Quantum two-state level-crossing models in terms of the Heun functions

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Quantum two-state level-crossing models in terms of the Heun functions

Tigran Ishkhanyan

To cite this version:

Tigran Ishkhanyan. Quantum two-state level-crossing models in terms of the Heun functions. Math-

ematical Physics [math-ph]. Université Bourgogne Franche-Comté; Institute for Physical Research

(Ashtarak), 2019. English. �NNT : 2019UBFCK026�. �tel-02318374�

UNIVERSITÉ BOURGOGNE FRANCHE-COMTÉ

Laboratoire Interdisciplinaire Carnot de Bourgogne – UMR CNRS 6303

NATIONAL ACADEMY OF SCIENCES OF ARMENIA

Institute for Physical Research

QUANTUM TWO-STATE LEVEL-CROSSING MODELS IN TERMS OF THE HEUN FUNCTIONS

by

Tigran Ishkhanyan

A Thesis in Physics

Submitted for the Degree of Doctor of Philosophy

Date of defense: September 18 2019

Jury

Mr Claude LEROY Professor Supervisor

Dijon, ICB – UBFC

Mr Aram PAPOYAN Professor Supervisor Ashtarak, IPR – NAS RA

Mrs Yevgenya PASHAYAN-LEROY Doctor of Physics Examiner Besançon, UBFC

Mr Gagik DEMIRKHANYAN Professor Examiner Yerevan, ASPU

Mr Victor RED’KOV Professor Examiner Minsk, IP – NASB

Mr Atom MURADYAN Professor Referee

Yerevan, YSU

Mr David SARKISYAN Professor Examiner Ashtarak, IPR – NAS RA Président du Jury

Referees

Mr Atom MURADYAN Professor Referee

Yerevan, YSU

Mr Jacek KARWOWSKI Professor Referee Torun, IP – NCU

Laboratoire Interdisciplinaire Carnot de Bourgogne – UMR CNRS 6303, Université Bourgogne Franche-Comté, 9 Avenue A. Savary 21078 Dijon, France

Institute for Physical Research – National Academy of Sciences of Armenia, 0203 Ashtarak-2, Armenia

ACKNOWLEDGEMENTS

I would like to express my sincere gratitude to my supervisors Prof. Claude Leroy and Prof. Aram Papoyan for their willingness to help and support, for their patience, energy and optimism. I am extremely thankful to my father, Prof. Artur Ishkhanyan for his continuous mentorship and contributions of time and ideas.

I am thankful to Prof. Gagik Demirkhanyan and Prof. Atom Muradyan for valuable discussions and critical analysis of my thesis; Prof. Jacek Karwowski for these beautiful words about my thesis;

Prof. Radik Kostanyan and Prof. David Sarkisyan for the words of encouragement; Prof. Geza Levai for the detailed feedback; Mr. Ashot Manukyan for the basic knowledge in Maths and Physics and many-many others from the Institute for Physical Research NAS RA and Laboratoire Interdisciplinaire Carnot de Bourgogne UBFC who helped/stimulated/motivated me to complete this PhD research project.

I express my deepest gratitude to the French Embassy in Armenia for the opportunity to go and study in France as well as for discovering French culture. I acknowledge financial support received from the Agence universitaire de la Francophonie and the Armenian Science Committee, the Foundation for Armenian Science and Technology (FAST), the Ecole Doctorale Carnot-Pasteur and the International Associated Laboratory IRMAS.

Finally, I would like to express my deep appreciation and indebtedness to my family and Sofia for

all the support I’ve been given over the years. Thank you for your patience. This thesis is dedicated

to you. 


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RgI: cgRg0p:T5R 5H C:pRmp0m :55qC 5H dp:1gdp:Tbpq 71VCTbC

56g(g0 mgC7T:g :1g b5RCTmg0prqg gHH50: mg(5:gm :5 :1g dp:1gdp:Tbpq 7057g0:TgC 5H :1g g)R g3)p:T5RC :1gV p0g C:Tqq d)b1 qgCC C:)mTgm :1pR :1gT0 70gmgbgCC50C HT0C: 5H pqq :1g 0gqp:T(gC 5H :1g 1V7g0cg5dg:0Tb bqpCC dpy50 0gpC5R H50 :1g Cq56 705c0gCC TR :1g mg(gq57dgR: 5H :1g :1g50V 5H :1g g)R g3)p:T5RC TC :1p: :1g Cg0TgC C5q):T5RC gT:1g0 TR :g0dC 5H 756g0C 50 TR :g0dC 5H :1g H)Rb:T5RC 5H 1V7g0cg5dg:0Tb bqpCC p0g c5(g0Rgm rV p: qgpC: :10gg :g0d 0gb)00gRbg 0gqp:T5RC rg:6ggR C)bbgCCT(g b5gHHTbTgR:C 5H gI7pRCT5RC w - TRC:gpm 5H :65 :g0d 5RgC p77gp0TRc TR :1g 1V7g0cg5dg:0Tb bpCg w - 50 :1TC 0gpC5R T: 6pC b5dd5RqV :15)c1: :1p: :1g gI7pRCT5R b5gHHTbTgR:C p0g R5 q5Rcg0 mg:g0dTRgm gI7qTbT:qV

Sg(g0:1gqgCC T: 1pC 0gbgR:qV rggR C156R :1p: H50 :1g F e s pRm vtF s UF sc F- g)R g3)p:T5RC :1g0g gITC: TRHTRT:gqV dpRV 7p0:Tb)qp0 b15TbgC 5H :1g TR(5q(gm 7p0pdg:g0C H50 61Tb1 :1g 0gb)00gRbg 0gqp:T5RC H50 756g0 Cg0TgC gI7pRCT5RC 5H C5q):T5RC rgb5dg :65 :g0d R :1gCg bpCgC :1g C5q):T5RC bpR rg gI7qTbT:qV 60T::gR gT:1g0 pC p qTRgp0 b5drTRp:T5R 5H p HTRT:g R)drg0 5H :1g 50mTRp0V 50 b5RHq)gR: 1V7g0cg5dg:0Tb H)Rb:T5RC 50 pq:g0Rp:T(gqV TR :g0dC 5H p CTRcqg 50mTRp0V 50 b5RHq)gR:

cgRg0pqT8gm 1V7g0cg5dg:0Tb H)Rb:T5R R5:1g0 0gC)q: 0gbgR:qV 0g750:gm TC :1p: TH :1g C5q):T5RC 5H :1g cgRg0pq pRm CTRcqg b5RHq)gR: g)R g3)p:T5RC p0g gI7pRmgm TR :g0dC 5H :1g p770570Tp:g H)Rb:T5RC 5H :1g 1V7g0cg5dg:0Tb bqpCC :1g0g pqC5 gITC: TRHTRT:gqV dpRV 7p0:Tb)qp0 b15TbgC 5H :1g TR(5q(gm 7p0pdg:g0C H50 61Tb1 :1g c5(g0RTRc :10gg :g0d 0gb)00gRbg 0gqp:T5RC H50 gI7pRCT5R b5gHHTbTgR:C rgb5dg :65 :g0d fg R5:g :1p: TR pqq :1gCg bpCgC 5H :65 :g0d 0gm)b:T5RC :1g gI7pRCT5R b5gHHTbTgR:C p0g gI7qTbT:qV 60T::gR TR :g0dC 5H :1g )qg0 cpddp H)Rb:T5RC gCTmgC 6g 1p(g 0gbgR:qV b5RC:0)b:gm gI7pRCT5RC 5H :1g C5q):T5RC 5H :1g t UF sc F- g)R g3)p:T5R TR :g0dC 5H :1g g0dT:g H)Rb:T5RC

