First order simulations on time measurements using inorganic scintillators for PET applications
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(88) . y «%YXdb^ mbdbVCYZV£^p]^oYXW_V\ubhRTCW_WZ[ri[rubtT+«=YX^WT!YX[rs^aYZdbWZ^hZdbVCp]` t TCWZ^ ^p][]st[]ubT+YX^`£YZdb^`n[]hZmK^(W_hZ[rV\u2VC« YZdb^st^T+uÅYZ[]st^ T [rubo(W_^TCh_^(h² [ YXd t TCoo(V\W_`b[]unYZVYZdb^UK^(dbTi[rV\W[rp]prkbh_YZWXT+YZ^(`®[]uAw[r\kbWZ^C «¦V\W T¤Sv¿ b.o(W_fihY TCpÁ§ dn^¡h_YXTCub`xTCW_`¹`b^£[]T+YX[rV\u[]h& CÈCmbh&¥¬V\$W CÈ\ÈCmnhR«=² dbs[]u±o(V\[rubo([r`b^(uno(^ª«¦V\W +ubh(§Rdb[rh oV\u ¸ W_shOYXdb^a[rsmKV\WY TCubo^}VC«YZWZ[r\\^(W_[]ub V\u YZdb^ ¸ W_h_YmbdnVCYXVi^(pr^(oYZWZV\unh)«¦V\WT\V£tVi`=YZ[]st^}W_^(hZVCp]k£ YZ[]V\u§ 02 M w #1%@T% wxV\W k/N h_s´TCprp YZdb^´hY TCub`bTCWZ` `n^i[qT+YZ[]V\uÅVC«YZdb^ T+WZWZ[ +TCp YX[rs^h V+«YXdb^ k mbdnVCYXVi^(pr^(oYZWZV\uÅ[]h op]V\h_^aYXV √k τ /N ¥¬h_^(^ ^(j9§¥ \ª_ª§ dn^}`b[rhZmK^(WZh_[]V\uVC«YZdb^aTCW_WZ[ CT+pbYX[]st^ VC«;YZdb^ ¸ WZh_YMmbdbVCYZV£^p]^oYXW_V\ubhO[]h@\^W_fp]V² TCub`[]uboWZ^(TChZ^h WZTCmb[]`nprf!² [rYZd YXdb^3VCWZ`b^W[]ub`n^FxTCub`dn^(ubo^a² [rYXd YZdb^ TCW_WZ[r+TCpxYZ[]st^}VC«YXdn^a`b^YZ^(oYX^(`mbdbV+YXVi^(p]^o YZWZV\ubh§ dn^&TCubTCp]V\!YZ[]st^amb[]o ¼\kbmYZ^(o dbun[]jgkb^&UbTChZ^`PV\uo(V\unh_Y T+ugYR«¦WXT+oYX[rV\u2`b[]h_o(W_[]st[]uxT+YZV\WMUK^(un^ ¸ YZh «¦W_V\s T+p]pFYZdb^(h_^mnWZV\mK^(WYX[]^h(§edb^3YZWZ[]C\^(W_[]ub¡[rh`b^YX^(W_s[rub^(`2Uvf YZdb^ []ub[ YX[qT+pKWZTCmb[r`bprfWZ[rhZ[]un¡^(`bC^ VC«"YXdn^h_[]\uxT+pTCub`[]\unV\WZ^h YZdb^ pqT+YZ^3mbdbVCYZV£^p]^(oYXW_V\ubh(b² dnV\hZ^ YX[rs^h TCWZ^ stV\WZ^ `b[rhZmK^(WZh_^(`§)db[]h TCubTCp]V\YX^(o dnub[]jgkb^ []hokbWZW_^(uvYXp fYXdb^ UK^(h_Y YZVtVCUnY TC[ru\ViV£`YX[rs^}WZ^(h_V\p]k£YX[]VCubh(§ y³uTYZ[]st^Rst^T+hZkbW_^(st^(uvYYX^o dbub[rjikn^aUxTCh_^(`V\utYXdb^a`n^YX^oYZ[]V\u V+«YXdb^ mbdbVCYZV£^p]^oYXW_V\uvYXdn^ `b[rhZmK^(W_hZ[]VCuV+«%YZ[]st^a[]uboWZ^(TChZ^h ² [ YXdYXdn^ VCWZ`b^WR[rub`b^ k VC«"YXdb^ mbdbV+YXVi^(p]^koYZWZV\u§ . c. m. c. c. th. . th. J.
(89) !.
(90) .
