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◆●❍■➊◆ ❈Ù❯ ❈⑩❈ ❚➑◆❍ ❈❍❻❚ P❍■ ❈✃ ✣■➎◆ ❈Õ❆ ❚❘❸◆● ❚❍⑩■ ❍❆■ ▼❖❉❊ ❑➌❚ ❍ÑP P❍❷◆ ✣➮■ ❳Ù◆● ❚❍➊▼ ❇❆ ❱⑨ ❇❰❚ ▼❐❚ P❍❖❚❖◆ ❚✃◆● ❍➬ ◆●➴❈ ❚❘❯◆●✱ ❚❘×❒◆● ▼■◆❍ t ỵ rữớ ữ ❤å❝ ❍✉➳ ✯❊♠❛✐❧✿ tr✉♦♥❣♠✐♥❤❞✉❝❅❞❤s♣❤✉❡✳❡❞✉✳✈♥ ❚â♠ t➢t✿ ❇➔✐ ❜→♦ ♥➔② tr➻♥❤ ❜➔② ♠ët ♥❣❤✐➯♥ ❝ù✉ ❝õ❛ ❝❤ó♥❣ tỉ✐ ✈➲ ❝→❝ t➼♥❤ ❝❤➜t ♣❤✐ ❝ê ✤✐➸♥ ❜➟❝ t❤➜♣ ✈➔ ❜➟❝ ❝❛♦ ❝õ❛ tr↕♥❣ t❤→✐ ❤❛✐ ♠♦❞❡ ❦➳t ❤ñ♣ ♣❤↔♥ ✤è✐ ①ù♥❣ t❤➯♠ ❜❛ ✈➔ ❜ỵt ♠ët ♣❤♦t♦♥ tê♥❣✳ ❑➳t q✉↔ ❦❤↔♦ s→t ❝❤♦ t❤➜② tr↕♥❣ ♥➔② t❤➸ ❤✐➺♥ t➼♥❤ ❝❤➜t ♥➨♥ tê♥❣ ❤❛✐ ♠♦❞❡ ♥❤÷♥❣ ❤♦➔♥ t♦➔♥ ❦❤ỉ♥❣ ❝â t➼♥❤ ❝❤➜t ♥➨♥ ❤✐➺✉ ❤❛✐ ♠♦❞❡✳ ❑❤✐ ❦❤↔♦ s→t sü ✈✐ ♣❤↕♠ ❜➜t ✤➥♥❣ t❤ù❝ ❈❛✉❝❤② ✲ ❙❝❤✇❛r③✱ ❝❤ó♥❣ tỉ✐ ♥❤➟♥ t❤➜② tr↕♥❣ t❤→✐ ♥➔② ❤♦➔♥ t♦➔♥ ✈✐ ♣❤↕♠ ❜➜t ✤➥♥❣ t❤ù❝ ❈❛✉❝❤② ✲ ❙❝❤✇❛r③✳ ❍ì♥ ♥ú❛✱ ❦❤✐ ♥❣❤✐➯♥ ❝ù✉ ❝→❝ t➼♥❤ ❝❤➜t ♣❤↔♥ ❦➳t ❝❤ò♠ ❤❛✐ ♠♦❞❡✱ ❦➳t q✉↔ ❦❤↔♦ s→t ❝❤♦ t❤➜② tr↕♥❣ t❤→✐ ❤❛✐ ♠♦❞❡ ❦➳t ❤ñ♣ ♣❤↔♥ ✤è✐ ①ù♥❣ t❤➯♠ ❜❛ ✈➔ ❜ỵt ♠ët ♣❤♦t♦♥ tê♥❣ t❤➸ ❤✐➺♥ t➼♥❤ ❝❤➜t ♣❤↔♥ ❦➳t ❝❤ò♠ ð ♠å✐ ❜➟❝ t❤➜♣ ✈➔ ❝❛♦✱ tr♦♥❣ ✤â ❜➟❝ ❝➔♥❣ ❝❛♦ t❤➻ ❝➜♣ ✤ë ♣❤↔♥ ❦➳t ❝❤ị♠ ❝➔♥❣ t❤➸ ❤✐➺♥ ♠↕♥❤ ❤ì♥✳ ❚ø ❦❤â❛✿ ◆➨♥ tê♥❣ ❤❛✐ ♠♦❞❡✱ ♥➨♥ ❤✐➺✉ ❤❛✐ ♠♦❞❡✱ sü ✈✐ ♣❤↕♠ ❜➜t ✤➥♥❣ t❤ù❝ ❈❛✉❝❤② ✲ ❙❝❤✇❛r③✱ ♣❤↔♥ ❦➳t ❝❤ò♠✳ ✶ ●■❰■ ❚❍■➏❯ ❱✐➺❝ t↕♦ r❛ ❝→❝ tr↕♥❣ t❤→✐ ♣❤✐ ❝ê ✤✐➸♥ õ ỵ rt q trồ t ố ợ ♥❣➔♥❤ ❦❤♦❛ ❤å❝ ❧÷đ♥❣ tû✱ ✈➻ ❦❤↔ ♥➠♥❣ ù♥❣ ❞ư♥❣ ú ỷ ỵ tổ t ữủ tỷ ữ t➠♥❣ tè❝ ✤ë tr✉②➲♥ t❤æ♥❣ t✐♥✱ t➠♥❣ t➼♥❤ ❜↔♦ ♠➟t✱ ỗ tớ t t tr t❤ü❝ ❝õ❛ t❤æ♥❣ t✐♥ ❬✶❪✳ ❇➯♥ ❝↕♥❤ ✤â✱ ❝→❝ tr↕♥❣ t❤→✐ ♥➔② ✤÷đ❝ ♥❣❤✐➯♥ ❝ù✉ ✤➸ →♣ ❞ư♥❣ ✈➔♦ ♥❤✐➲✉ ❧➽♥❤ ✈ü❝ ❦❤→❝ ♥❤÷ q✉❛♥❣ ❧÷đ♥❣ tû✱ ❦ÿ t❤✉➟t ❧÷đ♥❣ tỷ t ỵ t r tr t ♣❤✐ ❝ê ✤✐➸♥ ♥❣➔② ❝➔♥❣ ✤÷đ❝ ♥❤✐➲✉ ♥❤➔ ❦❤♦❛ ❤å❝ t✐➳♣ tư❝ ♥❣❤✐➯♥ ❝ù✉ ✈➔ ♣❤→t tr✐➸♥✱ ✈ỵ✐ ✈✐➺❝ ♥❣❤✐➯♥ ❝ù✉ ❝→❝ tr↕♥❣ t❤→✐ ♣❤✐ ❝ê ✤✐➸♥ ♥❤÷ tr↕♥❣ t❤→✐ ♥➨♥✱ tr↕♥❣ t❤→✐ ❦➳t ❤ñ♣ ✤è✐ ①ù♥❣✱ ♣❤↔♥ ✤è✐ ①ù♥❣✳ r r t ỵ tữ ✈➲ tr↕♥❣ t❤→✐ ❦➳t ❤ñ♣ t❤➯♠ ♣❤♦t♦♥ ❬✸❪✱ s❛✉ ✤â ữủ t ỵ ự st ❬✹✱ ✺❪✳ ◆❣♦➔✐ t❤➯♠ ♣❤♦t♦♥ ❝á♥ ❝â ❜ỵt ♣❤♦t♦♥ ✈➔♦ ❝→❝ tr↕♥❣ t❤→✐ ❦➳t ❤đ♣ ❝ơ♥❣ ✤÷đ❝ ♥❣❤✐➯♥ ❝ù✉ ❬✻❪ ✈➔ ❝❤♦ r❛ ✤í✐ ❝→❝ tr↕♥❣ t❤→✐ ♣❤✐ ❝ê ✤✐➸♥ ♠ỵ✐ ❦❤→❝✳ ❱✐➺❝ ♥❣❤✐➯♥ ❝ù✉ t➼♥❤ ❝❤➜t ❝õ❛ ❝→❝ tr↕♥❣ t❤→✐ ♣❤✐ ❝ê ✤✐➸♥ t❤➯♠ ✈➔ ❜ỵt ♣❤♦t♦♥ ❧➔ ✈✐➺❝ ❤➳t sù❝ q✉❛♥ trå♥❣✱ ❦❤æ♥❣ ❝❤➾ t↕♦ r❛ ❝→❝ tr↕♥❣ t❤→✐ ♣❤✐ ❝ê ✤✐➸♥ ♠ỵ✐✱ ♠➔ ❝á♥ ♠ð r❛ ♥❤✐➲✉ ữợ ự ợ ứ ❦➳t q✉↔ t❤✉ ✤÷đ❝✱ ♥❣÷í✐ t❛ ù♥❣ ❞ư♥❣ ❝→❝ tr↕♥❣ t❤→✐ ♥➔② ✈➔♦ ❝→❝ ♥❣➔♥❤ ❦❤♦❛ ❤å❝ ❚↕♣ ❝❤➼ ❑❤♦❛ ❤å❝✱ ❚r÷í♥❣ ✣↕✐ ❤å❝ ❙÷ ♣❤↕♠✱ ✣↕✐ ❤å❝ ❍✉➳ ■❙❙◆ ✶✽✺✾✲✶✻✶✷✱ ❙è ✸✭✺✺✮✴✷✵✷✵✿ tr✳✹✵✲✺✵ ◆❣➔② ♥❤➟♥ ❜➔✐✿ ✺✴✽✴✷✵✶✾❀ ❍♦➔♥ t❤➔♥❤ ♣❤↔♥ ❜✐➺♥✿ ✶✴✸✴✷✵✷✵❀ ◆❣➔② ♥❤➟♥ ✤➠♥❣✿ ✶✺✴✸✴✷✵✷✵ ✹✶ ◆●❍■➊◆ ❈Ù❯ ❈⑩❈ ❚➑◆❍ ❈❍❻❚ P❍■ ❈✃ ✣■➎◆ ❈Õ❆ ❚❘❸◆● ❚❍⑩■✳✳✳ ❦ÿ tt t ố ợ tổ t ữủ tû ✈➔ ♠→② t➼♥❤ ❧÷đ♥❣ tû✳ ◗✉→ tr➻♥❤ ❦❤↔♦ s→t ❝→❝ t➼♥❤ ❝❤➜t ♣❤✐ ❝ê ✤✐➸♥ ❝õ❛ tr↕♥❣ t❤→✐ t❤➯♠ ✈➔ ❜ỵt ♣❤♦t♦♥ ❧➯♥ ❤❛✐ ♠♦❞❡ ❦➳t ❤đ♣ ♣❤↔♥ ✤è✐ ①ù♥❣ ✤➣ ✤÷đ❝ ♠ët sè t→❝ ❣✐↔ t❤ü❝ ❤✐➺♥ ❬✼✱ ✽❪✳ ❚r♦♥❣ ❜➔✐ ❜→♦ ♥➔②✱ ❝❤ó♥❣ tỉ✐ ✤÷❛ r❛ tr↕♥❣ t❤→✐ ❣å✐ ❧➔ tr↕♥❣ t❤→✐ ❤❛✐ ♠♦❞❡ ❦➳t ❤ñ♣ ♣❤↔♥ ố ự t ợt ởt t tờ ữ s❛✉✿ |ψ ab = Nαβ (ˆ a†3 + ˆb) (|α a |β b ✭✶✮ − |β a |α b ) , tr♦♥❣ ✤â Nα,β ={|α|6 + |β|6 + 9(|α|4 + |β|4 ) + 19(|α|2 + |β|2 ) + 12 + 2Re[α3 β + αβ ] − exp[−|α − β|2 ](2Re[α∗3 β + 9α∗2 β + 19α∗ β + α3 β + αβ ] + 12)}− , ✭✷✮ ❧➔ ❤➺ sè ❝❤✉➞♥ ❤â❛✱ a ˆ† b ữủt t tỷ s ố ợ ♠♦❞❡ a ✈➔ t♦→♥ tû ❤õ② ✤è✐ ✈ỵ✐ ♠♦❞❡ b✱ ❘❡❬❩❪ ❧➔ ❦➼ ❤✐➺✉ ♣❤➛♥ t❤ü❝ ❝õ❛ ♠ët sè ♣❤ù❝ ởt tr t ợ ữ ữủ ❝ù✉✱ ❦❤↔♦ s→t✳ ❱➻ ✈➟②✱ tr♦♥❣ ❜➔✐ ❜→♦ ♥➔②✱ ❝❤ó♥❣ tæ✐ ♥❣❤✐➯♥ ❝ù✉ ❝→❝ t➼♥❤ ❝❤➜t ♣❤✐ ❝ê ✤✐➸♥ ❝õ❛ tr↕♥❣ t❤→✐ ❤❛✐ ♠♦❞❡ ❦➳t ❤ñ♣ ♣❤↔♥ ✤è✐ ①ù♥❣ t❤➯♠ ❜❛ ✈➔ ❜ỵt ♠ët ♣❤♦t♦♥ tê♥❣ t❤ỉ♥❣ q✉❛ t➼♥❤ ❝❤➜t ♥➨♥ tê♥❣ ❤❛✐ ♠♦❞❡ ✈➔ ♥➨♥ ❤✐➺✉ ❤❛✐ ♠♦❞❡✱ sü ✈✐ ♣❤↕♠ ❜➜t ✤➥♥❣ t❤ù❝ ❈❛✉❝❤② ✲ ❙❝❤✇❛r③ ✈➔ t➼♥❤ ❝❤➜t ♣❤↔♥ ❦➳t ❝❤ò♠ ❜➟❝ ❝❛♦ ❤❛✐ ♠♦❞❡✳ ✷ ❚➑◆❍ ❈❍❻❚ ◆➆◆ ❈Õ❆ ❚❘❸◆● ❚❍⑩■ ❍❆■ ▼❖❉❊ ❑➌❚ ❍ÑP P❍❷◆ ✣➮■ ❳Ù◆● ❚❍➊▼ ❇❆ ❱⑨ ❇❰❚ ▼❐❚ P❍❖❚❖◆ ❚✃◆● ✷✳✶✳ ◆➨♥ tê♥❣ ❤❛✐ ♠♦❞❡ ❍❛✐ ❦✐➸✉ ♥➨♥ ❜➟❝ ❝❛♦ ❧➔ ♥➨♥ tê♥❣ ✈➔ ♥➨♥ ❤✐➺✉ ❤❛✐ ♠♦❞❡ ✤➣ ✤÷đ❝ ❍✐❧❧❡r② ❬✾❪ ✤÷❛ r❛ ✈➔♦ ♥➠♠ ✶✾✽✾✳ ❚❤❡♦ ✤â✱ ♠ët tr↕♥❣ t❤→✐ ✤÷đ❝ ❣å✐ ❧➔ ♥➨♥ tê♥❣ ♥➳✉ tr✉♥❣ ❜➻♥❤ tr♦♥❣ tr↕♥❣ t❤→✐ ✤â t❤ä❛ ♠➣♥ ❜➜t ✤➥♥❣ t❤ù❝ ∆Vˆϕ tr♦♥❣ ✤â Vˆϕ = 2 = Vˆϕ2 − Vˆϕ < n ˆa + n ˆb + , ✭✸✮ eiϕ a ˆ†ˆb† + e−iϕ a ˆˆb ✱ n ˆa = a ˆ† a ˆ✱n ˆ b = ˆb†ˆb ❧➛♥ ❧÷đt ❧➔ t♦→♥ tû sè ❤↕t ❝õ❛ ❤❛✐ ♠♦❞❡ a ✈➔ b✳ ✣➸ t❤✉➟♥ t✐➺♥ ❝❤♦ ✈✐➺❝ ❦❤↔♦ s→t t❛ ✤➦t S ❧➔ t❤❛♠ sè ♥➨♥ tê♥❣ ❝â ❞↕♥❣ S = Vˆϕ2 − Vˆϕ − (ˆ na + n ˆ b + 1) ✭✹✮ ▼ët tr↕♥❣ t❤→✐ ❣å✐ ❧➔ ♥➨♥ tê♥❣ ❤❛✐ ♠♦❞❡ ♥➳✉ t❤❛♠ sè S < 0✳ ❱➻ α ✈➔ β ❧➔ ❝→❝ sè ♣❤ù❝ ♥➯♥ t❛ ✤➦t α = exp (iϕa )✱ β = rb exp (iϕb ) ✈➔ φh,k,m = hϕ + kϕa + mϕb ✱ ✈ỵ✐ h, k, m ❧➔ ❝→❝ sè ♥❣✉②➯♥✱ , rb , ϕa , ϕb ❧➔ ❝→❝ sè t❤ü❝✳ ❙û ❞ö♥❣ tr↕♥❣ t❤→✐ ❤❛✐ ♠♦❞❡ ❦➳t ❤ñ♣ ♣❤↔♥ ✤è✐ ①ù♥❣ t❤➯♠ ❜❛ ✈➔ ❜ỵt ♠ët ♣❤♦t♦♥ tê♥❣ ✈➔♦ ❝ỉ♥❣ t❤ù❝ ✭✹✮ t❛ ♥❤➟♥ ✤÷đ❝ S = Nαβ {2{(ra8 rb2 + ra2 rb8 + 15(ra6 rb2 + ra2 rb6 ) + 61(ra4 rb2 + ra2 rb4 ) + 240ra2 rb2 ) cos(φ2,−2,−2 ) + (ra5 rb3 + 6ra3 rb3 + 6ra rb3 ) cos(φ2,1,−1 ) + ra5 rb3 cos(φ2,−5,−3 ) + ra3 rb5 cos(φ2,−3,−5 ) ✹✷ ❍➬ ◆●➴❈ ❚❘❯◆●✱ ❚❘×❒◆● ▼■◆❍ ✣Ù❈ + (ra3 rb5 + 6ra3 rb3 + 6ra3 rb ) cos(φ2,−1,1 ) − x(2ra5 rb5 (cos(φ2,−5,1 ) + cos(φ2,1,−5 )) + 15ra4 rb4 (cos(φ2,−4,0 ) + cos(φ2,0,−4 )) + 61ra3 rb3 (cos(φ2,−3,−1 ) + cos(φ2,−1,−3 )) + (ra3 rb5 + 6ra3 rb ) cos(φ2,−1,1 ) + 120ra2 rb2 cos(φ2,−2,−2 ) + ra5 rb3 cos(φ2,−5,−3 ) + ra3 rb5 cos(φ2,−3,−5 ) + (ra5 rb3 + 6ra rb3 ) cos(φ2,1,−1 ) + 6(ra2 rb4 + ra4 rb2 ) cos(φ2,0,0 )} + 2(ra8 rb2 + ra2 rb8 ) + 31(ra6 rb2 + ra2 rb6 ) + 137(ra4 rb2 + ra2 rb4 ) + 350ra2 rb2 + 139(ra2 + rb2 ) + ra8 + rb8 + 16(ra6 + rb6 ) + 73(ra4 + rb4 ) + 48 + 2(2ra5 rb3 + 7ra3 rb3 + ra5 rb + 4ra3 rb ) cos(φ0,3,1 ) + 2(2ra3 rb5 + 7ra3 rb3 + rb5 + 4ra rb3 ) cos(φ0,1,3 ) − x(350ra2 rb2 + 48 + 2[ra4 rb4 cos(φ0,4,−4 ) + 73ra2 rb2 cos(φ0,2,−2 ) + 31ra4 rb4 cos(φ0,2,−2 ) + (137ra3 rb3 + 139ra rb ) cos(φ0,1,−1 ) + (2ra3 rb5 + 4ra rb3 ) cos(φ0,1,3 ) + ra4 rb2 cos(φ0,4,0 ) + (2ra5 rb5 + 16ra3 rb3 ) cos(φ0,3,−3 ) + (2ra5 rb3 + 4ra3 rb ) cos(φ0,3,1 ) + ra2 rb4 cos(φ0,0,4 ) + 7(ra2 rb4 + ra4 rb2 ) cos(φ0,2,2 )])} − {(16(ra6 + rb6 ) + ra8 + rb8 + 73(ra4 + rb4 ) + 103(ra2 + rb2 ) + 48 + ra6 