TCb)CCTRc :1g b5RmT:T5RC H50 mg0T(TRc HTRT:g C)d bq5Cgm H50d C5q):T5RC rV dgpRC 5H :g0dTRp:T5R 5H :1g dgR:T5Rgm Cg0TgC T: bpR rg C156R :1p: :1g :g0dTRp:T5R 5bb)0C TH p 0gc)qp0 CTRc)qp0T:V 5H :1g rT b5RHq)gR: g)R g3)p:T5R TC e F- pRm :1g vvUeg 7p0pdg:g0 5rgVC p 75qVR5dTpq g3)p:T5R fg p77qV :1gCg 0gC)q:C :5 mg0T(g C5dg 7p0:Tb)qp0 :65 C:p:g d5mgqC H50 61Tb1 :1g 705rqgd TC C5q(gm TR :g0dC 5H C7gbTpq dp:1gdp:Tbpq H)Rb:T5RC CTd7qg0 :1pR :1g g)R H)Rb:T5RC :1p: TC 6g TmgR:THV C5dg 7p0:Tb)qp0 d5mgqC H50 61Tb1 :1g TR(5q(gm g)R H)Rb:T5RC p0g gI70gCCgm TR :g0dC 5H :1g HpdTqTp0 H)Rb:T5RC 5H :1g 1V7g0cg5dg:0Tb bqpCC

i1g dpTR 5rygb:T(gC 5H :1TC 0gCgp0b1 p0g

:5 TmgR:THV pRm bqpCCTHV :1g 57:Tbpq HTgqm b5RHTc)0p:T5RC 0gHg00gm :5 pC :65 C:p:g d5mgqC H50 61Tb1 :1g CgdTbqpCCTbpq :Tdg mg7gRmgR: :65 C:p:g 705rqgd bpR rg C5q(gm TR :g0dC 5H :1g HT(g g)R H)Rb:T5RC

:5 TmgR:THV :1g qg(gq b05CCTRc HTgqm b5RHTc)0p:T5RC 6T:1TR :1g Cg: 5H 3)pR:)d :65 C:p:g

d5mgqC C5q(prqg TR :g0dC 5H :1g g)R H)Rb:T5RC

:5 b5RC:0)b: gI7qTbT: HTRT:g C)d bq5Cgm H50d C5q):T5RC 5H :1g cgRg0pq CTRcqg pRm rT b5RHq)gR: g)R g3)p:T5RC TR :g0dC 5H CTd7qg0 C7gbTpq H)Rb:T5RC pRm :5 TmgR:THV :1g :65 C:p:g g)R d5mgqC H50 61Tb1 :1g C5q):T5R 5H :1g 705rqgd TC 60T::gR pC pR T00gm)bTrqg b5drTRp:T5R 5H H)Rb:T5RC 5H :1g 1V7g0cg5dg:0Tb bqpCC

:5 gI:gRm :1g vR56qgmcg cpTRgm 5R :1g gIpb: 50 b5RmT:T5RpqqV C5q(prTqT:V 5H :1g :65 C:p:g 705rqgd TR :g0dC 5H :1g g)R H)Rb:T5RC :5 R5R 0gqp:T(TC:Tb pRm 0gqp:T(TC:Tb 6p(g g3)p:T5RC

: C15)qm rg R5:gm :1p: :1g rpCTb Cg: 5H pRpqV:Tb d5mgqC 5H :1g :65 C:p:g 705rqgd 1pC rggR mg(gq57gm TR :1g 7pC: rV C5q(TRc :1g :Tdg mg7gRmgR: tb10FmTRcg0 g3)p:T5RC TR :g0dC 5H C7gbTpq H)Rb:T5RC 5H :1g 1V7g0cg5dg:0Tb bqpCC g0g 6g C156 :1p: d)b1 d50g d5mgqC p0g mg0T(gm 61gR gI70gCCTRc :1g C5q):T5R 5H :1g 705rqgd TR :g0dC 5H :1g H)Rb:T5RC 5H :1g g)R bqpCC tTRbg :1g g)R H)Rb:T5RC 0g70gCgR: mT0gb: cgRg0pqT8p:T5RC 5H :1g 1V7g0cg5dg:0Tb H)Rb:T5RC :1g C5q):T5RC TR :g0dC 5H :1g qp::g0 H)Rb:T5RC cgRg0pqT8g pqq 1V7g0cg5dg:0Tb bpCgC

dpy50 0gC)q: 6g 0g750: TC :1p: :1g0g gITC: TR :5:pq TRHTRT:g bqpCCgC 5H :65 C:p:g d5mgqC C5q(prqg TR :g0dC 5H :1g HT(g g)R H)Rb:T5RC .50g C7gbTHTbpqqV 6g 1p(g C156R :1p: :1g0g gITC:

:1T0:V HT(g bqpCCgC H50 61Tb1 :1g 705rqgd bpR rg C5q(gm TR :g0dC 5H :1g cgRg0pq g)R H)Rb:T5RC w - HTH:ggR bqpCCgC C5q(prqg TR :g0dC 5H :1g CTRcqg b5RHq)gR: g)R H)Rb:T5RC 1p(g 70g(T5)CqV rggR mg0T(gm TR w - pRm 6g 1p(g 5r:pTRgm HT(g bqpCCgC C5q(prqg TR :g0dC 5H :1g m5)rqg b5RHq)gR: g)R H)Rb:T5RC w - HT(g 5:1g0 bqpCCgC TR :g0dC 5H :1g rT b5RHq)gR: g)R H)Rb:T5RC w - pRm p bqpCC TR :g0dC 5H :1g :0T b5RHq)gR: g)R H)Rb:T5RC w -

