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s# O=wt |vwQDmr= Q=DN=U�|Qiv QY=vCLD ,q=tDL= w OvQ=O |vrwm VvmtyQ@ =yxDUy =@ w Qo}Om} =@ =yuwQDmr=u}= j}kO pL "OvQ=O Q=Qk R}v |HQ=N |U}]=vetwQDmr= |=yu=O}t Q}F-=D"CU= xOw@v Q}PB u=mt= OQ=wt QFm = QO R}v xr�Ut%OQ=O OwHw |@} QkD pL x=Q wO|m} R}i X=wN uDW=O Q_v QO =@ '=Q |vwQDmr= x=oDUO *|vwDr}t=y "1|} wor= |vwDr}t=y l} Qo}O CQ=@ax@ "s}vm xO=U CU= umtt xm =Hv; =D 'u;|i}m Qw]x@ sm CUO =Q x=oDUO |m} R}i X=wN CU= QO=k xm s} R=U@xm OvDUy |}=ywor= wOv=m w uwUQOv= 'OQ=@=y '|=xrS |=ywor= "Ovm |v}@V}B"OvQ=O =Q Q_v OQwt x=oDUO h}YwD |}=v=wD l} Qy|}=yVwQ R= x=oDUO |vwQDmr= T@ Gwt `@=D uOQw; CUOx@ |=Q@ "2"OvyO|t =Q x=oDUO |m} R}i |=yC}tm |@ wN ?} QkD =@ xm s}vm|t xO=iDU=`@=D '(DFT) |r=oJ |a@=D -x} Q_v '|WOQw |=yVwQ R= u=wD|t =Hv}= QO"OQ@ s=v xDU@ty -x}=B `@=wD =} w wQDU=H Gwts}v=wD@ QmPr= jwi j} Q] wO R= |m} ltm x@ xm |DQwY QO 'p=LQyx@x @W R= pmWDt |y=oDUO RQ=sy =Q | vwQ Dm r= VvmtyQ @ = @ x=oDUOh}a[ VvmtyQ@ =@ |}=yuwQDmr= x@W =} w VvmtyQ@ uwO@ |=yuwQDmr="OwW|t pL p@=k xr�Ut 's}yO Q=Qk|Oq}t CYW -xyO QO w w�=Ovq |tQi `}=t -x} Q_v |Oq}t x=HvB -xyO QOx�=Q= h}a[ |oDU@ty =@ |}=yx=oDUO h}YwD |=Q@ |r=oJ |a@=D -x} Q_vl} x@ l} -x]@=Q l} xm OwW|t ZQi w�=Ovq |tQi `}=t -x} Q_v QO "Ov=xOWC=QP x@W w VvmtyQ@ uwO@ x=oDUO l} O=R; C=QP -xDN}ov=Q@ Cq=L u}@VvmtyQ@ xm OwW|t ZQi u}vJty "CU= Q=QkQ@ VvmtyQ@ =@ x=oDUO l}w CU= |DN=vWxO}OB -x} Q_v l} x} Q_v u}= "CU= h}a[ C=QP x@W u}@Q=DiQ x@=Wt |i}m Qw]x@ VvmtyQ@ =@ p=tQv |tQi `}=t l} Q=DiQ u; j@=]t"CU= (OriQtwR |wor=) VvmtyQ@ uwO@ |tQi R=o l}CU= |vD@t (HK) uywm w nQ@vywy -x}[k wO Q@ |r=oJ |a@=D -x} Q_v|vwQDmr= Q=DN=U u}}@D |=Q@ (KS) sW�uywm |Ov@pwtQi R= pta QO w [2]u}= QO "CU= xOW xO=iDU= |SQv= |=yQ=wv -x@U=Lt w x}=B Cr=L QO O=wtR= |y=oDUO RQ=sy =Q |vwQDmr= VvmtyQ@ =@ x=oDUO l} R}v |Ov@pwtQiQF-wt p}Uv=DB l} Q}F-=D CLD xm OvQ}o|t VvmtyQ@ uwO@ |=yuwQDmr= x@W"OQ=O Q=Qk|=y|a@=D x=oDUO l} Q}PBxOy=Wt |=yC}tm 'HK |=}=[k j@=]tQ@ |vD@t C=@U=Lt QDW}@ u}vJty "OvDUy |r=oJ R= |OQix@ QYLvtQO w CU= xOw@ Q=wDU= (LDA) |r=oJ |a[wt ?} QkD -x}=B Q@ DFT"CU= xDW=O x@ QHD =@ |@ wN Ck@=]t xOt; CUOx@ G}=Dv OQ=wt R= |Q=}U@