(91) # . Q . #56. ! N = 1400 ! N = 1400 N = 1400. #56 #56. P%#
(92) "#. "&%. #56. τ N τ = 40ns H σ = 0.065ns τ = 20ns H σ = 0.032ns τ = 10ns σ = 0.016ns. . H+ " 6
(93) #0 ") (. H. " . #56. . D (
(94). . 2. 1
(95) "# H %". k=. +. dn^¡UF^YZYZ^(W}[rhoW_fih_YXTCppr[]\dvY fi[]^p]`9YXdb^p]V²)^(h_Y² []prp"UK^YZdb^&`n[]hZmK^(W_hZ[rV\uPVC«eYZdb^¡T+WZWZ[ +TCpYX[rs^ VC«"YXdn^ k mbdbV+YXVi^(p]^oYZWZV\u§ dn^3hZo([ruvYX[]prpqT+YZ[]V\u¤YX[rs^Ro(VCubh_YXTCuvY VC«YXdb^aoW_fih_YXTCp[rhTCp]h_V!TCu[rsmKV\W_YXTCuvY)«¬T+oYXVCWM«¦V\W)YZdb^3WZ^hZV+ prknYX[rV\u VC«"YXdb[rhYX[]st^ast^TCh_kbWZ^s^uvYst^YZdbVi`§ th. .
(96)
(97) K "3+4 " #. N=. J&K==.
(98) . ". - #. k. #56. A>CED5F.
(99) 4
(100) *, ! 4", + 4 IH. τ=. #5 . <=. . "&%P (. %".
(101) #. (5. (. A>CED5F. ? 4 #56. #56-A . N=. +. . ==. k th. + . (" "3+4 "# 2. $ .
(102). 45
(103) *,. ? 4 LGN. 3 #56. τ=. . . (. . #56. "&%GA>CED5F. ? 4 #56. A>CED5F. 'D> #56 66! 3
(104)
(105) "#9"&% (. "#5
(106) 6!1 6 H %" (. 4". N=. . . . %#
(107) "#. A . +. . ==. 3 #56. #5 P%". (. A . 2. ? 4 L . <. N . . ()
(108) *.4
(109) "# #5 . %". . A . (. 2. *,I +7 . 2. (" . ? 4 L . 3. "76!+P
(110) #56!. *)+ 1 . 3. . τ=. %#
(111) "#"&%B (.
(112) *04
(113) "#. " 6!1O"&%P (96I 16. "%@ (. ? 4 L . . N=. k. "&% (. J&K==. #56. 2. (" "3+4 "#. τ =. <>=. #5 . %". !.
(114) .
(115) ) @" 14
(116) "# I : = !
(117) "#0"%
(118) 4
(119) *, "%5 (5 . N=. $ . J&K==.
(120) ,. #56. .
(121) 2. τ=. <=. #5 . +1#9 (E*, #. k th. %". 1
(122) "#"%B (. 2. $ .
(123). 4
(124) *,. . . (. A>CED5F. 5 ?! 1#> +. ? 4 #56. . . N=. %5#
(125) "#. . +. . !
(126) @ #56 (5O6
(127) . #60A . (" "3+4 "#0%"'A>CODF. +. . "% (. ==. 1
(128) "# ?9 3
(129) "% ( 6!
(130)
(131) 2 ? 4 B L N , (
(132) *04
(133) "# * + +7 2 3 ? 4 L #56 #5 P%" ( A . τ=. ! .
(134) *,. . τ=. 3. <=. # . #56. N=. J&K==. L. !.
(135) B . db^!VCmnYX[rs´TCp ¸ p YX^(W_[]ubst^YZdbVi`®[]haokbWZW_^(uvYXp f®kbhZ^`A[ru®db[]Cd®^(ub^WZCf®mndgfih_[]o(h ^nmK^(W_[]st^(uvYXh^(h mK^(o[qTCprprfPS"º}l ^£mK^(W_[]st^(uvYXh´¥¬e S3Kl½Pbª§½±V\hY&W_^(o(^uvY¡WZ^hZkbp YXh o(VCubo(^WZu o(TCp]V\W_[]st^YZW_f±VC« h_kbo d±^£mF^WZ[]st^(uvYZh w SS"È)# §edn[]hst^YXdnV£`[rhkbhZ^`«¦V\W)YXdb^3^h_YX[rs´TIYX[]VCu VC«"^(ub^WZCfTCub`YX[rs^ «¦W_V\s#`b[]\[ Y TCpxhZTCstmbp]^hMVC«YZdb^}st^TCh_kbWZ^`hZ[r\uxTCpÁ§db^3T+p]\V\W_[rYZdbs WZ^jgkb[]W_^(hYXdn^}mbW_^(p][rs[ruxTCWf!