R5:1g0 Cg: 5H 5)0 0gC)q:C b5RCTC:C 5H :1g gI7pRCT5RC 5H :1g C5q):T5RC 5H :1g cgRg0pq CTRcqg b5RHq)gR: pRm rT b5RHq)gR: g)R g3)p:T5RC TR :g0dC 5H TRb5d7qg:g g:p w - 2)ddg0 b5RHq)gR:

1V7g0cg5dg:0Tb w - pRm R5R TR:gcg0 50mg0 g0dT:g H)Rb:T5RC w - i1g b5RmT:T5RC H50 :g0dTRp:T5R 5H :1gCg Cg0TgC TR 50mg0 :5 705m)bg HTRT:g C)d bq5Cgm H50d C5q):T5RC p0g mTCb)CCgm TR mg:pTq

:1T0m Cg: 5H 5)0 0gC)q:C b5dgC 5): TH :1g mg(gq57gm Cg0TgC gI7pRCT5RC p0g p77qTgm :5 TmgR:THV :1g 7p0:Tb)qp0 bpCgC H50 61Tb1 :1g g)R H)Rb:T5RC TR(5q(gm TR :1g C5q):T5RC 5H :1g 70gCgR:gm :65 C:p:g d5mgqC bpR rg 60T::gR pC C)b1 qTRgp0 b5drTRp:T5RC 5H :1g H)Rb:T5RC 5H :1g 1V7g0cg5dg:0Tb bqpCC :1p: bpRR5: rg 0gm)bgm :5 :1g 5Rg :g0d pRCp:8 TR(5q(TRc 5RqV 5Rg 1V7g0cg5dg:0Tb H)Rb:T5R R :1TC 6pV dpRV Rg6 qg(gq b05CCTRc d5mgqC p0g mg0T(gm i1gCg 0gC)q:C p0g 70gCgR:gm TR w -

TRpqqV p H5)0:1 Cg: 5H 0gC)q:C TC pb1Tg(gm rV p77qVTRc :1g pr5(g p7705pb1gC :5 R5R 0gqp:T(TC:Tb pRm 0gqp:T(TC:Tb 6p(g g3)p:T5RC TR 50mg0 :5 mg0T(g Rg6 gRg0cV TRmg7gRmgR: 3)pR:)d dgb1pRTbpq 75:gR:TpqC H50 :1g tb10FmTRcg0 g3)p:T5R :1p: p0g C5q(gm TR :g0dC 5H :1g H)Rb:T5RC 5H :1g 1V7g0cg5dg:0Tb bqpCC w - pRm :5 0g(gpq :1g RTRg 75:gR:TpqC H50 61Tb1 :1g C:p:T5Rp0V 2qgTR

50m5R g3)p:T5R bpR rg C5q(gm TR :g0dC 5H :1g b5RHq)gR: g)R H)Rb:T5RC w -

pCgm 5R :1gCg 0gC)q:C :1g vgV 5rCg0(p:T5RC 5H :1TC 0gCgp0b1 p0g

i1g0g gITC: TRHTRT:g bqpCCgC 5H :1g 3)pR:)d :Tdg mg7gRmgR: :65 C:p:g 705rqgd C5q(prqg TR :g0dC 5H cgRg0pq CTRcqg b5RHq)gR: pRm d)q:T b5RHq)gR: g)R H)Rb:T5RC

i1g TRHTRT:g bqpCCgC 5H :65 C:p:g d5mgqC C5q(prqg TR :g0dC 5H :1g g)R H)Rb:T5RC b5R:pTR R)dg05)C d5mgqC :1p: mgCb0Trg 5Rg :65 50 TRHTRT:g R)drg0 5H 7g0T5mTbpqqV 5bb)00TRc qg(gq b05CCTRcC 5H :1g 0gC5RpRbg THHg0gR: gIpd7qgC 5H C)b1 d5mgqC p0g 70gCgR:gm

: TC 75CCTrqg :5 b5RC:0)b: C5q):T5RC 5H :1g g)R g3)p:T5RC pC TRHTRT:g Cg0TgC TR :g0dC 5H :1g H)Rb:T5RC 5H :1g 1V7g0cg5dg:0Tb bqpCC 5H p mTHHg0gR: C:0)b:)0g tg(g0pq gIpd7qgC 5H C)b1 Cg0TgC gI7pRCT5RC p0g 70gCgR:gm

i1g pRpqV:Tb C5q):T5RC 5H :1g :65 C:p:g 705rqgd bpR rg 705ygb:gm 5R :1g 0gqp:T(TC:Tb pRm R5R 0gqp:T(TC:Tb 6p(g g3)p:T5RC :5 mg0T(g Rg6 C5q):T5RC 5H :1gCg g3)p:T5RC

i1g mg:pTqgm 0gC)q:C 5r:pTRgm p0g pC H5qq56C

R C-a37e5 1 H5qq56TRc 5)0 650v w - 6g mg0T(g HT(g 7p0pdg:0Tb bqpCCgC 5H :1g 3)pR:)d :Tdg mg7gRmgR: :65 C:p:g d5mgqC C5q(prqg TR :g0dC 5H :1g cgRg0pq g)R H)Rb:T5RC pb1 5H :1g bqpCCgC TC mgHTRgm rV p 7pT0 5H cgRg0p:TRc H)Rb:T5RC :1g HT0C: 5H 61Tb1 TC 0gHg00gm :5 pC :1g pd7qT:)mg pRm :1g Cgb5Rm 5Rg pC :1g mg:)RTRc d5m)qp:T5R H)Rb:T5R i1g bqpCCgC C)ccgC: R)dg05)C HpdTqTgC 5H C7gbTHTb HTgqm b5RHTc)0p:T5RC 6T:1 mTHHg0gR: 71VCTbpq 7057g0:TgC cgRg0p:gm rV p770570Tp:g b15TbgC 5H :1g :0pRCH50dp:T5R 5H :1g TRmg7gRmgR: (p0Tprqg 0gpq 50 b5d7qgI i1g0g p0g dpRV HpdTqTgC 5H d5mgqC 6T:1 b5RC:pR: mg:)RTRc 50 b5RC:pR: pd7qT:)mg R)dg05)C bqpCCgC 5H b1T07gm 7)qCgC 5H b5R:05qqprqg pd7qT:)mg pRm 50 mg:)RTRc HpdTqTgC 5H d5mgqC 6T:1 m5)rqg 50 d)q:T7qg 7g0T5mTb b05CCTRcC 7g0T5mTb pd7qT:)mg d5m)qp:T5R HTgqm b5RHTc)0p:T5RC g:b

i1g mg:)RTRc d5m)qp:T5R H)Rb:T5R TC :1g Cpdg H50 pqq :1g mg0T(gm bqpCCgC i1TC H)Rb:T5R TR(5q(gC H5)0 p0rT:0p0V 7p0pdg:g0C :1p: TC :65 d50g :1pR :1g 70g(T5)CqV vR56R 1V7g0cg5dg:0Tb bqpCCgC i1gCg 7p0pdg:g0C TR cgRg0pq p0g b5d7qgI pRm C15)qm rg b15CgR C5 :1p: :1g 0gC)q:pR:

mg:)RTRc TC 0gpq H50 :1g p77qTgm p0rT:0p0V b5d7qgI (pq)gm :0pRCH50dp:T5R 5H :1g TRmg7gRmgR:

(p0Tprqg i1g cgRg0pqT8p:T5R 5H :1g mg:)RTRc d5m)qp:T5R H)Rb:T5R :5 :1g H5)0 7p0pdg:0Tb bpCg TC :1g

d5C: R5:prqg gI:gRCT5R CTRbg dpRV )CgH)q 7057g0:TgC 5H :1g :65 C:p:g d5mgqC mgCb0Trgm rV :1g g)R

g3)p:T5R p0g m)g :5 RpdgqV :1g pmmT:T5Rpq 7p0pdg:g0C TR(5q(gm TR :1TC H)Rb:T5R .pRV 5H :1g mg0T(gm

pd7qT:)mg d5m)qp:T5R H)Rb:T5RC 70gCgR: mTHHg0gR: cgRg0pqT8p:T5RC 5H :1g vR56R 1V7g0cg5dg:0Tb

d5mgqC R Cg(g0pq bpCgC :1g cgRg0pqT8p:T5R TC pb1Tg(gm rV d)q:T7qVTRc :1g pd7qT:)mg d5m)qp:T5R

H)Rb:T5R 5H :1g b500gC75RmTRc 705:5:V7g 1V7g0cg5dg:0Tb bqpCC rV pR gI:0p Hpb:50 TRbq)mTRc pR

pmmT:T5Rpq 7p0pdg:g0 TRpqqV dpRV bqpCCgC C)ccgC: pd7qT:)mg d5m)qp:T5R H)Rb:T5RC 1p(TRc H50dC

R5: mTCb)CCgm 70g(T5)CqV

fg 70gCgR: Cg(g0pq HpdTqTgC 5H b5RC:pR: mg:)RTRc HTgqm b5RHTc)0p:T5RC cgRg0p:gm rV p 0gpq :0pRCH50dp:T5R 5H :1g TRmg7gRmgR: (p0Tprqg i1g dgdrg0C 5H :1gCg HpdTqTgC p0g CVddg:0Tb 50 pCVddg:0Tb :65 7gpv HTRT:g p0gp 7)qCgC 6T:1 b5R:05qqprqg mTC:pRbg rg:6ggR :1g 7gpvC pRm b5R:05qqprqg pd7qT:)mg 5H gpb1 5H :1g 7gpvC fg C156 :1p: :1g gmcg C1p7gC :1g mTC:pRbg rg:6ggR :1g 7gpvC pC 6gqq pC :1g pd7qT:)mg 5H :1g 7gpvC p0g b5R:05qqgm pqd5C: TRmg7gRmgR:qV rV mTHHg0gR:

7p0pdg:g0C fg TmgR:THV :1g 7p0pdg:g0C b5R:05qqTRc gpb1 5H :1g dgR:T5Rgm Hgp:)0gC pRm mTCb)CC 5:1g0 rpCTb 7057g0:TgC 5H 7)qCg C1p7gC fg C156 :1p: :1g 7)qCg gmcgC dpV rgb5dg C:g7 6TCg H)Rb:T5RC pRm mg:g0dTRg :1g 75CT:T5RC 5H :1g qTdT:TRc (g0:Tbpq 6pqq gmcgC fg C156 :1p: :1g 7)qCg 6Tm:1 TC b5R:05qqgm rV 5RqV :65 5H :1g TR(5q(gm 7p0pdg:g0C 50 C5dg (pq)gC 5H :1gCg 7p0pdg:g0C :1g 7)qCg 6Tm:1 mT(g0cgC pRm H50 C5dg 5:1g0 (pq)gC :1g 7)qCgC rgb5dg TRHTRT:gqV Rp0056 fg C156 :1p: :1g gHHgb: 5H :1g :65 dgR:T5Rgm 7p0pdg:g0C TC pqd5C: CTdTqp0 :1p: TC r5:1 7p0pdg:g0C p0g prqg :5 TRmg7gRmgR:qV 705m)bg 7)qCgC 5H pqd5C: :1g Cpdg C1p7g pRm 6Tm:1 fg mg:g0dTRg :1g b5RmT:T5RC H50 cgRg0p:T5R 5H 7)qCgC 5H pqd5C: TRmTC:TRc)TC1prqg C1p7g pRm 6Tm:1 pRm 70gCgR: Cg(g0pq C)b1 gIpd7qgC

TRpqqV 6g 70gCgR: p b5RC:pR: pd7qT:)mg 7g0T5mTb qg(gq b05CCTRc d5mgq pRm Cg(g0pq HpdTqTgC 5H b5RC:pR: mg:)RTRc HTgqm b5RHTc)0p:T5RC cgRg0p:gm rV b5d7qgI :0pRCH50dp:T5RC 5H :1g (p0Tprqg

SgI: H5qq56TRc 5)0 650v w - 6g 70gCgR: p C7gbTHTb b5RC:pR: pd7qT:)mg 7g0T5mTb qg(gq b05CCTRc d5mgq 5H :1g CgdTbqpCCTbpq 3)pR:)d :Tdg mg7gRmgR: :65 C:p:g 705rqgd :1p: rgq5RcC :5 p cgRg0pq g)R bqpCC 5H HTgqm b5RHTc)0p:T5RC i1g gIpb: pRpqV:Tb C5q):T5R H50 :1g 705rprTqT:V pd7qT:)mg cgRg0pqqV 60T::gR H50 :1TC bqpCC TR :g0dC 5H :1g cgRg0pq g)R H)Rb:T5RC TR :1TC C7gbTHTb bpCg pmdT:C Cg0TgC gI7pRCT5R TR :g0dC 5H :1g TRb5d7qg:g g:p H)Rb:T5RC w - ig0dTRp:TRc :1TC Cg0TgC 0gC)q:C TR pR TRHTRT:g 1Tg0p0b1V 5H HTRT:g C)d bq5Cgm H50d C5q):T5RC gpb1 C:pRmTRc H50 p 7p0:Tb)qp0 :65 C:p:g d5mgq 61Tb1 cgRg0pqqV TC 5RqV UF t-tUF ssg TR:gc0prqg TR :1g CgRCg :1p: H50 :1gCg HTgqm b5RHTc)0p:T5RC :1g pd7qT:)mg pRm 71pCg d5m)qp:T5R H)Rb:T5RC p0g R5: (p0Tgm TRmg7gRmgR:qV 56g(g0 :1g0g gITC:C p:

qgpC: 5Rg gIbg7:T5R 61gR :1g d5mgq TC cF UF t-tUF ssg TR:gc0prqg :1p: TC :1g uprT H0g3)gRbV pRm :1g mg:)RTRc 5H :1g m0T(TRc 57:Tbpq HTgqm p0g b5R:05qqgm TRmg7gRmgR:qV i1TC TC p b5RC:pR: pd7qT:)mg 7g0T5mTb qg(gq b05CCTRc d5mgq H50 61Tb1 :1g mg:)RTRc TR p qTdT: rgb5dgC p T0pb mgq:p b5dr b5RHTc)0p:T5R 6T:1 (p0Tprqg H0g3)gRbV 5H :1g qg(gq b05CCTRcC fg mg0T(g :1g gIpb: C5q):T5R H50 :1TC d5mgq mg:g0dTRg :1g q53)g: gI75RgR:C pRm C:)mV :1g 757)qp:T5R mVRpdTbC TR :1g CVC:gd H50 (p0T5)C 0gcT5RC 5H :1g TR7): 7p0pdg:g0C

R C-a37e5 2 6g 70gCgR: :1g HTH:ggR bqpCCgC 5H :1g :65 C:p:g d5mgqC H50 61Tb1 :1g C5q):T5R

5H :1g 705rqgd TC 60T::gR TR :g0dC 5H :1g CTRcqg b5RHq)gR: g)R H)Rb:T5RC :1gCg bqpCCgC 1p(g rggR

mg0T(gm TR w -

SgI: H5qq56TRc 5)0 650v w - 6g gIpdTRg :1g Cg0TgC gI7pRCT5RC 5H :1g C5q):T5RC 5H :1g CTRcqg b5RHq)gR: g)R g3)p:T5R TR :g0dC 5H mTHHg0gR: Cg:C 5H b5RHq)gR: 1V7g0cg5dg:0Tb H)Rb:T5RC

T0C: 6g b5RC:0)b: Cg(g0pq gI7pRCT5RC TR :g0dC 5H :10gg mTC:TRb: 2)ddg0 0gc)qp0 H)Rb:T5RC fg C156 :1p: :1g C)bbgCCT(g b5gHHTbTgR:C 5H :1g gI7pRCT5RC TR cgRg0pq 5rgV :10gg :g0d 0gb)00gRbg 0gqp:T5RC mgHTRTRc m5)rqg CTmgm TRHTRT:g Cg0TgC 156g(g0 H5)0 :g0d pRm :65 :g0d 0gqp:T5RC p0g pqC5 75CCTrqg H50 7p0:Tb)qp0 b15TbgC 5H :1g TR(5q(gm 7p0pdg:g0C i1g b5RmT:T5RC H50 qgH: pRm 50 0Tc1: 1pRm CTmg :g0dTRp:T5R 5H :1g Cg0TgC p0g mTCb)CCgm TR mg:pTq

)0:1g0d50g )CTRc :1g 0gb)00gRbg 0gqp:T5RC 5rgVgm rV :1g i0Tb5dT T00gc)qp0 b5RHq)gR:

1V7g0cg5dg:0Tb H)Rb:T5RC 6g b5RC:0)b: 5Rg d50g b5RHq)gR: 1V7g0cg5dg:0Tb gI7pRCT5R 5H :1g C5q):T5RC 5H :1g CTRcqg b5RHq)gR: g)R g3)p:T5R

SgI: 6g C156 :1p: :1g0g gITC: TRHTRT:gqV dpRV R5R:0T(Tpq b15TbgC 5H 7p0pdg:g0C 5H :1g CTRcqg b5RHq)gR: g)R g3)p:T5R H50 61Tb1 :1g :10gg :g0d 0gb)00gRbg 0gqp:T5RC c5(g0RTRc :1g gI7pRCT5RC 5H :1g C5q):T5RC TR :g0dC 5H :1g b5RHq)gR: 1V7g0cg5dg:0Tb H)Rb:T5RC p0g 0gm)bgm :5 :65 :g0d 5RgC R C)b1 bpCgC :1g gI7pRCT5R b5gHHTbTgR:C p0g gI7qTbT:qV bpqb)qp:gm TR :g0dC 5H :1g )qg0 cpddp H)Rb:T5RC

: C15)qm rg R5:gm :1p: :1g HTRT:g C)d 0gm)b:T5RC 5H Cg0TgC C5q):T5RC 5H :1g qTRgp0 Cgb5Rm 50mg0 50mTRp0V mTHHg0gR:Tpq g3)p:T5RC TR :g0dC 5H C7gbTpq H)Rb:T5RC 705(Tmg p dpy50 Cg: 5H vR56R bq5Cgm H50d pRpqV:Tb C5q):T5RC 5H (p0T5)C qTRgp0 mTHHg0gR:Tpq g3)p:T5RC gRb5)R:g0gm TR b5R:gd750p0V 71VCTbC 0gCgp0b1 cgRg0pq 5rCg0(p:T5R b5Rbg0RTRc C)b1 0gm)b:T5RC TC :1p: TH :1g C7gbTpq H)Rb:T5RC 5H :1g 1V7g0cg5dg:0Tb bqpCC p0g p77qTgm pC gI7pRCT5R H)Rb:T5RC 56TRc :5 :1g qTRgp0 0gqp:T5RC rg:6ggR pRV :10gg b5R:Tc)5)C 1V7g0cg5dg:0Tb H)Rb:T5RC p :g0dTRp:TRc Cg0TgC bpR rg 0gm)bgm :5 p qTRgp0 b5drTRp:T5R 6T:1 cgRg0pqqV 0p:T5Rpq b5gHHTbTgR:C 5H y)C: :65 gI7pRCT5R H)Rb:T5RC fg C:0gCC :1p: :1TC b5drTRp:T5R TC tee c t s :5 p H50d b5R:pTRTRc 5RqV 5Rg C7gbTpq H)Rb:T5R )g :5 :1TC 5rCg0(p:T5R 5Rg bpR mT0gb:qV p77qV p -oU - en Fv -a H50 C5q(TRc qTRgp0 50mTRp0V mTHHg0gR:Tpq g3)p:T5RC TR :g0dC 5H 1V7g0cg5dg:0Tb H)Rb:T5RC