|Qiv QY=v'=ypwmrwt '=ysD= X=wN u}}@D w xOy=Wt x@ ,qwtat p=oJ -xO=t u=v=Om} R}i'=yQwr@ x@W 'u} Qwr@ C=Ot=H 'wv=v |=yQ=DN=U '=yQt}rwB '=yu}�DwQB '=yxWwN|w=L |oty =yx=oDUO u }= "O vR=OQ B|t =yR=o w =y` }=t '` }=t |=yQwr @|U=U= |=y w[wt R= |m} "OvDUy =yxDUy w =yuwQDmr= R= |=xawtHt"CU= O=wt u}= |vwQDmr= Q=DN=U w[wt p=oJ -xO=t l} R}i|=xO=Di= =B *V}B Q=m |}=yx=oDUO u}vJ |vwDr}t=y Qorta uDWwv"CU}v Q}PBu=mt= OQ=wt QFm = QO =yv; Qov}OwQW -xrO=at j}kO pL =t= 'CU="s}vm pL |@} QkD Qw]x@ =Q xr�Ut O}=@|t |ak=w OQ=wt QFm = QO 'wQu}= R=?} QkD u}= QO "CU= hwQat (BO) Qt}=yvB w=�uQw@?} QkD x@ ?} QkD u}rw=CQwY x@ u=wD|t =Q |=xQPT@ x=oDUO l} pm Gwt `@=D xm OwW|t ZQi?} QkD u}= j]vt "CWwv |vw} Gwt `@=D w |vwQDmr= Gwt `@=D ?Q[ pY=Lx@ =yuwQDmr= "CU= |vD@t =yxDUy x@ C@Uv =yuwQDmr= uOw@ QDl@UQ@CmQL p}rO x@ w Ovvm|t =O}B |O=} R |W@vH |SQv= u=W|m@U p}rO"Ovv}@|t (=DU}=) CmQL|@ ,=@} QkD =Q =yxDUy 'x_Lr Qy QO 'u=W`} QU|SQv= h=o R= (=yuwvwi |SQv=) |W=aDQ= |SQv= xm |OQ=wt QO ?} QkD u}=QO '=t= "CU= |@ wN ?} QkD OW=@ QDtm =yv; |oDN}ov=Q@ |=Q@ |vwQDmr=u=wvax@ "CU}v |@U=vt ?} QkD 'CU= QiY |SQv= h=o xm C=Rri OQwt|rw 'OvRri q=@ |=y=tO QO xm OQm O=} hQ=aDt |=y=v=UQQ@= R= u=wD|t xvwtv|tyt Q=}U@ Vkv uwvwi�uwQDmr= VvmtyQ@ '|}=v=UQQ@= R=i x@ Q=Po QO"O};|t V}B xO}}q;=v *u}i=Qo QO BO ?} QkD Zkv Qo}O OQwt "Ovm|t |R=@QiY |SQv= h=o =@ =v=UQs}v l} CU= xOW hWm 2004 p=U QO xm u}i=Qo-xrHt QO ,=Q}N= xm |=xr=kt x@ "CU}v ?U=vt u; |=Q@ BO ?} QkD =Pr "CU="[1] O}vm xaH=Qt �OvQ=O |O@ Q=DiQ u}i=Qo QO =yuwvwi� u=wva CLD QJ}v?r]t uOW xO=U w '|vwQDmr= Q=DN=U |UQQ@ Qw_vtx@ 'CQwY Qy QO=yv; |=Q@ BO ?} QkD xm s} Q=O Q=mwQU |}=yx=oDUO =@ s}vm|t ZQi ,qai"CU= |@ wN ?} QkDw Ov=xDUWv CmQL|@ u=W|rO=aD |=yu=mt QO =yxDUy ZQi u}= =@6 a 45 |B=}B -xQ=tW

s#p}rO x@ xm |R=i Q=Po =@ CU= hwQat C=t Q=Po x@ xm Q=Po u}= xm CU="OQ=O Cw=iD ,=D}y=t O};|t V}B |tQi K]U QO |SQv= h=o Qw[L"|Ut O}Um = |=y=v=UQQ@= R=i Q=Po |q=@ |=tO "2"u}ovU |vw}tQi |=yx=oDUO QO hrDNt |U}]=vet |=yR=i x@ Q=Po "3= U;pw e | U } ]= v e t xS } w C tw= k t w [w t "4u; O= } R Q= } U @ C } U= U L w (colossal magneto resistirity)"|HQ=N |U}]=vet u=O}t C=Q}}eD Q@=Q@ QOKQ]t 'Q}N= uQk s}v |] 'R=@ Q}O R= SCES w WCES w[wt wOxOW s}UkD xDUO wO x@ p=oJ xO=t u=v=Om} R}i \=@DQ= u}= QO w Ov=xOw@xO=iDU= DFT-KS R= w OvDN=OQB|t WCES |UQQ@ x@ pw= -xDUO "OvOw@|O}WQwN O=Diy w CYW |=yxyO QO ?v=Hv}= |k}kLD |=yQ=m "OvOQm|t"[3] OQ=O Q=Qk xDUO u}ty |=yQ=m <RHR= w O v=x DN=OQ B SCES |UQQ @ x @ x m O v=xOw @ | v= U m swO -x DUOpL |=Q @ xQ}e w uwU }=O -x rO=at 'u } Qo ` @=w D '|=xQP T @ |=yl}vm DQ=Po uwJ |r}=Ut K} QWD x@ w Ov=xOQm xO=iDU= |} wor= |=y|vwDr}t=y"Ov=xDN=OQB OW QmP q=@ QO xm |U}]=vet |=yQ=Po w C=t j}=a�Rriu=w D|t = }; x m CU= xOW KQ]t p=-wU u }= Q }N= -xyO wO |] QOp=oJ -xO=t u=Om} R}i xDUO wO u}= u}@ |DOLw xm OQm x�=Q= |=|Ov@pwtQi|oDU@ty =@ xJ '|vwQDmr= |=yx=oDUO h}YwD -xOya R= w OQw=}@ OwHw@"CU= C@Ft p=-wU u}= ?=wH "O};Q@ |wk |oDU@ty =@ xJ w h}a[QO u=vJty w xOW KQ]t '\=@DQ= u}= QO 'Q}N= -xyO wO QO xm |Di=}yQw (DMFT) |m}t=v}O u}ov=}t u=O}t -x} Q_v 'CU= |Q}o pmW p=L"CU= |r=oJ |a@=D -x} Q_v =@ u; j}irD|=yx=oDUO |=Q@ u}ov=}t u=O}t -x} Q_v s}taD DMFT Ck}kL QOQ} R |WywSB G}=Dv T=U= Q@ ,qw= s}taD u}= "CU= |vwQDmr= T@ |twDv=wm%CU= Q=wDU=x m O v=xO=O u=W v (Metzner) Q vR Dt w (Vollhardt) CQ= y rw "1| }=Q;sy OL QO 'VvmtyQ @ = @ | vw }tQi T @ x=oDUO l } |SQ v=�OwN"[4] (� � �(iwn)) "OQ=Ov |oDU@ xv=mD x@ 'C}=yv}@ |=xm@WCW=ov l} xm Ov=xO=O u=Wv (Georges) SQS w (Kotliar) Q}}rD=m "2|Yr=N=v |wor= w OQ=@=y |wor= |Oa@ C}=yv}@ x=oDUO u}@ Q=oR=U OwN"[5] OQ=O OwHw uwUQOv="[6] OwW|t xO=iDU= Q F-wt Vvm |Ov @pwtQi R= x } Q_ v u }= QO ,=} v= F` @= D "Ov m|t xU= m l } =Q Cw= i Dt Qy=_ x @ |=yVwQ |Ov @pwtQi u }=xOr=QoDv= =@ |r=QoDv= CQwY x@ =Q x=oDUO O=R; |SQv= u; `@D x@ w VQ=B|=yQ}eDt R= |a@=D S Vvm u; QO xm Ovvm|t h} QaD exp(�S( �; ))|vwDr}t=y =@ uwUQOv= |Yr=N=v |wor= R= TBU "CU= |vtU=QoHAIM = HsD= +Hs=tL +HSqB wm;QO xm OvDUy | }=yQDt=Q= B u=ty HSqB wm |=yQDt=Q= B w OwW|t xO=iDU=