`b^ YZ^(WZst[]ubT+YX[rV\u¡VC«KY³²MV hZ^YXhOVC«Fo(Vi^ to([r^(uvYXh@«¦WZV\s hXTCstmbpr^(h@VC«KYXdb^ hZ[r\uxTCpÁ§ÃkbWZ[rub3YXdb^RTCojikn[]hZ[ YX[rV\u YZ[]st^´TCun`°^(ub^WZCf·TCWZ^´WZ^(oV\ubhYXWZknoYX^`UgfAY³²MV®h_kbsth¡VC«YXdn^ hZ[r\uxTCpOhXTCstmbpr^(h²)^([r\db^`°UgfÅYXdn^ oV£^ o[]^ugYZh(§@db^ V\mnYZ[]sTCp ¸ prYX^WZ[rub!s^YXdbVi`2[]hmbW_^(h_^(uvYX^`¹[]u2}mnmF^ub`b[ 2wM§ M02% w @EA/ 06 ]P!$< ' . */!1 !$ @ "V¤[]stmbp]^s^ugYMYXdb^ V\mnYZ[]sTCp ¸ prYZ^(WZ[rub!st^YXdnV£`Ç T¯WZ^«¦^WZ^ubo(^s^(TCuhZ[r\uxTCp ¥¬TCstmbp][ YXkb`b^³ubVCWZsTCp][ U(^(`xª3[rh!oTCpro(kbp]T+YX^`»TCub`o(Vi^ to([r^(uvYXhTCW_^ • `b^YZ^(W_s[rub^(` UxT+YZo db^(hRVC« |CÈ\È\È!^\^(uvYZhaTCW_^3hZ[]s&kbpqT+YZ^(`2TCun`YZdb^3YX[]st^(h T+WZ^3WZ^o(V\unh_YXW_kboYZ^(` • T+YZo db^(h V+«K|CÈ\È\È ^C^(uvYXh@T+WZ^Mh_[]s¡knpqT+YZ^(` ² [rYXdmbdbVCYZV£^p]^oYXW_V\ubh"ugkbs¡UK^(W N ¸ £^(`YXV&È\ÈnnjWvÈ\Èn |JCÈ\Èn§}dn^!TCWZW_[r+TCpYX[rs^h}VC«eYZdb^ mbdbVCYZV£^p]^oYXW_V\ubh TCWZ^\^(ub^WXT+YZ^(`ÅTCoo(V\W_`b[]ub YZV¤YZdb^ hZo[]uvYX[rp]pqTIYX[]VCu´pqT² ¥7ªb`b[r\[rNYZ[ U(^`´² [rYZdPT¤Èn§ ubh (tUb[ru, tTCub. `2. . hZ,V\tWYX)^`±Uvf2[]uno(WZ^(TChZ[rub!YX[rs^+§ ©@TCo dmbdbVCYZV£^p]^oYXW_V\u¤o(V\uvYZWZ[]UnknYX^hOYZV YZdb^ \p]V\UbTCpbmbkbprhZ^RTCoo(V\W_`b[]ub3YZV YZdb^ WZ^(h_mFVCubhZ^ «¦kbuboYX[]VCu VC«"YXdn^ CR − RC hZdbTCmF^WRYZVtTtÃ[]WXT+o3o(kbW_WZ^(uvYmbkbprhZ^C§ x ¥\ª x − f (x) = exp(−x) y³u YXdn[]h^£mbW_^(h_hZ[]VCu x = (t − t )/λ 2t UK^([r6ub°YXdb^¯o(knWZWZ^uvY±YZ[]st^¹VC« YXdb^¯^C^(uvY t YXdn^ ^s[rhZhZ[rV\uYX[rs^3VC«%YXdb^ o(VCubhZ[r`b^(W_^(`PmndbVCYXVi^(pr^(oYXWZVCuKTCub` λ YZdb^ YX[]st^3o(VCubh_YXTCuvY}oV\sstV\uYXV¤YXdn^ mbW_^TCstmbpr[ ¸ ^WTCub`2YXdn^ h_dxTCmK^(W§Odn[]h mxTCWZTCs^YX^W[]hhZ^Y YXV 150ns, 50ns, 20ns § w%[]\kbW_^|RhZdnV7² h%YXdb^)WZ^(h_mFVCubhZ^h VC« CR−RC TCub` CR−RC hZdxT+mF^WZh%² [ YXd YX[]st^Oo(V\ubhY TCuvYZh ! +ÈCubh( CÈCubhK|CÈCubhYXVtT¤Ã}[rWXTCo3mbknp]hZ^+§ 1. 2. N. 2. 3. 2. i. i. 2.
(136) J&=. #5 @ ". . J. . . . "# O"&% 2 CR −
(137) O +#> 4 L 2. RC. O #56. CR − RC 2. . ( 2.
(138) #5. :.
(139) (.
