg ffl uo ou h uo 9 y y y 8 h h oluo C oo follow h g h o Lg fuo h g h Lg olyol h u o h l uo y y whh h h oluo y l o fouh whh ff fo ov o o z houl olv To f h oluo of fouh w uu z z 8 o v h ffl uo z y z y y 8 z Clly 8 f of 8 fo Aog o 8 h oluo of h uo vly z C z z z z z z z z z z z z z 8
o fuh l fuo h lo H l u l h h o fuo vy l h Hlholz uo hl oo h o I oh wo f h uo U θ Φ U θ Φ o vl oy uo h o of h uo h fo y θ y θ 8 θ θ θ θ whh uvl o uo 8 fo oθ H f z oθ o z 8 o uvlly z 8 h l of 8 fo y o z y y 85 z h h followg oluo z z z C z 86 z z z z Th u wll fuly h gv ol of h o 8 Alo of f fuo 86 h oluo of ol h wv uo hl oo Uully o of h ouy vlu ol l o h wv h ol uo hl oo u o h Hlholz l ffl uo U θ Φ U θ Φ Bu fo h l of h lo w hv U U U θ o θ U θ U θ Φ 87 whh ow h ol Ll uo hl oo Now f h l vl uo 87 U θ Φ R A θ B Φ h h followg oy ffl uo wll v R R λ R B λ B 88 λ A o θ A λ A θ A w h oluo of Ll ol uo glly wh h ouy oo ow vhl f 88 λ λ
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