Q}osWJ |=yC}kiwt seQ|ra 'DFT QO |r=oJ |a[wt ?} QkD =t=QO LDA |=y|v}@V}B p=Ft u=wvax@ "CU= xDW=O R}v |}=y|t=m =v 'u;CUQO=v u}ovU |vw}tQi |=yx=oDUO =} w |=x]U=w C=Rri O}Um = OQwtp=L 'OvRri V2O3 =} La2CuO4 xm Ovm|t |v}@V}B LDA "CU= xOw@?wN LDA-DFT xm |OQ=wt QO "Ov=j}=a O=wt u}= O} wo|t V}=tR; xmv;|oDU@ty =@ |vwQDmr= |=yx=oDUO =@ =t xm OvDUy |OQ=wt Ovm|t Q=mG }= D v x @ LDA-DFT x m | }=y=H "s } Q=O Q= mwQU (WCES) h}a[|wk |oDU@ty =@ |vwQDmr= |=yx=oDUO =@ ,=DOa=k =t OUQ|t CUQO=v"s} Q=O Q=mwQU (SCES)x @ | vwQDm r= x=oDUO l } s} v=O @ xm v; |=Q @ |DWo v=QU Q= }at l }u}= |Q=wv Q=DN=U x@ xm CU= u; CU= jraDt SCES x@ =} wWCES|SQ v= 'OW= @ uy B Q_ v OQwt |=yuwQ Dm r= |SQ v= Q=w v Q o = "s } Qov @ O=wt|y=Dwm COt =yuwQDmr= CQwY u; QO w CU= O=} R =yuwQDmr= |W@vHQ=}U |=yuwQDmr= = @ =t xH}D v QO "Ovvm|t |QBU =ys D= CQw=Ht QO =QQ@ =Q |Y=N |=H =yuwQDmr= Qo}O CQ=@ax@ "s} Q=O Q=mwQU (itinerant)u=wD|t =Q =yuwQDmr= xvwou}= Gwt `@=wD "OvQ=O xvwoGwt |Q=DiQ w Ovv} Ro|tv=@ |O=wt "OQw; CUOx@ QF-wt |vwQDmr= lD |@ w=vD p}Uv=DB l} R= xO=iDU= =@QO |r=oJ |a@=D -x} Q_v R= xO=iDU= w OvQ=O jraD WCES x@ C=YNWt u}="CU= |k]vt |Q=m (DFT-KS) sW�uywm ?wJQ=J|SQv= uOw@ QDtm p}rOx@ 'OW=@ l} Q=@ =yuwQDmr= |SQv= Q=wv Qo = =t==@ =t xH}DvQO "Ovv=QPo|t =ysD= CQw=Ht QO |QDW}@ COt '=yv; |W@vHxvwoxQP =yuwQDmr= Q=DiQ w CW=O s}y=wN Q=mwQU xO} Ro}=H |=yuwQDmr=QO O}=@|t w OvQ=O jraD SCES x@ C=YNWt u}= =@ |O=wt "Ow@ Oy=wN"s}W=@ DFT-KS R= Q}e |Di=}yQ |wHDUHx@ =Q x} Q_v l} s}v=wD|t =}; xm CU}v u; QU Q@ EL@ CQwY Qy QOxr�Ut l} R}i x@ O}=@|t xm CU=Hv}= xDmv "s}vm hPL Qo}O -x} Q_v `iv"CU= ?U=vt pLx=Q s=Om O}UQB w CU} Qovxm@W |wor= xQNq=@ w wOv=m 'uwUQOv= 'OQ=@=y |=ywor= 'Ck}kL QOuWwQ Qw_vtx@ "Ov=xOW |iQat SCES h}YwD |=Q@ xm Ov=|}=yp=Ft wOv=m=@ |vwQDmr= |Dkw "svm|t xQ=W= Q} R -xDmv x@ |wk |oDU@ty swyit uOWu}= x@ Oy=wN@ |Qo}O uwQDmr= w OW=@ xDUWv |tD= p=D}@ Qw= QO q=@ u}BU=u}}=B u}BU= =@ |vwQDmr= O}=@ ,=L}HQD |rw�=B OQ] pY= p}rOx@ 'OwQ@ p=D}@ Qw=Qo}O x=o}=H x@ x=o}=H l} R= uwQDmr= l} VQB 'Qo}O CQ=@a x@ "OW=@x=o}=H u; QO u}BU= u=ty =@ |vwQDmr= Qw[L sOa =} Qw[L x@ ,=O}OW=} d -xDUwB w QB |vwQ}@ -xDUwB =@ |}=yx=oDUO p}rO u}= x@ "OQ=O |oDU@u}= QO "OvQ=O jraD |wk |oDU@ty =@ |=yx=oDUO x@ QB ,=WN@ |vwQO fQ=@ 'u}BU= p}@k R= 'f =} d |=yuwQDmr= |O=R; C=HQO p}rO x@ =yx=oDUOu=wva x@ "Ow@ s}y=wN =yR=i Q=Po `=wv= Oy=W =t '|Q=Ot Qw=DWo '|m} QDmr=%OQ@ s=v Q} R OQ=wt R= u=wD|t xvwtvQmP u=}=W "V2O3 QO j}=a�Rri Q=Po QO xS} w Ctw=kt O}OW C=Q}}eD "17 a 1386 u=DU@=D