rb2 + ra2 rb6 + 9(ra4 rb2 + ra2 rb4 ) + (8ra3 rb + 2ra5 rb ) cos(φ0,3,1 ) + 38ra2 rb2 + 2ra3 rb3 (cos(φ0,3,1 ) + cos(φ0,1,3 )) + (8ra rb3 + 2ra rb5 ) cos(φ0,1,3 ) − x(2ra4 rb4 cos(φ4,0,0 ) + 32ra3 rb3 cos(φ3,0,0 ) + (2ra4 rb2 + 2ra2 rb4 ) cos(φ0,2,2 ) + (146ra2 rb2 + 2ra4 rb4 ) cos(φ2,0,0 ) + (206ra rb + 18ra3 rb3 ) cos(φ1,0,0 ) + 48 + 2ra4 rb2 cos(φ0,4,0 ) + 2ra2 rb4 cos(φ0,0,4 ) + 8ra3 rb cos(φ0,3,1 ) + 8ra rb3 cos(φ0,1,3 ) {((2ra2 rb4 + 6ra2 rb2 ) cos(φ1,0,2 ) + 2(ra7 rb + rb7 + 12(ra5 rb + 38ra2 rb2 )} − Nαβ + rb5 ) + 48ra rb + 37(ra3 rb + rb3 )) cos(φ1,−1,−1 ) + (2rb3 + 2ra3 rb ) cos(φ1,−1,−1 ) + (2ra4 rb2 + 6ra2 rb2 ) cos(φ1,2,0 ) + 2ra4 rb2 cos(φ1,−4,−2 ) + 2ra2 rb4 cos(φ1,−2,−4 ) − x(2ra2 rb4 cos(φ1,0,2 ) + 2ra2 rb4 cos(φ1,−2,−4 ) + 6(ra3 rb + rb3 ) cos(φ1,1,1 ) + 2ra4 rb2 cos(φ1,2,0 ) + 2ra4 rb4 (cos(φ1,−4,2 ) + cos(φ1,2,−4 )) + 2ra4 rb2 cos(φ1,−4,−2 ) + 24ra3 rb3 (cos(φ1,−3,1 ) + cos(φ1,1,−3 )) + 96ra rb cos(φ1,−1,−1 ) + 74ra2 rb2 (cos(φ1,−2,0 ) ✭✺✮ + cos(φ1,0,−2 )))}2 , tr♦♥❣ ✤â Nα,β =(ra6 + rb6 + 9(ra4 + rb4 ) + 19(ra2 + rb2 ) + 2ra3 rb cos(φ0,3,1 ) + 2ra rb3 cos(φ0,1,3 ) + 12 − x(2ra3 rb3 cos(φ0,3,−3 ) + 18ra2 rb2 cos(φ0,2,−2 ) + 38ra rb cos(φ0,1,−1 ) + 2ra3 rb cos(φ0,3,1 ) + 2ra rb3 cos(φ0,1,3 ) + 12)− , ✭✻✮ ✈ỵ✐ x = exp[−ra2 − rb2 + 2ra rb cos(0,1,1 )] ỗ t st sỹ tở ❝õ❛ t❤❛♠ sè ❙ ✈➔♦ ❜✐➯♥ ✤ë ❦➳t ❤ñ♣ rb ✈ỵ✐ ✤✐➲✉ ❦✐➺♥ ❦❤↔♦ s→t ❧➔ = rb , ϕ = π2 , ϕa = π, ϕb = π2 rb ỗ t t❛ t❤➜② t❤❛♠ sè ♥➨♥ tê♥❣ S ❧✉ỉ♥ ❜➨ ❤ì♥ ❤♦➦❝ ❜➡♥❣ 0✱ ♥❣❤➽❛ ❧➔ ❧✉æ♥ ①✉➜t ❤✐➺♥ q✉→ tr➻♥❤ ♥➨♥ tê♥❣ tr♦♥❣ tr↕♥❣ t❤→✐ ❤❛✐ ♠♦❞❡ ❦➳t ❤ñ♣ ♣❤↔♥ ✤è✐ ①ù♥❣ t❤➯♠ ❜❛ ✈➔ ❜ỵt ♠ët ♣❤♦t♦♥ tê♥❣✳ ❑❤✐ ❝→❝ t❤❛♠ sè ✱ rb ❝➔♥❣ t➠♥❣ t❤➻ t❤❛♠ sè ❙ ❝➔♥❣ ➙♠✱ ♥❣❤➽❛ ❧➔ q✉→ tr➻♥❤ ♥➨♥ tê♥❣ ❝➔♥❣ t❤➸ ❤✐➺♥ rã✳ ❱ỵ✐ ◆●❍■➊◆ ❈Ù❯ ❈⑩❈ ❚➑◆❍ ❈❍❻❚ P❍■ ❈✃ ✣■➎◆ ❈Õ❆ ❚❘❸◆● ❚❍⑩■✳✳✳ ✹✸ ❍➻♥❤ ✶✿ ❑❤↔♦ s→t sü ♣❤ö t❤✉ë❝ ❝õ❛ t❤❛♠ sè ❙ ✈➔♦ ❜✐➯♥ ✤ë ❦➳t ❤ñ♣ rb ❝õ❛ tr↕♥❣ t❤→✐ ❤❛✐ ♠♦❞❡ ❦➳t ❤đ♣ ♣❤↔♥ ✤è✐ ①ù♥❣ t❤➯♠ ❜❛ ✈➔ ❜ỵt ♠ët ♣❤♦t♦♥ tê♥❣✳ ✤✐➲✉ ❦✐➺♥ ❦❤↔♦ s→t tr➯♥✱ ❝❤ù♥❣ tä tr↕♥❣ t❤→✐ ❤❛✐ ♠♦❞❡ ❦➳t ❤ñ♣ ♣❤↔♥ ✤è✐ ①ù♥❣ t❤➯♠ ❜❛ ✈➔ ❜ỵt ♠ët ♣❤♦t♦♥ tê♥❣ ❝â t➼♥❤ ♥➨♥ tê♥❣✳ ❑❤✐ ❝→❝ t❤❛♠ sè ✱ rb ❝➔♥❣ t➠♥❣ t❤➻ t➼♥❤ ♥➨♥ tê♥❣ ❝õ❛ tr↕♥❣ t❤→✐ ❝➔♥❣ t❤➸ ❤✐➺♥ rã✳ ✷✳✷✳ ◆➨♥ ❤✐➺✉ ❤❛✐ ♠♦❞❡ ❚❤❡♦ ❍✐❧❧❡r② ❬✾❪ ♠ët tr↕♥❣ t❤→✐ ✤÷đ❝ ❣å✐ ❧➔ ♥➨♥ ❤✐➺✉ ❤❛✐ ♠♦❞❡ ♥➳✉ ❦❤✐ tr✉♥❣ ❜➻♥❤ tr♦♥❣ tr↕♥❣ t❤→✐ ✤â t❤ä❛ ♠➣♥ ❜➜t ✤➤♥❣ t❤ù❝ ˆ2 − W ˆϕ W ϕ − (|ˆ na − n ˆ b |) < ✭✼✮ ✣➸ ✤ì♥ ❣✐↔♥ ❝❤♦ ✈✐➺❝ ❦❤↔♦ s→t t➼♥❤ ❝❤➜t ♥➨♥ ❤✐➺✉✱ t❛ ✤➦t t❤❛♠ sè ♥➨♥ ❤✐➺✉ D ❝â ❞↕♥❣ ˆ ϕ2 − W ˆϕ D= W ˆϕ = tr♦♥❣ ✤â W 2 − (|ˆ na − n ˆ b |) , ✭✽✮ eiϕ a ˆˆb† + e−iϕ a ˆ†ˆb ✱ n ˆa = a ˆ† a ˆ, n ˆ b = ˆb†ˆb ❧➛♥ ❧÷đt ❧➔ t♦→♥ tû sè ❤↕t ❝õ❛ ❤❛✐ ♠♦❞❡ a ✈➔ b✳ ▼ët ❝→❝❤ t÷ì♥❣ tü ♣❤➛♥ ♥➨♥ tê♥❣✱ ❦❤✐ ❦❤↔♦ s→t t➼♥❤ ♥➨♥ ❤✐➺✉ ❝õ❛ tr↕♥❣ t❤→✐ ❤❛✐ ♠♦❞❡ ❦➳t ❤ñ♣ ♣❤↔♥ ✤è✐ ①ù♥❣ t❤➯♠ ❜❛ ✈➔ ❜ỵt ♠ët ♣❤♦t♦♥ tê♥❣ t❛ t❤✉ ✤÷đ❝ ❦➳t q✉↔ ❝ư t❤➸ ♥❤÷ s❛✉ {(2ra2 rb8 + 30ra2 rb6 + 120ra2 rb4 + 120ra2 rb2 + 2ra4 rb2 ) cos(φ2,−2,2 ) + (2ra5 rb3 + 12ra3 rb3 D = Nαβ + 12ra rb3 ) cos(φ2,−1,−3 ) + 2ra3 rb5 cos(φ2,−1,5 ) + 2ra5 rb3 cos(φ2,5,−1 ) + (2ra3 rb5 + 12ra3 rb3 + 12ra3 rb ) cos(φ2,−3,−1 ) + (2ra8 rb2 + 30ra6 rb2 + 120ra4 rb2 + 120ra2 rb2 + 2ra2 rb4 ) cos(φ2,2,−2 ) − x(2ra3 rb7 cos(φ2,−3,3 ) + 2ra rb7 cos(φ2,1,3 ) + 2ra7 rb3 cos(φ2,3,−3 ) + 2ra7 rb cos(φ2,3,1 ) + (120ra rb5 + 2ra5 rb ) cos(φ2,−1,1 ) + (120ra5 rb + 2ra rb5 ) cos(φ2,1,−1 ) + 30ra2 rb6 cos(φ2,−1,1 ) + 30ra6 rb2 cos(φ2,1,−1 ) + (2ra3 rb5 + 12ra3 rb ) cos(φ2,−3,−1 ) + 12ra2 rb4 cos(φ2,−2,−2 ) + 12ra4 rb2 cos(φ2,−2,−2 ) + (2ra5 rb3 + 12ra rb3 ) cos(φ2,−1,−3 ) + 120(ra4 + rb4 ) cos(φ2,0,0 )) + 2(ra8 rb2 + ra2 rb8 ) + 31(ra6 rb2 + ra2 rb6 ) + 137(ra4 rb2 + ra2 rb4 ) + 350ra2 rb2 + 120(ra2 + rb2 ) + ra8 + rb8 ✹✹ ❍➬ ◆●➴❈ ❚❘❯◆●✱ ❚❘×❒◆● ▼■◆❍ ✣Ù❈ + 64(ra4 + rb4 ) + 15(ra6 + rb6 ) + (4ra5 rb3 + 14ra3 rb3 + 2ra5 rb + 6ra3 rb ) cos(φ0,3,1 ) + (4ra3 rb5 + 14ra3 rb3 + 2ra rb5 + 6ra rb3 ) cos(φ0,1,3 ) + 36 − x(2ra4 rb4 cos(φ0,4,−4 ) + (4ra5 rb5 + 30ra3 rb3 ) cos(φ0,3,−3 ) + 128ra2 rb2 cos(φ0,2,−2 ) + 350ra2 rb2 + 36 + (4ra3 rb5 + 6ra rb3 ) cos(φ0,1,3 ) + 2ra2 rb4 cos(φ0,0,4 ) + (4ra5 rb3 + 6ra3 rb ) cos(φ0,3,1 ) + (62ra4 rb4 + 274ra3 rb3 + 240ra rb ) cos(φ0,1,−1 ) + 2ra4 rb2 cos(φ0,4,0 ) + 14(ra2 rb4 + ra4 rb2 ) cos(φ0,2,2 ) − |(36 + ra8 + rb8 + 15(ra6 + rb6 ) + 62(ra4 + rb4 ) + (2ra5 rb + 6ra3 rb − 2ra3 rb3 ) cos(φ0,3,1 ) − 34ra2 rb2 − (ra6 rb2 + ra2 rb6 ) + 72(ra2 + rb2 ) + (2ra rb5 + 6ra rb3 − 2ra3 rb3 ) cos(φ0,1,3 ) − 9(ra4 rb2 + ra2 rb4 ) − x(36 − 34ra2 rb2 + (124ra2 rb2 − 2ra4 rb4 ) cos(φ2,0,0 ) + 2ra4 rb4 cos(φ4,0,0 ) + 2ra2 rb4 cos(φ0,0,4 ) + 2ra4 rb2 cos(φ0,4,0 ) + 6ra3 rb cos(φ0,3,1 ) + 30ra3 rb3 cos(φ3,0,0 ) + (144ra rb − 18ra3 rb3 ) cos(φ1,0,0 ) {(2ra7 rb + 24ra5 rb + 72ra3 rb − (2ra2 rb4 + 2ra4 rb2 ) cos(φ0,2,2 ) + 6ra rb3 cos(φ0,1,3 )))|} − Nαβ + 48ra rb + 2ra rb3 ) cos(φ1,1,−1 ) + 2ra4 rb2 cos(φ1,4,0 ) + (2ra rb7 + 24ra rb5 + 72ra rb3 + 48ra rb + 2ra3 rb ) cos(φ1,−1,1 ) + 2ra2 rb4 cos(φ1,0,4 ) + (2ra4 rb2 + 2ra2 rb4 + 12ra2 rb2 ) cos(φ1,−2,−2 ) − x(2ra rb5 cos(φ1,1,3 ) + (72ra rb3 + 2ra3 rb ) cos(φ1,−1,1 ) + 48(ra2 + rb2 ) cos(φ1,0,0 ) + 2ra3 rb3 cos(φ1,−1,−3 ) + (72ra3 rb + 2ra rb3 ) cos(φ1,1,−1 ) + 2ra3 rb3 cos(φ1,−3,−3 ) + 2ra5 rb cos(φ1,3,1 ) + 2ra5 rb3 cos(φ1,3,−3 ) + 24ra2 rb4 cos(φ1,−2,2 ) + 24ra4 rb2 cos(φ1,2,−2 ) + 12ra2 rb2 cos(1,2,2 ) + 2ra3 rb5 cos(1,3,3 ))}2 ỗ t❤à ✷ ❦❤↔♦ s→t t❤❛♠ sè D t❤❡♦ ❜✐➯♥ ✤ë t ủ rb ữợ ợ ❦❤↔♦ ❍➻♥❤ ✷✿ ❑❤↔♦ s→t sü ♣❤ö t❤✉ë❝ ❝õ❛ t❤❛♠ số t ủ rb ữợ ♥➨♥ ϕ ❝õ❛ tr↕♥❣ t❤→✐ ❤❛✐ ♠♦❞❡ ❦➳t ❤ñ♣ ♣❤↔♥ ✤è✐ ①ù♥❣ t❤➯♠ ❜❛ ✈➔ ❜ỵt ♠ët ♣❤♦t♦♥ tê♥❣✳ s→t ❧➔ = 2rb , ϕa = 0, ϕb = π2 , ≤ rb ≤ ✈➔ ≤ ỗ t t t t❤❛♠ sè ♥➨♥ ❤✐➺✉ D ❧✉ỉ♥ ❧ỵ♥ ❤ì♥ ❤♦➦❝ ❜➡♥❣ ú õ t t t ữợ ϕ✳ ❑❤✐ ❝→❝ t❤❛♠ sè ✱ rb ❝➔♥❣ t➠♥❣ t❤➻ t❤❛♠ sè D ❝➔♥❣ ❞÷ì♥❣✱ tù❝ ❧➔ ❝➔♥❣ ❦❤ỉ♥❣ õ t t ữ ợ ✤✐➲✉ ❦✐➺♥ ❦❤↔♦ s→t ♥❤÷ tr➯♥✱ tr↕♥❣ t❤→✐ t❤➯♠ ❜❛ ✈➔ ❜ỵt ♠ët ♣❤♦t♦♥ tê♥❣ ❤♦➔♥ t♦➔♥ ❦❤ỉ♥❣ ❝â t➼♥❤ ♥➨♥ ❤✐➺✉ ❤❛✐ ♠♦❞❡✳ ✹✺ ◆●❍■➊◆ ❈Ù❯ ❈⑩❈ ❚➑◆❍ ❈❍❻❚ P❍■ ❈✃ ✣■➎◆ ❈Õ❆ ❚❘❸◆● ❚❍⑩■✳✳✳ ✸ ❙Ü ❱■ P❍❸▼ ❇❻❚ ✣➃◆● ❚❍Ù❈ ❈❆❯❈❍❨✲❙❈❍❲❆❘❩ ❱⑨ ❚➑◆❍ P❍❷◆ ❑➌❚ ❈❍Ò▼ ❈Õ❆ ❚❘❸◆● ❚❍⑩■ ❍❆■ ▼❖❉❊ ❑➌❚ ❍ÑP P❍❷◆ ✣➮■ ❳Ù◆● ❚❍➊▼ ❇❆ ❱⑨ ❇❰❚ ▼❐❚ P❍❖❚❖◆ ❚✃◆● ✸✳✶✳ ❙ü ✈✐ ♣❤↕♠ ❜➜t ✤➥♥❣ t❤ù❝ ❈❛✉❝❤② ✲ ❙❝❤✇❛r③ ❇➜t ✤➥♥❣ t❤ù❝ ❈❛✉❝❤② r trữớ ủ ố ợ tr÷í♥❣ ❝ê ✤✐➸♥ ❝â ❞↕♥❣ a ˆ†2 a ˆ2 I= ˆb†2ˆb2 − ≥ a ˆ†ˆb†ˆbˆ a ✭✶✵✮ ❙ü ✈✐ ♣❤↕♠ ❜➜t ✤➥♥❣ t❤ù❝ tr➯♥✱ ♥❣❤➽❛ ❧➔ I < 0✱ ❝❤ù♥❣ tä tr↕♥❣ t❤→✐ ❦❤↔♦ s→t ❧➔ ♣❤✐ ❝ê ✤✐➸♥✳ ✣è✐ ✈ỵ✐ tr↕♥❣ t❤→✐ ❤❛✐ ♠♦❞❡ ❦➳t ❤đ♣ ♣❤↔♥ ✤è✐ ①ù♥❣ t❤➯♠ ❜❛ ✈➔ ❜ỵt ♠ët ♣❤♦t♦♥ tê♥❣ t❛ t❤✉ ✤÷đ❝ ❦➳t q✉↔ ❝õ❛ t❤❛♠ sè I ♥❤÷ s❛✉✿ I ={{ra10 + rb10 + 21(ra8 + rb8 ) + 138(ra6 + rb6 ) + 330(ra4 + rb4 ) + 250(ra2 + rb2 ) + ra4 rb2 + ra2 rb4 + (2ra7 rb + 12ra5 rb + 12ra3 rb ) cos(φ0,3,1 ) + (2ra rb7 + 12ra rb5 + 12ra rb3 ) cos(φ0,1,3 ) + 72 − x(72 + 2ra5 rb5 cos(φ5,0,0 ) + (504ra rb + 2ra3 rb3 ) cos(φ1,0,0 ) + 42ra4 rb4 cos(φ4,0,0 ) + 2ra3 rb5 cos(φ0,1,−5 ) + 2ra5 rb3 cos(φ0,5,−1 ) + 276ra3 rb3 cos(φ3,0,0 ) + 660ra2 rb2 cos(φ2,0,0 ) + 12ra3 rb cos(φ0,3,1 ) + 12ra rb3 cos(φ0,1,3 ) + 12ra4 rb2 cos(φ0,4,0 ) + 12ra2 rb4 cos(φ0,0,4 ))} × {6(ra4 + rb4 ) + 2ra3 rb5 cos(φ0,3,1 ) + 2ra5 rb3 cos(φ0,1,3 ) + ra6 rb4 + ra4 rb6 + 18ra4 rb4 + 18(ra4 rb2 + ra2 rb4 ) + (ra6 + rb6 ) − x(2ra3 rb3 cos(φ3,0,0 ) + 2ra5 rb3 cos(φ0,1,3 ) + 2ra3 rb5 cos(φ0,3,1 ) + (2ra5 rb5 + 36ra3 rb3 ) cos(φ1,0,0 ) + 12ra2 rb2 cos(φ2,0,0 )) + 18ra4 rb4 }} /{ra8 rb2 + ra2 rb8 + 15(ra6 rb2 + ra2 rb6 ) + 18(ra2 + rb2 ) + 64(ra4 rb2 + ra2 rb4 ) + 156ra2 rb2 + (2ra3 rb5 + 6ra3 rb3 ) cos(φ0,1,3 ) + (2ra5 rb3 + 6ra3 rb3 ) cos(φ0,3,1 ) − x((6ra2 rb4 + 6ra4 rb2 ) cos(φ0,2,2 ) + 2ra5 rb5 cos(φ3,0,0 ) + 30ra4 rb4 cos(φ2,0,0 ) + (128ra3 rb3 + 36ra rb ) cos(φ1,0,0 ) + 156ra2 rb2 + 2ra3 rb5 cos(φ0,1,3 ) + 2ra5 rb3 cos(φ0,3,1 ))} − ✭✶✶✮ ❚❤❡♦ ✤✐➲✉ ❦✐➺♥ ð ✭✶✵✮✱ ♥➳✉ t❤❛♠ sè I tr♦♥❣ ❜✐➸✉ t❤ù❝ ✭✶✶✮ ♥❤➟♥ ❣✐→ trà ➙♠ t❤➻ tr↕♥❣ t❤→✐ ❤❛✐ ♠♦❞❡ ❦➳t ❤đ♣ ♣❤↔♥ ✤è✐ ①ù♥❣ t❤➯♠ ❜❛ ✈➔ ❜ỵt ♠ët ♣❤♦t♦♥ tê♥❣ ✈✐ ♣❤↕♠ ❜➜t ✤➥♥❣ t❤ù❝ ❈❛✉❝❤② ✕ r ỗ t st t số I t ❜✐➯♥ ✤ë ❦➳t ❤đ♣ rb ✈ỵ✐ ✤✐➲✉ ❦✐➺♥ ❦❤↔♦ s→t ❧➔ = rb , ≤ rb ≤ 1, ϕ = ϕa = π, ϕb = 0✳ ◆❤➻♥ ✈➔♦ ỗ t t t số I tr tr♦♥❣ ❦❤♦↔♥❣ −1 ≤ I ≤ 0✳ ❑❤✐ t❤❛♠ sè , rb ❝➔♥❣ ❣✐↔♠ t❤➻ t❤❛♠ sè I ❝➔♥❣ ➙♠✳ ❈→❝ ❦➳t q✉↔ ✤â ❝❤♦ t❤➜② tr↕♥❣ t❤→✐ ❤❛✐ ♠♦❞❡ ❦➳t ❤đ♣ ♣❤↔♥ ✤è✐ ①ù♥❣ t❤➯♠ ❜❛ ✈➔ ❜ỵt ♠ët ♣❤♦t♦♥ tê♥❣ ✈✐ ♣❤↕♠ ❜➜t ✤➥♥❣ t❤ù❝ ❈❛✉❝❤② ✕ ❙❝❤✇❛r③ ✈➔ ❦❤✐ , rb ❝➔♥❣ ❣✐↔♠ t❤➻ I ❝➔♥❣ ➙♠ ✈➔ ❞➛♥ t✐➳♥ ✈➲ ❣✐→ trà ♥❤ä ♥❤➜t ❧➔ −1✱ ♥❣❤➽❛ ❧➔ sü ✈✐ ♣❤↕♠ ❜➜t ✤➥♥❣ t❤ù❝ ❈❛✉❝❤② ✕ ❙❝❤✇❛r③ t❤➸ ❤✐➺♥ ❝➔♥❣ ♠↕♥❤✳ ✹✻ ❍➬ ◆●➴❈ ❚❘❯◆●✱ ❚❘×❒◆● ▼■◆❍ ✣Ù❈ ❍➻♥❤ ✸✿ ❑❤↔♦ s→t sü ♣❤ư t❤✉ë❝ ❝õ❛ t❤❛♠ sè ■ ✈➔♦ ❜✐➯♥ ✤ë ❦➳t ❤ñ♣ rb ❝õ❛ tr↕♥❣ t❤→✐ ❤❛✐ ♠♦❞❡ ❦➳t ❤ñ♣ ♣❤↔♥ ✤è✐ ①ù♥❣ t❤➯♠ ❜❛ ✈➔ ❜ỵt ♠ët ♣❤♦t♦♥ tê♥❣✳ ✸✳✷✳ ❚➼♥❤ ♣❤↔♥ ❦➳t ❝❤ò♠ ◆➠♠ ✶✾✾✵✱ ❈❤✐♥❣ ❚s✉♥❣ ▲❡❡ ❬✶✵❪ ✤➣ ✤÷❛ r❛ t➼♥❤ ♣❤↔♥ ❦➳t ❝❤ị♠ ✈➔ t❤❛♠ sè Ra,b (l, p) ✤➦❝ tr÷♥❣ ❝❤♦ t➼♥❤ ❝❤➜t ✤â✳ ❚❤❡♦ ỉ♥❣✱ ♠ët tr↕♥❣ t❤→✐ ❝â t➼♥❤ ❝❤➜t ♣❤↔♥ ❦➳t ❝❤ò♠ ❦❤✐ t❤❛♠ sè Ra,b (l, p) t❤ä❛ ♠➣♥ (l+1) (p−1) n ˆb (p−1) (l+1) n ˆb + n ˆa n ˆa Rab (l, p) = (l) (p) (p) (l) n ˆa n ˆb ✭✶✷✮ − < 0, + n ˆa n b ợ l, p số ữỡ ✭l ≥ p > 0✮✱ n ˆa = a ˆ† a ˆ, n ˆ b = ˆb†ˆb ❧➔ t♦→♥ tû sè ❤↕t ❝õ❛ ❤❛✐ ♠♦❞❡ a✱ b✱ ❦❤✐ ✤â t❤❛♠ sè Ra,b (l, p) ð ✭✶✷✮ ✤÷đ❝ ✈✐➳t ❧↕✐ ♥❤÷ s❛✉✿ a ˆ†(l+1) a ˆ(l+1)ˆb†(p−1)ˆb(p−1) + a ˆ†(p−1) a ˆ(p−1)ˆb†(l+1)ˆb(l+1) Rab (l, p) = − ˆ†p a ˆpˆb†lˆbl a ˆ†l a ˆlˆb†pˆbp + a ✭✶✸✮ ◆➳✉ t❤❛♠ sè R(l, p) ❝➔♥❣ ➙♠ t❤➻ t➼♥❤ ♣❤↔♥ ❦➳t ❝❤ò♠ ❤❛✐ ♠♦❞❡ t❤➸ ❤✐➺♥ ❝➔♥❣ ♠↕♥❤✳ ❇➙② ❣✐í t❛ ❦❤↔♦ s→t ❝ư t❤➸ t➼♥❤ ❝❤➜t ♣❤↔♥ ❦➳t ❝❤ò♠ ❝õ❛ tr↕♥❣ t❤→✐ ❤❛✐ ♠♦❞❡ ❦➳t ❤đ♣ ♣❤↔♥ ✤è✐ ①ù♥❣ t❤➯♠ ❜❛ ✈➔ ❜ỵt ♠ët ♣❤♦t♦♥ tê♥❣ t❤æ♥❣ q✉❛ t➼♥❤ sè ❤↕♥❣ tê♥❣ q✉→t a l a lbpbp ữ ỵ r số ❤↕♥❣ ❝á♥ ❧↕✐ ❝â tr♦♥❣ ❜✐➸✉ t❤ù❝ ✭✶✸✮ ✤➲✉ ✤÷đ❝ s✉② r❛ tø sè ❤↕♥❣ tê♥❣ q✉→t ♥➔②✳ ❚❤ü❝ ❤✐➺♥ ♠ët sè ♣❤➨♣ ❜✐➳♥ ✤ê✐ t❛ t❤✉ ✤÷đ❝ ❝→❝ ❦➳t q✉↔ ♥❤÷ s❛✉✿ 2(l+3) a ˆ†l a ˆlˆb†pˆbp = Nαβ (ra2(l+3) rb2p + ra2p rb 2(l+1) + 18)(ra2(l+1) rb2p + ra2p rb 2(l−1) (ra2(l−1) rb2p + ra2p rb 2(l−2) rb 2(l+2) ) + (6l + 9)(ra2(l+2) rb2p + ra2p rb ) + (15l2 + 30l ) + (20l3 + 30l2 + 22l + 6))(ra2l rb2p + ra2p rb2l ) + (15l4 + 3l2 ) ) + ra2l rb2p+2 + rb2l ra2p+2 + (6l5 − 15l4 + 12l3 − 3l2 )(ra2(l−2) rb2p + ra2p 2(l−3) ) + l2 (l − 1)2 (l − 2)2 (ra2(l−3) rb2p + ra2p rb ) + (2ra2l+3 rb2p+1 + 6lra2l+1 rb2p+1 + 6l(l − 1) ra2l−1 rb2p+1 + (2l3 − 6l2 + 4l)ra2l−3 rb2p+1 ) cos(φ0,3,1 ) + (2rb2l+3 ra2p+1 + 6lrb2l+1 ra2p+1 + 6l(l − 1) ◆●❍■➊◆ ❈Ù❯ ❈⑩❈ ❚➑◆❍ ❈❍❻❚ P❍■ ❈✃ ✣■➎◆ ❈Õ❆ ❚❘❸◆● ❚❍⑩■✳✳✳ ✹✼ rb2l−1 ra2p+1 + (2l3 − 6l2 + 4l)rb2l−3 ra2p+1 ) cos(φ0,1,3 ) − x((12l + 18)ral+p+2 rbl+p+2 + 2ral+p+3 rbl+p+3 cos((n + 3)φ0,1,−1 ) + (30l2 + 60l + 36)ral+p+1 rbl+p+1 cos((n + 1)φ0,1,−1 ) + (40l3 + 60l2 + 44l + 12)ral+p rbl+p cos(nφ0,1,−1 ) + (12l + 18)ral+p+2 rbl+p+2 ) cos((n + 2)φ0,1,−1 ) + (40l3 + 60l2 + 44l + 12)ral+p rbl+p + (30l2 + 60l + 36)ral+p+1 rbl+p+1 + 6lral+p+2 rbl+p cos(φ0,n+2,−(n−2) ) + (2l3 − 6l2 + 4l)ral+p rbl+p−2 cos(φ0,−(n−4),n ) + 6lral+p rbl+p+2 cos(φ0,n−2,−(n+2) ) + 2l2 (l − 1)2 (l − 2)2 ral+p−3 rbl+p−3 cos((n − 3)φ0,1,−1 ) + 2ral+p+1 rbl+p+1 cos((n − 1)φ0,1,−1 ) + 2ral+p+3 rbl+p+1 cos(φ0,n+3,−(n−1) ) + 2ral+p+1 rbl+p+3 cos(φ0,n−1,−(n+3) ) + (12l5 − 30l4 + 24l3 − 6l2 )ral+p−2 rbl+p−2 cos((n − 2)φ0,1,−1 ) + (6l2 − 6l)ral+p−1 rbl+p+1 cos(φ0,n−3,−(n−1) ) + (30l4 + 6l2 )ral+p−1 rbl+p−1 cos((n − 1)φ0,1,−1 ) + 6l(l − 1)ral+p+1 rbl+p−1 cos(φ0,n−1,−(n+3) ) + (2l3 − 6l2 + 4l)ral+p rbl+p−2 cos(φ0,n,−(n−4) ), ✭✶✹✮ ✈ỵ✐ n = l − p✳ ❇➙② ❣✐í t❛ s➩ ❦❤↔♦ s→t ❝→❝ tr÷í♥❣ ❤đ♣ ❝ư t❤➸ ♥❤÷ s❛✉✿ ❛✮ ❚r÷í♥❣ ❤đ♣ (l = 4, p = 3)❀ (l = 5, p = 3)❀ (l = 6, p = 3)✱ ✈ỵ✐ ❝ị♥❣ ✤✐➲✉ ❦✐➺♥ ❦❤↔♦ s→t ❧➔ π rb = ra3 ✱ ϕ = ϕa = ✈➔ ϕb = ✳ ❍➻♥❤ ✹✿ ❑❤↔♦ s→t sü ♣❤ư t❤✉ë❝ ❝õ❛ R(4, 3) ✧✤÷í♥❣ ❧✐➲♥ ♥➨t✧ ✱ R(5, 3) ✧✤÷í♥❣ ❝❤➜♠ ❝❤➜♠✧✱ R(6, 3) ✧✤÷í♥❣ ❝❤➜♠ ❣↕❝❤✧ ✈➔♦ ❜✐➯♥ ✤ë rb ❝õ❛ tr↕♥❣ t❤→✐ ❤❛✐ ♠♦❞❡ ❦➳t ❤đ♣ ♣❤↔♥ ✤è✐ ①ù♥❣ t❤➯♠ ❜❛ ✈➔ ❜ỵt ♠ët ♣❤♦t♦♥ tê♥❣✳ ❜✮ ❚÷ì♥❣ tü✱ t❛ ①➨t ❝→❝ tr÷í♥❣ ❤đ♣ (l = 4, p = 2)❀ (l = 5, p = 2)❀ (l = 6, p = 2)✱ ✈ỵ✐ ❝ị♥❣ π ✤✐➲✉ ❦✐➺♥ ❦❤↔♦ s→t ❧➔ rb = ra3 ✱ ϕ = ϕa = ✈➔ ϕb = ✳ ✹✽ ❍➬ ◆●➴❈ ❚❘❯◆●✱ ❚❘×❒◆● ▼■◆❍ ✣Ù❈ ❍➻♥❤ ✺✿ ❑❤↔♦ s→t sü ♣❤ư t❤✉ë❝ ❝õ❛ R(4, 2) ✧✤÷í♥❣ ❧✐➲♥ ♥➨t✧✱ R(5, 2) ✧✤÷í♥❣ ❝❤➜♠ ❝❤➜♠✧✱ R(6, 2) ✤÷í♥❣ ✧✤÷í♥❣ ❝❤➜♠ ❣↕❝❤✧ ✈➔♦ ❜✐➯♥ ✤ë rb ❝õ❛ tr↕♥❣ t❤→✐ ❤❛✐ ♠♦❞❡ ❦➳t ❤đ♣ ♣❤↔♥ ✤è✐ ①ù♥❣ t❤➯♠ ❜❛ ✈➔ ❜ỵt ♠ët ♣❤♦t♦♥ tê♥❣✳ ❝✮ ❱ỵ✐ ✤✐➲✉ ❦✐➺♥ ❦❤↔♦ s→t ❧➔ = rb ✱ ϕ = ϕa = 3ϕb ✈➔ ϕb = ✭l = 3, p = 2✮✱ ✭l = 5, p = 4✮ ✈➔ ✭l = 6, p = 5✮✳ π ✱ t❛ ①➨t ❝→❝ tr÷í♥❣ ❤đ♣ ❍➻♥❤ ✻✿ ❑❤↔♦ s→t sü ♣❤ư t❤✉ë❝ ❝õ❛ R(3, 2) ✧✤÷í♥❣ ❧✐➲♥ ♥➨t✧✱ R(5, 4) ✧✤÷í♥❣ ❝❤➜♠ ❝❤➜♠✧✱ R(6, 5) ✤÷í♥❣ ✧✤÷í♥❣ ❝❤➜♠ ❣↕❝❤✧ ✈➔♦ ❜✐➯♥ ✤ë rb ❝õ❛ tr↕♥❣ t❤→✐ ❤❛✐ ♠♦❞❡ ❦➳t ❤đ♣ ♣❤↔♥ ✤è✐ ①ù♥❣ t❤➯♠ ❜❛ ✈➔ ❜ỵt ♠ët t tờ ỗ t ✻ t❛ ♥❤➟♥ t❤➜② t❤❛♠ sè R{l, p} ✤➲✉ ①✉➜t ♣❤→t tø ❣✐→ trà −1✱ ✤➙② ❧➔ ❣✐→ trà ❝ü❝ t✐➸✉ ❝õ❛ ♥â✱ t❤❛♠ sè R{l, p} < ❦❤✐ ❝→❝ t❤❛♠ sè , rb r➜t ❜➨✱ ✈➔ ❦❤✐ ❝→❝ t❤❛♠ sè , rb t➠♥❣ t❤➻ t❤❛♠ sè R{l, p} ❞➛♥ t✐➳♥ ✤➳♥ ✈➔ ♥➳✉ t❤❛♠ sè , rb ❧ỵ♥ ❤ì♥ ♠ët ❣✐→ trà ♥➔♦ ✤â t❤➻ R{l, p} ≥ 0✳ ❈→❝ ❦➳t q✉↔ ♥➔② ❝❤ù♥❣ tä tr↕♥❣ t❤→✐ ❤❛✐ ♠♦❞❡ ❦➳t ❤ñ♣ ♣❤↔♥ ✤è✐ ①ù♥❣ t❤➯♠ ❜❛ ✈➔ ❜ỵt ♠ët ♣❤♦t♦♥ tê♥❣ ❝â t➼♥❤ ❝❤➜t ♣❤↔♥ ❦➳t ❝❤ò♠ ❦❤✐ ❝→❝ t❤❛♠ sè , rb r➜t ❜➨✱ ♥❣❤➽❛ ❧➔ tr↕♥❣ t❤→✐ ✤â ♠❛♥❣ t➼♥❤ ❝❤➜t ♣❤✐ ❝ê ✤✐➸♥✳ ❚r♦♥❣ tr÷í♥❣ ❤đ♣ , rb t➠♥❣ ❞➛♥ t❤➻ t❤❛♠ sè R{l, p} ❝ô♥❣ t➠♥❣ ❞➛♥ ✤➳♥ 0✱ ❦❤✐ ✤â t➼♥❤ ❝❤➜t ♣❤✐ ❝ê ✤✐➸♥ ❝õ❛ tr↕♥❣ t❤→✐ ◆●❍■➊◆ ❈Ù❯ ❈⑩❈ ❚➑◆❍ ❈❍❻❚ P❍■ ❈✃ ✣■➎◆ ❈Õ❆ ❚❘❸◆● ❚❍⑩■✳✳✳ ✹✾ ❞➛♥ ❜✐➳♥ ♠➜t✳ ◆➳✉ t✐➳♣ tö❝ t➠♥❣ , rb ữủt q ởt tr ợ ♥➔♦ ✤â t❤➻ t❤❛♠ sè R{l, p} ≥ 0✱ ♥❣❤➽❛ ❧➔ t➼♥❤ ❝❤➜t ♣❤✐ ❝ê ✤✐➸♥ ❝õ❛ tr↕♥❣ t❤→✐ ❤❛✐ ♠♦❞❡ ❦➳t ❤đ♣ ♣❤↔♥ ✤è✐ ①ù♥❣ t❤➯♠ ❜❛ ✈➔ ❜ỵt ♠ët ♣❤♦t♦♥ tê♥❣ ❦❤æ♥❣ ❝á♥✱ t❤❛② ✈➔♦ ✤â tr↕♥❣ t❤→✐ ♠❛♥❣ t➼♥❤ ❝❤➜t ❝ê ✤✐➸♥✳ ✹ ❑➌❚ ▲❯❾◆ ❇➔✐ ❜→♦ ♥➔② tr➻♥❤ ❜➔② ❦➳t q✉↔ ❦❤↔♦ s→t t➼♥❤ ❝❤➜t ♥➨♥ tê♥❣ ❤❛✐ ♠♦❞❡✱ ♥➨♥ ❤✐➺✉ ❤❛✐ ♠♦❞❡✱ sü ✈✐ ♣❤↕♠ ❜➜t ✤➥♥❣ t❤ù❝ ❈❛✉❝❤② ✲ ❙❝❤✇❛r③ ✈➔ t➼♥❤ ♣❤↔♥ ❦➳t ❝❤ị♠ ❜➟❝ ❝❛♦ ❝õ❛ tr↕♥❣ t❤→✐ ❤❛✐ ♠♦❞❡ ❦➳t ❤đ♣ ♣❤↔♥ ✤è✐ ①ù♥❣ t❤➯♠ ❜❛ ✈➔ ❜ỵt ♠ët ♣❤♦t♦♥ tê♥❣✳ q tr st t t ỗ t❤à t❤ỉ♥❣ q✉❛ ❝→❝ t❤❛♠ sè✱ ❝❤ó♥❣ tỉ✐ t❤✉ ✤÷đ❝ ❦➳t q✉↔ ♥❤÷ s❛✉✿ ❚❤ù ♥❤➜t✱ ❦➳t q✉↔ ❦❤↔♦ s→t ❝❤♦ t❤➜② tr↕♥❣ t❤→✐ ❤❛✐ ♠♦❞❡ ❦➳t ❤ñ♣ ♣❤↔♥ ✤è✐ ①ù♥❣ t❤➯♠ ❜❛ ✈➔ ❜ỵt ♠ët ♣❤♦t♦♥ tê♥❣ t❤➸ ❤✐➺♥ t➼♥❤ ❝❤➜t ♥➨♥ tê♥❣ ❤❛✐ ♠♦❞❡ ♠↕♥❤ ✈➔ ❤♦➔♥ ❤♦➔♥ ❦❤æ♥❣ ❝â t➼♥❤ ❝❤➜t ♥➨♥ ❤✐➺✉ ❤❛✐ ♠♦❞❡✳ ❚❤ù ❤❛✐✱ t❤æ♥❣ q✉❛ t❤❛♠ sè I ❞ü❛ ✈➔♦ ✤✐➲✉ ❦✐➺♥ ✈✐ ♣❤↕♠ ❜➜t ✤➥♥❣ t❤ù❝ ❈❛✉❝❤② ✲ ❙❝❤✇❛r③ ✤➣ ✤÷đ❝ ✤÷❛ r❛ ✈➔ ❦❤↔♦ s→t ❝❤✐ t✐➳t ✈➔ ❝ö t❤➸✳ ❑➳t q✉↔ ❝❤♦ t❤➜② tr↕♥❣ t❤→✐ ❤❛✐ ♠♦❞❡ ❦➳t ❤ñ♣ ♣❤↔♥ ✤è✐ ①ù♥❣ t❤➯♠ ❜❛ ✈➔ ❜ỵt ♠ët ♣❤♦t♦♥ tê♥❣ ❤♦➔♥ t♦➔♥ ✈✐ ♣❤↕♠ ❜➜t ✤➥♥❣ t❤ù❝ ❈❛✉❝❤② ✲ ❙❝❤✇❛r③ ♥❣❤➽❛ ❧➔ t➼♥❤ ❝❤➜t ♣❤✐ ❝ê ✤✐➸♥ t❤➸ ❤✐➺♥ t÷ì♥❣ ✤è✐ ♠↕♥❤✳ ◆❣♦➔✐ r❛✱ ❦❤✐ ❦❤↔♦ s→t t➼♥❤ ❝❤➜t ♣❤↔♥ ❦➳t ❝❤ị♠✱ ❝❤ó♥❣ tỉ✐ ❝ơ♥❣ ✤➣ ✤÷❛ r❛ ❜✐➸✉ t❤ù❝ tê♥❣ q✉→t ❝❤♦ t❤❛♠ sè ♣❤↔♥ ❦➳t ❝❤ò♠ tr♦♥❣ tr↕♥❣ t❤→✐ ❤❛✐ ♠♦❞❡ ❦➳t ❤ñ♣ ♣❤↔♥ ✤è✐ ①ù♥❣ t❤➯♠ ❜❛ ✈➔ ❜ỵt ♠ët ♣❤♦t♦♥ tê♥❣✳ ◗✉❛ ✤â✱ ❝❤ó♥❣ tỉ✐ ✤➣ ❦❤↔♦ s→t ❝❤♦ tø♥❣ tr÷í♥❣ ❤đ♣ ❝ư t❤➸ ✈➔ ❦➳t q✉↔ ❧➔ tr↕♥❣ t❤→✐ ❤❛✐ ♠♦❞❡ ❦➳t ❤ñ♣ ♣❤↔♥ ✤è✐ ①ù♥❣ t❤➯♠ ❜❛ ✈➔ ❜ỵt ♠ët ♣❤♦t♦♥ tê♥❣ t❤➸ ❤✐➺♥ t➼♥❤ ❝❤➜t ♣❤↔♥ ❦➳t ❝❤ò♠ ❜➟❝ t❤➜♣ ✈➔ ❜➟❝ ❝❛♦✱ tr♦♥❣ ✤â sè ❜➟❝ ❝➔♥❣ t➠♥❣ ♥❤÷♥❣ ❤✐➺✉ ❝→❝ ❜➟❝ ❝➔♥❣ ❜➨ t❤➻ t➼♥❤ ❝❤➜t ♣❤↔♥ ❦➳t ❝❤ò♠ ❝➔♥❣ t❤➸ ❤✐➺♥ rã r➺t ❤ì♥✳ ▲❮■ ❈❷▼ ❒◆ ◆❣❤✐➯♥ ❝ù✉ ♥➔② ✤÷đ❝ t➔✐ trđ ❜ð✐ ◗✉ÿ P❤→t tr✐➸♥ ❦❤♦❛ ❤å❝ ✈➔ ❝ỉ♥❣ ♥❣❤➺ ◗✉è❝ ❣✐❛ ✭◆❆❋❖❙✲ ❚❊❉✮ tr♦♥❣ ✤➲ t➔✐ ♠➣ sè ✶✵✸✳✵✶✲✷✵✶✽✳✸✻✶✳ ❚⑨■ ▲■➏❯ ❚❍❆▼ ❑❍❷❖ ❬✶❪ ▲✳ ▲✳ ❍♦✉✱ ❳✳ ❋✳ ❈❤❡♥✱ ❳✳ ❋✳ ❳✉ ✭✷✵✶✺✮✱ ✧❈♦♥t✐♥✉♦✉s✲✈❛r✐❛❜❧❡ q✉❛♥t✉♠ t❡❧❡♣♦rt❛t✐♦♥ ✇✐t❤ ♥♦♥✲●❛✉ss✐❛♥ ❡♥t❛♥❣❧❡❞ st❛t❡s ❣❡♥❡r❛t❡❞ ✈✐❛ ♠✉❧t✐♣❧❡✲♣❤♦t♦♥ s✉❜tr❛❝t✐♦♥ ❛♥❞ ❛❞❞✐t✐♦♥✧✱ P❤②s✐❝❛❧ ❘❡✈✐❡✇ ❆✱ ✾✶✱ ✵✻✸✽✸✷✳ ❬✷❪ ❳✳ ❲✳ ❳✉✱ ❍✳ ❲❛♥❣✱ ❏✳ ❩❤❛♥❣✱ ❨✳ ▲✐✉ ✭✷✵✶✸✮✱ ✧❊♥❣✐♥❡❡r✐♥❣ ♦❢ ♥♦♥❝❧❛ss✐❝❛❧ ♠♦t✐♦♥❛❧ st❛t❡s ✐♥ ♦♣t♦♠❡❝❤❛♥✐❝❛❧ s②st❡♠s✧✱ P❤②s✐❝❛❧ ❘❡✈✐❡✇ ❆✱ ✽✽✱ ✵✻✸✽✶✾✳ ❬✸❪ ●✳ ❙✳ ❆❣❛r✇❛❧ ❛♥❞ ❑✳ ❚❛r❛ ✭✶✾✾✶✮✱ ✧◆♦♥❝❧❛ss✐❝❛❧ ♣r♦♣❡rt✐❡s ♦❢ st❛t❡s ❣❡♥❡r❛t❡❞ ❜② t❤❡ ❡①❝✐t❛t✐♦♥s ♦♥ ❛ ❝♦❤❡r❡♥t st❛t❡✧✱ P❤②s✐❝❛❧ ❘❡✈✐❡✇ ❆✱ ✹✸✱ ✹✾✷✳ ✺✵ ❍➬ ◆●➴❈ ❚❘❯◆●✱ ❚❘×❒◆● ▼■◆❍ ✣Ù❈ ❬✹❪ ❙✳ ❙✐✈❛❦✉♠❛r ✭✶✾✾✾✮✱ ✧P❤♦t♦♥✲❛❞❞❡❞ ❝♦❤❡r❡♥t st❛t❡s ❛s ♥♦♥❧✐♥❡❛r ❝♦❤❡r❡♥t st❛t❡s✧✱ P❤②s✳ ❆✿ ▼❛t❤✳ ●❡♥✱ ✸✷✱ ✸✹✹✶✳ ❏✳ ❬✺❪ ❚✳ ▼✳ ❉✉❝ ❛♥❞ ❏✳ ◆♦❤ ✭✷✵✵✽✮✱ ✧❍✐❣❤❡r✲♦r❞❡r ♣r♦♣❡rt✐❡s ♦❢ ♣❤♦t♦♥✲❛❞❞❡❞ ❝♦❤❡r❡♥t st❛t❡s✧✱ ❖♣t✳ ❈♦♠♠✉♥✳ ✷✽✶✱ ✷✽✹✷✳ ❬✻❪ ❈✳ ◆✳ ❇❡♥❧❧♦❝❤✱ ❘✳ ●✳ P❛tr♦♥✱ ❏✳ ❍✳ ❙❤❛♣✐r♦✱ ◆✳ ❏✳ ❈❡r❢ ✭✷✵✶✷✮✱ ✧❊♥❤❛♥❝✐♥❣ q✉❛♥t✉♠ ❡♥t❛♥❣❧❡♠❡♥t ❜② ♣❤♦t♦♥ ❛❞❞✐t✐♦♥ ❛♥❞ s✉❜tr❛❝t✐♦♥✧✱ P❤②s✳ ❘❡✈✳ ❆ ✽✻✱ ✵✶✷✸✷✽✳ ❬✼❪ ◆❣✉②➵♥ ❱ơ ❚❤ư② ✭✷✵✶✼✮✱ ▲✉➟♥ ✈➠♥ s t ỵ ỵ tt t ỵ rữớ ữ ❬✽❪ ◆❣✉②➵♥ ❚❤à ❚❤❛♥❤ ❍÷ì♥❣ ✭✷✵✶✾✮✱ ▲✉➟♥ ✈➠♥ ❚❤↕❝ s➽ t ỵ ỵ tt t ỵ ❚r÷í♥❣ ✣↕✐ ❤å❝ ❙÷ ♣❤↕♠✱ ✣↕✐ ❤å❝ ❍✉➳✳ ❬✾❪ ▼✳ ❍✐❧❧❡r② ✭✶✾✽✾✮✱ ✧❙✉♠ ❛♥❞ ❞✐❢❢❡r❡♥❝❡ sq✉❡❡③✐♥❣ ♦❢ t❤❡ ❡❧❡❝tr♦♠❛❣♥❡t✐❝ ❢✐❡❧❞✧✱ ✐❝❛❧ ❘❡✈✐❡✇ ❆✱ ✹✵✱ ✸✶✹✼✳ P❤②s✲ ❬✶✵❪ ❈✳ ❚✳ ▲❡❡ ✭✶✾✾✵✮✱ ✧▼❛♥②✲♣❤♦t♦♥ ❛♥t✐❜✉♥❝❤✐♥❣ ✐♥ ❣❡♥❡r❛❧✐③❡❞ ♣❛✐r ❝♦❤❡r❡♥t st❛t❡s✧✱ P❤②s✐❝❛❧ ❘❡✈✐❡✇ ❆✱ ✹✶✱ ✶✺✻✾✳ ❚✐t❧❡✿ ◆❖◆❈▲❆❙❙■❈❆▲ P❘❖P❊❘❚■❊❙ ❖❋ ❚❍❊ ❚❍❘❊❊✲P❍❖❚❖◆✲❆❉❉❊❉ ❆◆❉ ❖◆❊✲P❍❖❚❖◆✲❙❯❇❚❘❆❈❚❊❉ ❚❲❖✲▼❖❉❊ ❖❉❉ ❈❖❍❊❘❊◆❚ ❙❚❆❚❊ ❆❜str❛❝t✿ ■♥ t❤❡ ♣❛♣❡r✱ ✇❡ ❝♦♥s✐❞❡r t❤❡ ❧♦✇❡r✲♦r❞❡r ❛♥❞ ❤✐❣❤❡r✲♦r❞❡r ♥♦♥❝❧❛ss✐❝❛❧ ♣r♦♣❡r✲ t✐❡s ♦❢ t❤❡ t❤r❡❡✲♣❤♦t♦♥✲❛❞❞❡❞ ❛♥❞ ♦♥❡✲♣❤♦t♦♥✲s✉❜tr❛❝t❡❞ t✇♦✲♠♦❞❡ ♦❞❞ ❝♦❤❡r❡♥t st❛t❡ ❛s t✇♦✲♠♦❞❡ s✉♠ sq✉❡❡③✐♥❣✱ t✇♦✲♠♦❞❡ ❞✐❢❢❡r❡♥❝❡ sq✉❡❡③✐♥❣✱ ✈✐♦❧❛t✐♦♥ ♦❢ t❤❡ ❈❛✉❝❤②✲❙❝❤✇❛r③ ✐♥❡q✉❛❧✐t②✱ ❛♥❞ t✇♦✲♠♦❞❡ ❤✐❣❤❡r✲♦r❞❡r ❛♥t✐❜✉♥❝❤✐♥❣✳ ❚❤❡ r❡s✉❧ts s❤♦✇ t❤❛t t❤✐s st❛t❡ ❡①✲ ❤✐❜✐ts t✇♦✲♠♦❞❡ s✉♠ sq✉❡❡③✐♥❣ ❜✉t ❞♦❡s ♥♦t ❡①❤✐❜✐t t✇♦✲♠♦❞❡ ❞✐❢❢❡r❡♥❝❡ sq✉❡❡③✐♥❣✳ ■♥ ❛❞❞✐t✐♦♥✱ t❤✐s st❛t❡ ✈✐♦❧❛t❡s t❤❡ ❈❛✉❝❤②✲❙❝❤✇❛r③ ✐♥❡q✉❛❧✐t② ❛♥❞ ❜❡❝♦♠❡s ♥♦♥❝❧❛ss✐❝❛❧ st❛t❡✳ ❲❡ ❛❧s♦ s❤♦✇ t❤❛t t❤❡ t❤r❡❡✲♣❤♦t♦♥✲❛❞❞❡❞ ❛♥❞ ♦♥❡✲♣❤♦t♦♥✲s✉❜tr❛❝t❡❞ t✇♦✲♠♦❞❡ ♦❞❞ ❝♦✲ ❤❡r❡♥t st❛t❡ ❛♣♣❡❛rs t✇♦✲♠♦❞❡ ❤✐❣❤❡r✲♦r❞❡r ❛♥t✐❜✉♥❝❤✐♥❣ ✐♥ ❛♥② ♦r❞❡r✱ ❛♥❞ t❤❡ ❞❡❣r❡❡ ♦❢ ❛♥t✐❜✉♥❝❤✐♥❣ ❜❡❝♦♠❡s ♠♦r❡ ❛♥❞ ♠♦r❡ ♣r♦♥♦✉♥❝❡❞ ✇❤❡♥ ✐♥❝r❡❛s✐♥❣ t❤❡ ❤✐❣❤❡r✲♦r❞❡r✳ ❑❡②✇♦r❞s✿ ❙✉♠ sq✉❡❡③✐♥❣✱ ❞✐❢❢❡r❡♥❝❡ sq✉❡❡③✐♥❣✱ ✈✐♦❧❛t✐♦♥ ❈❛✉❝❤②✲❙❝❤✇❛r③ ✐♥❡q✉❛❧✐t②✱ t✇♦✲♠♦❞❡ ❛♥t✐❜✉♥❝❤✐♥❣✳