TRpqqV H5qq56TRc 5)0 650v w - 6g p77qV :1g pr5(g 70gCgR:gm gI7pRCT5RC :5 :1g HTH:ggR

bqpCCgC 5H :1g g)R :65 C:p:g d5mgqC C p 0gC)q: 5Rg 5r:pTRC p 70gC)dprqV TRHTRT:g Cg: 5H C5q(prqg

d5mgqC 61Tb1 TR cgRg0pq p0g UF t-tUF ssg TR:gc0prqg rgCTmgC TR dpRV bpCgC :1gCg d5mgqC mgCb0Trg

tvvt -tr 705bgCCgC d5Rc :1TC Cg: 6g TmgR:THV :1g 5RqV Rg6 dgdrg0 61Tb1 TC i -sg

TR:gc0prqg TR :1p: :1g TR(5q(gm 7p0pdg:g0C p0g (p0Tgm TRmg7gRmgR:qV i1TC TC p :10gg 7p0pdg:0Tb

b5RC:pR: pd7qT:)mg qg(gq b05CCTRc d5mgq i1g d5mgq 70gCgR:C p HTgqm b5RHTc)0p:T5R mgCb0TrTRc pR

vgnn -et tF -tn qg(gq b05CCTRc 705bgCC H50 61Tb1 :1g qpCg0 HTgqm mg:)RTRc d5m)qp:T5R H)Rb:T5R TC

cT(gR TR :g0dC 5H :1g 4pdrg0: f H)Rb:T5R i1g cgRg0pq C5q):T5R 5H :1g 705rqgd H50 :1TC d5mgq TC

60T::gR pC p qTRgp0 b5drTRp:T5R 6T:1 p0rT:0p0V b5RC:pR: b5gHHTbTgR:C 5H :65 H)RmpdgR:pq C5q):T5RC

gpb1 5H 61Tb1 70gCgR:C pR T00gm)bTrqg qTRgp0 b5drTRp:T5R 5H :65 b5RHq)gR: 1V7g0cg5dg:0Tb H)Rb:T5RC fg 70gCgR: :1g mg:pTqgm mg0T(p:T5R 5H :1g H)RmpdgR:pq C5q):T5RC pRm pRpqV8g :1g rg1p(T50 5H :1g CVC:gd TR :1g qpCg0 HTgqm cT(gR rV :1g C7gbTHTb b5RHTc)0p:T5R )Rmg0 b5RCTmg0p:T5R fg R5:g :1p:

gpb1 5H :1g H)RmpdgR:pq C5q):T5RC 1pC pR pq:g0Rp:T(g 0g70gCgR:p:T5R TR :g0dC 5H p CTRcqg 5)0Cp:

cgRg0pqT8gm b5RHq)gR: 1V7g0cg5dg:0Tb H)Rb:T5R

R C-a37e5 3 H5qq56TRc 5)0 650v w - 6g mg0T(g HT(g bqpCCgC 5H 3)pR:)d :Tdg mg7gRmgR:

:65 C:p:g d5mgqC C5q(prqg TR :g0dC 5H :1g m5)rqg b5RHq)gR: g)R H)Rb:T5RC HT(g 5:1g0 bqpCCgC C5q(prqg TR :g0dC 5H :1g rT b5RHq)gR: g)R H)Rb:T5RC pRm p bqpCC C5q(prqg TR :g0dC 5H :1g :0T b5RHq)gR: g)R H)Rb:T5RC i1gCg bqpCCgC cgRg0pqT8g pqq :1g vR56R HpdTqTgC 5H :65 50 :10gg 7p0pdg:0Tb d5mgqC C5q(prqg TR :g0dC 5H :1g b5RHq)gR: 1V7g0cg5dg:0Tb H)Rb:T5RC :5 d50g cgRg0pq H5)0 7p0pdg:0Tb bqpCCgC TR(5q(TRc :10gg 7p0pdg:0Tb mg:)RTRc d5m)qp:T5R H)Rb:T5RC i1g 7p0:Tb)qp0 d5mgqC mg0T(gm mgCb0Trg mTHHg0gR: R5R qTRgp0 7p0pr5qTb b)rTb CTR1 b5C1 g:b qg(gq C6gg7TRc 50 qg(gq cqpRbTRc 705bgCCgC m5)rqg 50 :0T7qg qg(gq b05CCTRc 705bgCCgC pC 6gqq pC 7g0T5mTbpqqV 0g7gp:gm 0gC5RpRbg cqpRbTRc 50 0gC5RpRbg b05CCTRc 705bgCCgC TRpqqV 6g C156 :1p: d50g bqpCCgC bpR rg mg0T(gm )CTRc :1g g3)p:T5RC 5rgVgm rV bg0:pTR H)Rb:T5RC TR(5q(TRc :1g mg0T(p:T(gC 5H :1g b5RHq)gR:

g)R H)Rb:T5RC fg 70gCgR: pR gIpd7qg 5H C)b1 p bqpCC H50 gpb1 5H :1g :10gg mTCb)CCgm b5RHq)gR:

g)R g3)p:T5RC

SgI: H5qq56TRc 5)0 650v w - 6g b5RC:0)b: pR gI7pRCT5R 5H :1g C5q):T5RC 5H :1g rT b5RHq)gR: g)R g3)p:T5R TR :g0dC 5H :1g R5R TR:gcg0 50mg0 g0dT:g H)Rb:T5RC 5H p C1TH:gm pRm Cbpqgm p0c)dgR: i1g Cg0TgC TC C156R :5 rg c5(g0Rgm rV p :10gg :g0d 0gb)00gRbg 0gqp:T5R rg:6ggR C)bbgCCT(g b5gHHTbTgR:C 5H :1g gI7pRCT5R fg gIpdTRg :1g 0gC:0Tb:T5RC :1p: p0g Td75Cgm 5R :1g TR(5q(gm 7p0pdg:g0C TR 50mg0 :1p: :1g Cg0TgC :g0dTRp:gC :1)C 0gC)q:TRc TR bq5Cgm H50d HTRT:g C)d C5q):T5RC 5H :1g rT b5RHq)gR: g)R g3)p:T5R fg C156 :1p: :1g :g0dTRp:T5R TC 75CCTrqg TH p 0gc)qp0 CTRc)qp0T:V 5H :1g rT b5RHq)gR: g)R g3)p:T5R TC pR TR:gcg0 pRm :1g pbbgCC50V 7p0pdg:g0 5rgVC p 75qVR5dTpq g3)p:T5R

TRpqqV 6g p77qV :1g b5RC:0)b:gm gI7pRCT5R :5 mTCb)CC :1g gIpb: pRm b5RmT:T5RpqqV TR:gc0prqg rT b5RHq)gR: g)R d5mgqC 5H :1g :65 C:p:g 705rqgd C5q(prqg TR :g0dC 5H :1g g0dT:g H)Rb:T5RC