s#OQ=O OwHw DMFT CqO=at -xawtHt pL |=Q@ |irDNt |OOa jQ]"non-crossing?} QkD "3 '|twDv=wm |wrQ=mxDvwt "2 'j}kO |R=U|Q]k "1wOv=m -xr=v=mwO w xr=v=m l} -xm@W |wor= |UQQ@ QO umi=Qwv =[Q w xOv@xO=iDU= DMFT CqO=at -xawtHt pL |=Q@ j}kO |R=U |Q]k VwQ R=VwQ xm OW ?=NDv= CyH u=O@ j}kO |R=U |Q]k VwQ "[7] s}=xOQmpmWt� =@ nQR@ |=ySqB wm |=Q@ w u}}=B |=y=tO QO wrQ=m xDvwt |twDv=wmj@=]D u=Qo}O G}=Dv =@ xr=v=m l} OQwt |=Q@ =t G}=Dv "OwW|t wQ@ wQ �CtqaQD`}Uw =Q u}}=B |=y=tO w |rO=@D SqB wm -xOW |UQQ@ Q}O=kt -xRwL w xDW=O"CU= xOQmQO xr=v=mwO |wOv=m -xm@W |wor= OQwt QO xm s}=xO=O u=Wv u}vJtyCUmW |awv '(Half �lling) OvQB xt}v =yQ=wv |Dkw '|U}]=vet=Q=B R=iQ=w v w x vwoj }=a =yQ=w v R= |m } u; QO xm OwW|t Q=O }O B |=x_Lr uQ=k DQO xm OyO|t u=Wv =t C=@U=Lt 'C}=yv QO "Ovm|t Q=DiQ xvwo Rri Qo}OO=B R=i QO x=oDUO |m} R}i |=ySqB wm Q}O=kt -x}rm |=R= x@ xr=v=m wO OQwtQ}O=kt |=R= x@ "O}vm xHwD Oa@ -xLiY pmW x@ "OQ=O Q=Qk T}]=vet wQi|=yTv=mQi ?UL Q@ (Im�(i!n)) |SQv=�OwN |twywt Q=Okt J � tR= |m} xm s} Q=O Cw=iDt Q=wv wO =t '=Pr "Ovm|t Q=}DN= Q=Okt wO =Q=@ wUD=t|Qo}O w OQ=O xvwoj}=a Q=DiQ w OwW|t Oa=@Dt sm |=yTv=mQi QO =yv;"CU= xvwo Rri u; Q=DiQ xH}Dv QO w Ovm|t Q=}DN= |OwOLt |OOa Q=Okt

R= |=xawtHt R= s=tL w OvwW|t OQ=w (�) uwUQOv= uw}U=R}O} Q@}y `@=D"OwW|t p}mWD VvmtyQ@ uwO@ |=yuw}tQi|=Q@ ' SQF-wt 'QF-wt Vvm 's=tL |O=R; C=HQO |wQ |Q}op=QoDv= R= TB"O};|tQO Q} R CQwY x@ |Yr=N=v p=D}@ Qw=SQF-wt = � Z �0 d� Z �0 d� 0X� Cy�(�)G�10 (� � � 0)C�(� 0)+ Z �0 d�(H(�) �H0(�)):|wor= |vwDr}t=y =} w OQ=@=y |wor= |vwDr}t=y Ov=wD|t H =Hv}= QOQO T}=w QF-wt u=O}t |twDv=wm s}taD G0(� � � 0) "OW=@ wOv=m |=xm@Wu}= QO wO u}= |U=U= jQi "CU= nv} R}; |wor= |=Q@ u}ov=}t u=O}t -x} Q_vp}rO u}ty x@ w CU= (u=tR =}) |SQv= R= |a@=D G0 u}ov=}t u=O}t xm CU="CU= xOW hwQat |m}t=v}O u}ov=}t u=O}t x@ VwQ u}=w Ovm|t |R=@ QF-wt Vvm |=Q@ =Q CNr u} Qo `@=D Vkv u}vJty G0Q@=Q@ =@ "OwW|t h} QaD |a[wt u} Qo `@=D ltm x@ |Yr=N=v |SQv=�OwN|Q=oR=U OwN -x]@=Q |Yr=N=v |SQv=�OwN =@ |=xm@W |SQv=�OwN uO=O Q=QkCQwY x @ DMFT CqO=at -xawtHt ?} DQ D u }= x @ w O };|t CUOx @"OwW pL Q=QmD j} Q] R= O}=@|t xm O};|t QO |=xDU@ -xawtHt

w T = 0 QO w (AJ CUO pmW) J=t = 0=2; 0=4; 0=6; 0=8 w T = 0 |=tO QO xr=v=mwO QB xt}v OQwt |=Q@ �(i!n) |SQv=�OwN |twywt VN@|=yCr=L '|a[wt |=yu}BU= =@ Q=wv wO Qy uwQDmr= 'SqB wm COWV}=Ri= QF= QO "OyO|t MQ J=t � 1 |=R= x@ uQ=kDCUmW "(CU=QCtU pmW) J=t = 1=2; 7=0"OvyO|t p}mWD O}kt1. A.H. Castro Neto, Nature Materials, 6, 178 (2007).2. P. Hohenberg and W. Kohn, Phys. Rev., 136, B864 (1964).3. M. Payami and N. Nafari, J. Chem. Phys. 109, 5730 (1998);R. Ziesche, R. Kaschner and N. Nafari, Phys. Rev. B 41,10553 (1990); N. Nafari and M.P. Das, J. Chem. Solids, 49,997 (1988).4. W. Metzner and D. Vollhardt, Phys. Rev. Lett. 62,"x=oWywSB 'l} R}i -xOmWywSB '|Qiv QY=v%`H=Qt324 (1989); Phys. Rev. B 37, 7382 (1988).5. A. Georges, G. Kotliar, W. Krauth, and J. Resenberg, Rev.Mod. Phys., 68, (1996).6. G. Kotliar, S.Y. Savrasov, K. Haule, V.S. Oudovenko, O.Parcollet, and C.A. Marianetti, Rev. Mod. Phys., 78, 865(2006).7. R. Nourfkan and N. Nafari, submitted to J. Phys. Con-densed Matter (2008).8 a 45 |B=}B -xQ=tW

s#O}OH T}�Q =@ woDio %l} R}i -xOmWywSB QO pwLD w Q}}eD|rY= VN@ wO =@ OvQ=O Qw[L =t `tH QO x=oWywSB u=DwUmW}B u=wvaR= |r=tH= Q=}U@ |UQQ@ l} |=Q@) OW p}mWD C=}[=} Q w |Q_v l} R}i'x=oWywSB u=wva =@ ?v=Hv}= -xr=kt x@ ,qFt O}v=wD|t x=oWywSB |N} Q=D Q}U("O}vm xaH=Qt Q=@N= -xrHt |r@k -xQ=tW QO xOv}; w p=L 'xDWPoQwWm |WywSB |=[i QO x=oWywSB u}= xm p=U CU}@ OwOL pw] QOQO p}rO u}ty x@ w xOW hQoW |DqwLD VwNDUO =[i u}= 'OQ=O Qw[Lw COt x=Dwm h=Oy= OwHwt \}=QW =@ ?U=vDt w |v=tR hrDNt |=yxyQ@|UQQ@ |=Q@ ,=a@] w CU= xOW p=@vO x=oWywSB QO |Dw=iDt COt u=}tl} R}i -xOmWywSB X=N Qw] x@ w =yxOmWywSB |@=} RQ= w OQmrta -xt=vQ=m"OQm xHwD R}v \w@ Qt |v=tR hQ_ x@ O}=@sy=wN @ ? v=Hv }= Qo = 'OwHwt \ }=QW x @ xHw D = @ 'xtOkt u }= R= Oa @\UwDt -xQt v 'syO @ xQt v =yp=U u }= QO l } R}i -xOmWywS B OQmrta x @QDW}@ p}YiD =@ =Q w[wt O} Q=Po@ "Ow@ Oy=wN CU}@ R= xOH}y xOmWywSB"s} wW OQ=w R}v swO p=-wU MU=B x@ j} Q] u}= R= w s}vm |UQQ@xm |DOt u=}t w COt x=Dwm hOy 'l} R}i -xOmWywSB T}U-=D u=w= QOw |Q=Pox}=B (xOmWywSB u=UU-wt R= pkv x@) Ow@ xOW xDiQo Q_v QO u; |=Q@VywSB� xm O}O u}= =@ |QDmO u=} wHWv=O C}@ QD w |WywSB Q=m uDN=Ov= =HOw@ Q_v Ot xQwO u}= QO xm |rY= Q=}at w Ow@ �CU}v u=QDy@ =t R= *Q=m \ki|=Q@ lQO p@=k w |v}a w Twtrt ,qt=m |Q=}at xm Ow@ xr=kt A=J |}=v=wDCqHt |NQ@ QO xr=kt A=J xmv}= x@ |y=ov s}v =@ xD@r= 'CU= O=Qi= s=tD"OQ=O |QDW}@ VRQ=s}OW |Q=Po hOy swO -xrLQt OQ=w smsm w[wt u}= uO=Di= =H R= Oa@,qt=m sy R= @ =t= '|DUO sO |=yQ=}at w Cq=kt C}i}m x @ xHw D u; xm*| :tm |=yQ=}at u }= "Ow @ Cq=kt | @= } RQ= |=Q @ '| :tm w |v}a w Twtrtu}= "CU= CqHt Q}F-=D ?} Q[ w C=a=HQ= O=OaD pt=W ,=twta |@=} RQ=|@=} RQ= l} |=Q@ |@ wN |=tvy=Q ,=twta xmv}= seQ|ra |:tm |=yQ=}at"OQ}o Q=Qk |@=} RQ= Q=}at =yvD Ov=wD|tv OQ=wt |Q=}U@ QO OW=@ Ov=wD|t |Q=t;|Q=PohOy swU -xrLQt OQ=w O}=@ uq=l} R}i -xOmWywSB?v=Hv}= saRx@hOy "OwW (OwN -xOv}; -xr=U CU}@ ,qFt) COt Ovr@ |DL w COt u=}t|=Q@ "CU= x=o}=H u}= ^iL w |v=yH K]U QO Q=m s=Hv= 'xrLQt u}= QOO}=@ |WywSB�|tra |=} wB nvyQi O=H}= x@ xS} w xHwD hOy u}= x@ p}vR= Qw_vt 'Twtrt w XNWt Qw]x@ "OQ}o Q=Qk xOmWywSB Q=m QwDUO QO<=kr= xvwo u}= O=Qi= x@ u; QO xm CU= |tra wH w \}Lt u=vJ =} wB nvyQixmr@ xr=kt A=J w O}rwD xv xOmWywSB QO u=kkLt Qw[L Cra xm OwWw O}=Ri}@ X=N -xDWQ u; QO |QW@ Vv=O -xawtHt x@ xm CU= |Dq=kt O}rwD"OW=@ x]w@ Qt -xN=W QO KQ]t p�=Ut x@ MU=B CyH QO xOW O}rwD Cq=kt