IpdTRTRc :1g :g0dTRp:T5R b5RmT:T5RC H50 :1g g0dT:g H)Rb:T5R gI7pRCT5R 6g 1p(g 70gCgR:gm TR :1g 70g(T5)C Cgb:T5R 6g C156 :1p: :1g0g gITC: 5RqV H5)0 gIpb:qV C5q(prqg d5mgqC pqq 5H 61Tb1 p0g :10gg 7p0pdg:0Tb i1g HT0C: :10gg 5H :1gCg bpCgC 0g705m)bg :1g vR56R 4pRmp) egRg0 STvT:TR pRm 05:1g0C )c1gC d5mgqC 61Tqg :1g H50:1 5Rg 70gCgR:C p Rg6 0gC)q: fg :1)C TR:05m)bg p Rg6 )Rb5RmT:T5RpqqV C5q(prqg d5mgq H50 :1g 3)pR:)d CgdTbqpCCTbpq :Tdg mg7gRmgR: :65 C:p:g 705rqgd i1TC TC p b5RC:pR:

pd7qT:)mg qg(gq b05CCTRc HTgqm b5RHTc)0p:T5R H50 61Tb1 :1g mg:)RTRc d5m)qp:T5R H)Rb:T5R rg1p(gC pC

:1g TR(g0Cg C3)p0g 055: p: :1g 50TcTR pRm :gRmC :5 p b5RC:pR: p: :1g TRHTRT:V fg 70gCgR: :1g mg:pTqgm mg0T(p:T5R 5H :1g d5mgq pRm b5RC:0)b: :1g gI7qTbT: cgRg0pq C5q):T5R 5H :1g 705rqgd :105)c1 p H)RmpdgR:pq C5q):T5R 60T::gR pC pR T00gm)bTrqg qTRgp0 b5drTRp:T5R 5H :65 R5R TR:gcg0 50mg0 g0dT:g H)Rb:T5RC 5H p C1TH:gm pRm Cbpqgm p0c)dgR:

R C-a37e5 4 6g b5RCTmg0 C5dg p77qTbp:T5RC 5H :1g p7705pb1gC mg(gq57gm TR 70g(T5)C b1p7:g0C :5 R5R 0gqp:T(TC:Tb tb10FmTRcg0 pRm 0gqp:T(TC:Tb 2qgTR 50m5R 6p(g g3)p:T5RC

T0C: H5qq56TRc 5)0 650v w - 6g TR:05m)bg :1g :1T0m tr e n -et 50mTRp0V 1V7g0cg5dg:0Tb gRg0cV TRmg7gRmgR: 3)pR:)d dgb1pRTbpq 75:gR:Tpq H50 :1g tb10FmTRcg0 g3)p:T5R pH:g0 :1g bvp0: pRm lFCb1q igqqg0 75:gR:TpqC 61Tb1 TC 705750:T5Rpq :5 pR p0rT:0p0V (p0Tprqg 7p0pdg:g0 pRm 1pC p C1p7g :1p: TC TRmg7gRmgR: 5H :1p: 7p0pdg:g0 g7gRmTRc 5R pR TR(5q(gm 7p0pdg:g0 :1g 75:gR:Tpq 70gCgR:C gT:1g0 p C150: 0pRcg CTRc)qp0 6gqq 61Tb1 rg1p(gC pC TR(g0Cg C3)p0g 055: p: :1g 50TcTR pRm (pRTC1gC gI75RgR:TpqqV p: TRHTRT:V 50 p Cd55:1 pCVddg:0Tb C:g7 rp00Tg0 6T:1 (p0Tprqg 1gTc1: pRm C:gg7RgCC i1g cgRg0pq C5q):T5R 5H :1g tb10FmTRcg0 g3)p:T5R H50 :1TC 75:gR:Tpq 61Tb1 TC p dgdrg0 5H p cgRg0pq g)R HpdTqV 5H 75:gR:TpqC TC 60T::gR :105)c1 H)RmpdgR:pq C5q):T5RC gpb1 5H 61Tb1 70gCgR:C pR T00gm)bTrqg qTRgp0 b5drTRp:T5R 5H :65 p)CC 50mTRp0V 1V7g0cg5dg:0Tb H)Rb:T5RC

SgI: H5qq56TRc 5)0 650v w - 6g b5RCTmg0 p 71VCTbpq p77qTbp:T5R 5H :1g bq5Cgm H50d C5q):T5RC 5H :1g rT b5RHq)gR: g)R H)Rb:T5RC TR :g0dC 5H :1g g0dT:g H)Rb:T5RC mTCb)CCgm TR :1g 70g(T5)C b1p7:g0 fg 70gCgR: :1g HT(g CTI 7p0pdg:0Tb 75:gR:TpqC H50 61Tb1 :1g cgRg0pq C5q):T5R 5H :1g 5Rg mTdgRCT5Rpq tb10FmTRcg0 g3)p:T5R TC 60T::gR TR :g0dC 5H :1g rT b5RHq)gR: g)R H)Rb:T5RC pRm H)0:1g0 TmgR:THV p 7p0:Tb)qp0 b5RmT:T5RpqqV TR:gc0prqg 75:gR:Tpq H50 61Tb1 :1g TR(5q(gm rT b5RHq)gR:

g)R H)Rb:T5R pmdT:C p H5)0 :g0d HTRT:g C)d gI7pRCT5R TR :g0dC 5H :1g g0dT:g H)Rb:T5RC i1TC TC pR TRHTRT:g 6gqq mgHTRgm 5R p 1pqH pITC fg 70gCgR: :1g gI7qTbT: C5q):T5R 5H :1g 5Rg mTdgRCT5Rpq tb10FmTRcg0 g3)p:T5R H50 :1TC 75:gR:Tpq pRm mTCb)CC :1g r5)Rm C:p:gC C)7750:gm rV :1g 75:gR:Tpq fg mg0T(g :1g gIpb: g3)p:T5R H50 :1g gRg0cV C7gb:0)d pRm b5RC:0)b: pR pbb)0p:g p7705ITdp:T5R H50 :1g r5)Rm C:p:g gRg0cV qg(gqC

TRpqqV H5qq56TRc 5)0 650v w - 6g 70gCgR: TR :5:pq HTH:ggR 75:gR:TpqC H50 61Tb1 :1g

C:p:T5Rp0V 2qgTR 50m5R g3)p:T5R TC C5q(prqg TR :g0dC 5H :1g b5RHq)gR: g)R H)Rb:T5RC gbp)Cg 5H

:1g CVddg:0V 5H :1g b5RHq)gR: g)R g3)p:T5R 6T:1 0gC7gb: :5 :1g :0pRC75CT:T5R 5H T:C 0gc)qp0