� �� �l} R}i -xOmWywSB CU=} Q R= =y}y=W}ra uULt QDmO |Q=H p=U x=t O=OQt QOQ=@N= -x} QWv "CUWv w= |=H x@ |Q=@H M}W |Oyt OtLt QDmO w CiQo xQ=vm=@ x} QWv u=oOvv=wN =D O=O ?}DQD Qiv wO u}= =@ |}=ywoDio OwN pwtat p=wQ j@]w u} QDsyt R= xm �� xOmWywSB u}= Q@ sm =L |=yx=oO}O w '=yxt=vQ@ 'xOv}; 'xDWPo=@ woDio uDt "OvwW =vW; QDW}@ �� CU= x=oWywSB |=yxOmWywSB u} QDp=aiR= TB =y}y=W}ra QDmO |=k; |rw 'O}v=wN|t Q} R QO =Q xOmWywSB O}OH T}�Qx@L=Yt QO xDmv wO |m} Q}}eD =} hPL |=Q@ =Q x} QWv O=yvW}B 'x@L=Yt s=Hv=Q_viQY u=W}= -x@L=Yt uDt A=J R= ,qai xm OW pY=L ji=wD u}= w CiQ}PBvCYQi QO s} Q=wO}t= w s} Q=O j}iwD |wRQ; x=oWywSB |t=Qo O=DU= u}= |=Q@ "OwW"s}vm A=J CU= |@r=H Q=}U@ C=mv |w=L xm =Q u=W}= -x@L=Yt '|Qo}O

|Q=@HM}W |Oyt OtLt-x}rw= -xDUy xm CU= |=xOmWywSB wO R= |m} l} R}i -xOmWywSB %Q=@N= �#O}vm|t |@=} RQ= xvwoJ =Q xOmWywSB u}= C}r=ai -xt=vQ=m "Ov=xOw@ x=oWywSBO}v}@|t xOmWywSB C}r=ai |rai OvwQ QO |Dq=mW= xJ 'xmv}= Qo}O p=-wU wu=QoWywSB |Q=mty -xwLv QO ,qFt =}; #O} Q=O =yv; `iQ |=Q@ |}=yQ=my=Q xJ w#O}; OwHw@ |D=Q}}eD O}=@ |WywSB C=aw[wt QO =} (""" w s}kt Q}e w s}kt)VN @ C= tLR R= sy=wN| t EL @ x @ OwQw R= p @ k %|Q= @HM}W �|v=OQOk |y=WwQUN QDmO xS} w x@ w Q=@N= -xrHt w x=oWywSB |v=UQ`q]=x@ OQ=wt |Q=}U@ QO w OwW|tv |yHwD `}=kw C@F x@ ,=twta =t QwWm QO "svm=Q xOwt}B |=yx=Q w Ov}=tR;|t xQ=@ OvJ =} xQ=@ wO =Q xOwtR; =yQ=@ Cra u}tyxm s=ovy u=ty R= w T}U-=D wO@ R= =t x=oWywSB QO "Ov}=t}B|t xQ=@ OvJx@ xv=DN@WwN 'OW|t xO}t=v �C=}[=} Q w |Q_v l} R}i C=k}kLD RmQt�x=oWywSB CqwLD \@[ w C@F x@ Q=@N= -xrHt |y=WwQUN QDmO Cty'CU= QU}t Q=@N= ut} x@ RmQt -xr=U xORwv -xv}W}B R= `q]= xRwQt= w xDN=OQB"CU= xOv}; x=Q d=QJ xDWPo xm Ov=xDio wx@ x=oWywSB xOt; Q=@N= -xrHt u}W}B |=yxQ=tW QO =yQ=@ xm Qw]u=tyx@ uwvm = sy xv=DN@WwN xm u=oW}B |[=} Q w l} R}i R= |atH Cty9 a 1386 u=DU@=D

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Q=v}tU w EL@ C=UrH |Q=RoQ@ (1 %OQ=O |v}a Owtv |ovyQi w =[i u}vJ|=yV }=ty w =yx=oQ=m w =yxUQOt |Q=RoQ @ (2 &|OH w s_vt |oDiyQD=wD =@ CU= p=ai =yv; QO xOmWywSB xm |}=yxN=W QO |rrtr=u}@ w |rN=OGQ=N R= u=oOvvmO}OR=@ w =yu=ty}t VQ}PB ?DQt -xt=vQ@ (3 &p=U wO =} l}"xOmWywSB u=kkLt |WywSB�|tra CQi=Ut s_vt -xt=vQ@ u}vJty w QwWmQ}}eD R= Q} Ro =v swU -xrLQt x@ OwQw w hOy u}= QO uDW=Po sOk |=Q@nvyQi O=H}= |=Q@ "s}DUy xOmWywSB u=Q=mty w u=kkLt x@ C@Uv x=oO}OxOmWywSB QO |QDW}@ |m} R}i Qw[L O=Qi= CU= sRq |WywSB |=} wBu=QoWywSB O=OaD x@ xm OwQ@ |DtU x@ O}=@ xOmWywSB 'u}=Q@=v@ "OvW=@ xDW=O|tyU ,=twta |rai CQwY x@ xm s}kt Q}e u=QoWywSB w OwW xOwRi= s}kth } Qa D = } w O vwW hPL O vQ=O v |WywS B |= } w B |=[i u }= p}mW D QOx@ O}=@ R}v s}kt u=QoWywSB u}@ QO "OwW x�=Q= s}kt Q}e QoWywSB R= |O}OHu=kkLt x@ C@Uv Ckw s=tD u=QoWywSB OYQO w C@Uv xm s} wQ@ |DtU-xOmWywSB QO xv=DN@WwN "O@=} V}=Ri= |rwkat OvwQ =@ xr=U Qy CkwxQ=BR=e; uqOQ= QDmO |OYD u=tR R= |va} 'p@k p=U OvJ R= OvwQ u}= l} R}ixQwO u}= QO w xOQm =O}B sw=OD R}v =y}y=W}ra QDmO CU=} Q -xQwO QO w xOW|DkwWwN |=H l} R}i -xOmWywSB QO xm |=xDmv "OQm Oy=wN =O}B xt=O= R}vQ}_v QDxk@=U =@ O=Qi= QtDUt |Qmity Cra x@ xm CU= u}= OQ=O Q=}U@|=QwW uOw@ p=ai Cra x@ u}vJty w QDu=wH pUv =@ |aiQ= w uqOQ= u=}=k;p=kDv= -xH}Dv xOmWywSB COtOvr@ |=y|Q=PoCU=}U 'xOmWywSB |traxOmWywSB CU=} Q uOW Zwa =@ w CU= u=w=Qi |=yEL@ w s}Ok C=}@ QHDumtt xm OvJQy 'OvwW|tv |rm C=Q}}eD VwNDUO =y|Q=PoCU=}U u}=QO ?wYt h=Oy= x@ p}v |=Q@ |Dw=iDt |=yQ=my=Q O}OH T}�Q Qy CU="Ovm P=ND= w KQ]t =QwWs} wo@ O}=@ xOmWywSB C}r=ai OvwQ QO Cq=mW= =} CqmWt -xQ=@ QO =t=|r=t Qwt= pw�Ut xm xOmWywSB T}�Q u=wva x@ w ?v=Hv}= Q_v x@ 'xmQ_v QO =@ xOmWywSB -xHOw@ Ow@tm =t |rY= pmWt 'CUy R}v xOmWywSB=@ xOmWywSB ,qwtat 'XNWt Qw]x@ "CU= u; |=yC}r=ai sHL uDiQosvm xi=[= =Q u}= O}=@ xD@r= "CU= xH=wt xHOw@ w Q=@Da= Ow@tm �10 OwOL-xyQ @ u }= QO =t= $OQ=O OwHw =} vO |WywS B Rm =Qt s=t D QO pmWt u }= xmQO Q=m j=D= w =[i Ow@tm -xr�Ut u; w OQ=O OwHw R}v |Qo}O pmWt X=Nw O}OH -xOmWywSB wO uOW xi=[= x@ xHwD =@ w[wt u}= "CU= xOmWywSBl} R}i -xOmWywSB pO R= O}OH -xOmWywSB wO OrwD QDk}kO w QDy@ Q}@aD x@lOwm l} -xv=RwQ |tUH OWQ xm CU= |Qw;O=} x@ sRq) "OQ=O Owtv QDW}@wO w CU= xOy=Wt p@=k R}v $KrUt Q}e sWJ =@ |DL pw= p=U OvJ QOOvDU}v |vFDUt xOa=k u}= R= 'xv=DN@WwN 'sy =t -xOW OrwDt xR=D -xOmWywSB("CU= CtqU |=yxv=Wv R= OwN u}= xm OW=@ u}vJ R}v O}=@ wwO@ R= l} R}i -xOmWywSB |WywSB C}r=ai R= |=xOta VN@ %Q=@N= �K]U QO OUQ|t Q_vx@ "CU= w xOw@ u=tU} Q -x} Q_v -xv}tR QO T}U-=DO}OB OwN |=yhOy x@ x} Q_v u}= *uO}UQ *u=mt= OQwt QO |}=yO}OQD |v=yH10 a 45 |B=}B -xQ=tW