CTRc)qp0T:TgC 5RqV RTRg 5H :1g 75:gR:TpqC p0g TRmg7gRmgR: 5)0 5H :1gCg TRmg7gRmgR: 75:gR:TpqC p0g

HT(g 7p0pdg:0Tb oRg 5H :1gd 75CCgCCgC p H5)0 7p0pdg:0Tb 50mTRp0V 1V7g0cg5dg:0Tb C)r 75:gR:Tpq

pR5:1g0 5Rg 75CCgCCgC p H5)0 7p0pdg:0Tb b5RHq)gR: 1V7g0cg5dg:0Tb C)r 75:gR:Tpq pRm 5Rg 75:gR:Tpq

75CCgCCgC H5)0 7p0pdg:0Tb C)r 75:gR:TpqC 5H r5:1 1V7g0cg5dg:0Tb :V7gC i1g H5)0:1 HT(g 7p0pdg:0Tb

75:gR:Tpq 1pC p :10gg 7p0pdg:0Tb b5RHq)gR: 1V7g0cg5dg:0Tb C)r 75:gR:Tpq 61Tb1 TC 156g(g0 5RqV b5RmT:T5RpqqV TR:gc0prqg i1g 0gdpTRTRc HT(g TRmg7gRmgR: g)R 75:gR:TpqC p0g H5)0 7p0pdg:0Tb pRm 1p(g C5q):T5RC 5RqV TR :g0dC 5H T00gm)bTrqg b5RHq)gR: g)R H)Rb:T5RC

i1g 0gC)q:C 5H :1TC 0gCgp0b1 1p(g rggR 70gCgR:gm TR 0gCgp0b1 7p7g0C 7)rqTC1gm m)0TRc :1g qpC: Vgp0C

i C1v1pRVpR pRm . C1v1pRVpR I7pRCT5RC 5H :1g C5q):T5RC :5 :1g b5RHq)gR: g)R g3)p:T5R TR :g0dC 5H :1g 2)ddg0 b5RHq)gR: 1V7g0cg5dg:0Tb H)Rb:T5RC l m(pRbgC 4

. .pR)vVpR i C1v1pRVpR . s pv5rVpR pRm . C1v1pRVpR Cg0TgC C5q):T5R 5H :1g cgRg0pq g)R g3)p:T5R TR :g0dC 5H TRb5d7qg:g g:p H)Rb:T5RC 13

. C1v1pRVpR i t1p1(g0mVpR i C1v1pRVpR i1T0:V HT(g bqpCCgC 5H C5q):T5RC 5H :1g 3)pR:)d :Tdg mg7gRmgR: :65 C:p:g 705rqgd TR :g0dC 5H :1g cgRg0pq g)R H)Rb:T5RC )0 l1VC

69

i t1p1(g0mVpR i C1v1pRVpR 0Tc50VpR . C1v1pRVpR RpqV:Tb C5q):T5RC 5H :1g 3)pR:)d :65 C:p:g 705rqgd TR :g0dC 5H :1g m5)rqg rT pRm :0T b5RHq)gR: g)R H)Rb:T5RC

5R:gd7 l1VCTbC 0dgRTpR b tbT 50

t ip0q5VpR i C1v1pRVpR pRm . C1v1pRVpR 5)0 HT(g 7p0pdg:0Tb pRm HT(g H5)0 7p0pdg:0Tb TRmg7gRmgR: b5RHq)gR: g)R 75:gR:TpqC H50 :1g C:p:T5Rp0V 2qgTR 50m5R g3)p:T5R

RR l1VC g0qTR 528

i C1v1pRVpR pRm . C1v1pRVpR t5q):T5RC 5H :1g rT b5RHq)gR: g)R g3)p:T5R TR :g0dC 5H :1g g0dT:g H)Rb:T5RC RR l1VC 383

tpcg: . C1v1pRVpR 4g05V pRm i C1v1pRVpR i65 C:p:g d5mgq 5H p cgRg0pq g)R bqpCC 6T:1 7g0T5mTb qg(gq b05CCTRcC 5R:gd7 l1VCTbC 0dgRTpR b tbT 52

i C1v1pRVpR pRm . C1v1pRVpR i1g :1T0m HT(g 7p0pdg:0Tb 1V7g0cg5dg:0Tb 3)pR:)d dgb1pRTbpq 75:gR:Tpq m(pRbgC TR Tc1 Rg0cV l1VCTbC 2018

i C1v1pRVpR 4pdrg0: f gIpb:qV C5q(prqg qg(gq b05CCTRc b5RHq)gR: 1V7g0cg5dg:0Tb

:65 C:p:g d5mgq 5R:gd7 l1VCTbC 0dgRTpR b tbT 54

C-a37e5 1

SOLUTIONS OF THE TWO-STATE P OBLEM IN TE MS OF THE GENE AL HEUN FUNCTIONS

1.1 T-.57y f.9e cla66e6 2f 62l87.216 2f 7-e 48a1780 7.0e-de3e1de17 7:2-67a7e 352ble0 .1 7e506 2f 7-e ,e1e5al He81 f81c7.216

i1g :65 C:p:g CVC:gd TC :1g CTd7qgC: R5R :0T(Tpq 3)pR:)d CVC:gd :1p: bpR rg :0gp:gm pRpqV:TbpqqV pRm T: TC p 0p:1g0 c55m p7705ITdp:T5R H50 dpRV 0gpq 3)pR:)d CVC:gdC TR Rp:)0g

Ipd7qgC 5H C)b1 CVC:gdC p0TCg TR p R)drg0 5H 71gR5dgRp 5H b5R:gd750p0V 71VCTbC b1gdTC:0V gRcTRgg0TRc g:b R :1g 70gCgR: 0gCgp0b1 6g b5RCTmg0 :1g 3)pR:)d R5R pmTprp:Tb :0pRCT:T5RC rg:6ggR qg(gqC m)0TRc :1g TR:g0pb:T5R 5H gI:g0Rpq 57:Tbpq HTgqmC 6T:1 :1g dp::g0 61gR 5RqV p :0pRCT:T5R rg:6ggR :65 5H :1g qg(gqC 5H p cgRg0pqqV d)q:T C:p:g CVC:gd TC Rgp0qV 0gC5RpR: 6T:1 :1g gI:g0Rpq m0T(TRc HTgqm t5 6g mTCb)CC :1g mVRpdTbC 5H y)C: :65 3)pR:)d qg(gqC T g :1g 3)pR:)d :65 C:p:g 705rqgd pCC)dTRc :1g gHHgb: 5H :1g HTgqm 5R 5:1g0 qg(gqC :5 rg RgcqTcTrqg pC :1gV p0g Hp0 5HH :1g 0gC5RpRbg

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