s#xOmWywSB Q=m R= xrLQt u}= QO xm CU= |=xDmv u}= ,=k=iD= w 'OQ=Ov OwHw =tK]U QO uOv=t |k=@ w uOW KQ]t |=Q@ &s} Q=O sQ@t R=}v u=O@ x=oWywSB w|WywS B�|tra `t=wH = @ QtDUt w s �=O -xOw=Qt O }= @ |rrt r=u} @ KQ]t"OW=@ xiQ] wO O}=@ xOw=Qt xm CU= K[=w QB =t= "s}W=@ xDW=O |rrtr=u}@w u=DUwO Q}=U =@ xm |}=yC@LY pY=L u}vJty w ut |YNW -x@ QHDw =} wB |tra |=[i Qo = xm CU= u}= s=xDW=O QwWm R= GQ=N s}kt u=Q=mtyCWoQ@ ?=@ s}W=@ xDW=O |rrtr=u}@ Q@Dat Rm =Qt Q}=U =@ C@=kQ w =vDa= p@=kQDmO sv=N w ut OwN &OW Oy=wN R=@ R}v x=oWywSB w QwWm x@ GQ=N R= O=Qi=x=oWywSB QO OwHwt C=v=mt= xm s}DUy w[wt u}= RQ=@ |=yxvwtv R= u=RQiQO uOv=t w CWoR=@ x@ =Q =t xOt; sy=Qi x=oWywSB u=DwUmW}B Cty x@ xm"OQm Oa=kDt u=Q}=|=[i w C=v=mt= u}= Ow@y@ w ^iL OvUt QO OwN xm p=L sQ=wO}t=w sQ=O@ T=B =Q u=DwUmW}B OQw=DUO u}= sv=wD@ 's=xDiQo Q=Qk |WywSB |=} wB"sW=@ jiwt x=Q u}= QO w sWwm@ u; |=kDQ= QO"O}W=@ jiwt u=D}=yxt=vQ@ QO s} Q=wO}t= w s} Q=RoU=BU =tW R= %Q=@N= �

-xRwL QO hrDNt p�=Ut pL |=Q@ x} Q_v u}= pO R= |OOaDt |=yxO}= wMU=B u=tU} Q -x} Q_v *OwN Qo = |DL ut Q_v x@ "xOt; uwQ}@ |Q_v l} R}i|=ve =@ x} Q_v u}= 'OW=@v xOW KQ]t l} Qw�D CqmWt x@ |}=yv w CUQO"CU= CqmWt u}= pL |=Q@ sRq |=yxO}= |w=L OwN l} Qw�DR= CQH=yt x@ |O=} R p}=tD |v=Q}= -xOQm p}YLD u=v=wH u}@ QO %Q=@N= �|WywSB u=} QH u=wD@ xm O}vm|t u=to hYw u}= =@ =}; "OwW|t xO}O QwWm#OQw; OwHw@ l} R}i QO ,qFt |mQLDQB w Q=O}=BseQ|ra =Q QwWm R= xOQm p}YLD u=v=wH CQH=yt -xO}OB %|Q=@HM}W �|=xO}OB OwN |OwN x@ ut 'OQ=O QwWm VywSB |=Q@ |Q=wo =v Qy=_ xmv}=|=Q@ VQ}PB uDiQo x@ QO=k =t u=v=wH xmv}= 'pw= -xryw QO "sv}@|tv |ivtw CU= C@Ft |=x]kv OvwW|t |QDmOCU)B =} w |r}tmD Cq}YLD `]=ktQ=OQwNQ@ |@ wN x=o}=H R= |rrtr=u}@ K]U QO =t VRwt; sDU}U xmv}= u}@t|tra |=y|@=} RQ= OW xDio QDV}B xm Qw]u=ty xm s} Qw; Q]=N x@) "CU=("OwW xO}HvU |rrtr=u}@ |=yQ=}at T=U= Q@ O}=@R= |}=yR}J uDNwt; w x@ QHD ?Um =yCQH=yt u}= Qo}O C@Ft -xDmvQwWm QO =yv; uDNwt; u=mt= xm CU=yQwWm Q}=U |tra `t=Ht w =y\}Lt

11 a 1386 u=DU@=D

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'Q}@mQ}t= |DavY x=oWv=O '|v=}m Vw} Q=O"|ywQo |=yQ@H '|}=Hx@=H h=Qo'|}=HQ O}yW srat C}@ QD x=oWv=O '|vt}t =[QO}tL"=yxkrL p=m} h=Qos}ktQ}e u=kkLt "2'OQmQyW x=oWv=O '|yr=OU= O=wH"u}=DWvQo |=ys}mU= w pt=m |Swrwtywm'Oy=W x=oWv=O '|OU= Qk=@OtLt"CWoQ@ |=Q=O |=ypwOt'Q}@mQ}t= |DavY x=oWv=O '|Q=ieu}t= =v}t"=ylHwt -xr}Uw@ s}kDUt Qw]@ =DU}= =v |=y|QU |v}@V}B'|Uw] u}Or=Q}YvxH=wN x=oWv=O '|t=e}B =[QOtLtR= xOQ l} R= xO=iDU= =@ u}at xt}v |R=Uxv}y@ |=Q@ |vwQO x]kv VwQ l}"O}OH -xR=Ov= `@=wD'OQmQyW x=oWv=O 'OwQxr}B |t=UL =v=}D=DApproximation to di�erences of digamma function values.'OQmQyW x=oWv=O 'OwQxr}B |t=UL VN@=ONTranscendence of certain in�nite series.'Q}@mQ}t= |DavY x=oWv=O '|wQUN RwQy@"pw= h=Qo -xr}Uwx@ L16(2) |Q}PB|}=U=vW x@W'OyWt |UwOQi x=oWv=O 'VvtQ=}WN s_=m"|m} Swrwty |=y=}=B w |a[wt |Swrwtywm |=ypwOt'Q}@mQ}t= |DavY x=oWv=O 'u=kyO |Oyt"p}Uv=Qi}O CqO=at pL QO |r}rLD xt}v w |OOa |=yVwQ'u} wRk '(xQ)|v}tN s=t= |rrtr=u}@ x=oWv=O '|v=R=Q utLQr=O@a"QqwOt |=[i QO C@=F x]kv -x} Q_v'u=yiY= x=oWv=O 'u=} Qq=U xr=QmW"CUOm} |=ypwOt |QwoD=m |B wDwty'u=Oty '=v}U |raw@ x=oWv=O '|at=U s} Qm"|Wy=m |@ Q[ |=ypwOt'x}twQ= x=oWv=O 'xO} RU =[Q"|a[wt |=ypwOt |Swrwtywm utHv= pw= |=yp=xO}= uOw@ |y=vDt'R} Q@D x=oWv=O 'QytQwB|Lr=Y O}aU"OwOLt |=y?=UL QO |Q}PBC=@F= pwtLt'u=yiY= x=oWv=O '|yr=O@a =[Q}ra"xwQo l} x@ xDU@=w pov= h=Qo'u=yiY= x=oWv=O 'Q=Ni O}Ht"pO=aD x@W p�=Ut w pO=aD p�=Ut13 a 1386 u=DU@=D

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Spin ip e�ect on electrical transport in magnetic quan-tum wire. 'Qwvs=}B x=oWv=O 'xO=RQ=iY =[Q}ra"|vwQDmr= u}BU='x=oWywSB 's=HQi |v=t|t}W |D=@U=Lt |=yxw}W R= xO=iDU= =@ u}i=Qo |m}vwQDmr= X=wN |UQQ@"|twDv=wm'u=HvR -x}=B swra QO |r}tmD Cq}YLD RmQt 'OvwOqwi s}y=Q@=Statistical analysis of oating-car data: An empiricalstudy. 'u=QyD x=oWv=O 'xO=R|OtLt =[QOtLtSuperconductivity in ultra-small radius SWCNT elec-tronic properties of Pr at R and Ba sites in RBa2Cu3O.'x=Wv=tQm |R=Q x=oWv=O 'u=}O=Qt sDUQFerromagnetic semiconductor single wall carbon nan-otube. 'OQmQyW x=oWv=O '|v=OQt OtLtTheoretical approach on spin-dependent conductance ina magnetic-quantum wire.'CavY w sra x=oWv=O 'u=}v=Q}tv u}Wi=Quantum interference e�ect in the nonlinear conduc-tance of metallic single-wall nanotubes. |tra C-=}y �"VN@ wQi p}Uv=DB OQm} wQ QO l}t=v}OwtQD wv=v '|wUwt xr=KwQ|WywSB KQ] �'|DWy@ O}yW x=oWv=O w x=oWywSB 'Q=@D|a}iQ sW=yQO Q@ R Kw]U u}@=t T=tD w l =m]Y= |=yxO}OB |U=}ktOvJ |R=UpOt"|QDtwv=v w wQm}t |=yT=}kt%u=Q=mty|=yQ=DN=Uwv=v QO VQ=W |U=}ktOvJ |R=UpOt '|O=Ry@ xQ=QW �"|v@ Qm"|WNQJ w |]N |=yu}W=tw}@ wv=v |R=UpOt 'u=} wQUN THQv �|=ypwmrwt pt=aD |R=Ux}@W '|r=tH hUw} w |@U=Qyr Q}t= �|= ypw rU Q= D iQ |UQQ @ '|m } t=QU w |R r i O=w t = @ | DU } RxO=iDU= OQwt |Q=DN=Uwv=v O=wt w}@ |wQ Q@ |v=wNDU= CUq@ w}DU=("|DWy@ O}yW |mWRB swra x=oWv=O =@ lQDWt -xSwQB) '|OB wDQ= QO17 a 1386 u=DU@=D

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