(140) *,. "#5 #> ,. + =. #5 H. + =. #5 H. A^&o dnV£V\h_^!T CR − RC hZdxT+mb[]ub¹¥¦² [ YXd±YZ[]st^oV\ubhY TCuvY¡ CÈCubh CÈ+ubh(|CÈCubhXªRTCun`¹hZ^Y}YXdn^ hZTCsmnp][]un&«¦WZ^jikn^(ubofYZV CÈv½PºyUCÈ\È\½PºVU+9|CÈ\Èv½±ºVU TCub`ÅK ºVUC§ w%[]\kbW_^a~ah_kbssTCW_[ U(^h%YZdb^YX[rs^)WZ^(h_V\p]k£YX[]VCubheT+«=YZ^(W V\m£YX[]sTCp ¸ prYZ^(W_[]ub3TIY CÈv½PºyU TCub`K ºVU hZTCsmnp][]una«¦WZ^(jgkb^ubofC§@db^}W_^(hZknprYXh@«¦V\WOTCprpb«¦WZ^(jgkb^ubo([r^(hOYX^(hYX^`TCWZ^ Y T+UbkbpqTIYX^(`t[]uTCmbmK^(un`b[ P¥¬ª§. 2. . .
(141)
(142) . . . N. (" "3+4 "#5 2. +. "&%O ( 2. +. .
(143) *). +#> L. #.
(144) * 454 +
(145) #5 "#5
(146) "# H % " #56, G * 4
(147) # % >1# I ?H 2 = 2 "#5 > H #56 % #
(148) "# # 8"&% ( + "% ( 3 # * 1 " % & CR − RC 2 N 2.
(149) *,' "4
(150) "#5 "%!". %5#
(151) "#. [rs^@W_^(hZVCp]knYZ[]V\u []stmbW_V7C^(h² db^(u YXdb^OhZdbTCmb[]unRYZ[]st^e[]h"hZdbV\WY%TCub`YZdb^Ouikns¡UF^W%V+«bmbdbV+YXVi^(p]^o YZWZV\ubhMdb[]\d TCub`o(pr^TCW_prft`b^sV\unh_YXWZT+YX^RYXdxTIYWZ^hZkbp YXh`bV!unVCY`b[ ¢;^WMhZ[r\ub[ ¸ oTCuvYZprf¤² [rYZd hXTCstmbpr[]ub «¦W_^(jgkb^(uno([]^h(§ M02 Z[A\F A\]^1 !_ 06 ]P!R<(' . *+/0!$1 !TF @ w[rWZhY7TWZ^«¦^(WZ^ubo(^OhZ[r\uxTCpI² [rYZd prV²·hY T+YZ[]h_YZ[]o(TCp xknoYXkbT+YX[rV\u3[]hoV\ubh_YZWZkboYX^`«¦WZVCs0TpqTCW_\^ ugkbs¡UK^(W VC«}\^(un^(WXTIYX^(`¶mbdbVCYZV£^p]^oYXW_V\ubh¥È\È£ È\ÈCÈvª¡\^(ub^WXT+YZ^(` TCo(oV\WZ`b[rub¯YXVAYZdb^hZo([ruvYX[]prpqT+YZ[]V\u·pqT² ¥{7ª§ db^OWZ^«¦^(W_^(ubo^MhXT+smbpr^(h7YZdb^@YX[]st^@T+YYXdn^Oh_[]\ubTCpvs´T7n[rs¡kbsÄTCub` YXdb^@o(Vi^ to[]^(uvYZh TCW_^Oo(TCp]okbpqTIYX^(` «¦W_V\sµYZdb^ WZ^«¦^WZ^ubo(^ hZ[r\uxTCpÁ§ db^(u;FT!UxTIYXo dVC«MÈn ÈCÈ\È!^\^uvYXh}[rh\^(un^(WXTIYX^(` db^ugkbs&UF^W V+«xmbdbVCYZV£^p]^oYXW_V\ubh"[]u YXdb^)^\^uvY@[]h"\^(ub^WXT+YZ^(`!T+o(o(VCWZ`b[rubYZVaT}ubVCWZsTCpvpqT² • o(^ugYZ^(W_^(`tV\u N TCub`!² [ YXd!h_YXTCub`xT+WZ`!`b^£[]T+YX[rV\u `n^YX^WZst[]ub^`!Uvf&YXdn^o(W_fihY TCpbW_^(h_V\p]knYZ[]V\u N σ Ç ' R σ = N R /2.35 R = 10% db^ TCW_WZ[ CT+pKYZ[]st^(h ¥ 1 YXV N ª)VC«"^T+o dmndbVCYXVi^(pr^(oYXWZVCubhTCW_^3\^(ub^WXT+YZ^(`TCoo(V\W_`b[]ubYXV • YXdb^ h_o([]uvYZ[]p]p]T+YX[rV\u´p]Tt² ¥{i7= ª db^ ¸ uxT+phZ[]CuxTCp;[rhhZdxT+mF^`PTCun`hZTCstmbp]^`2T+YYXdb^3«¦W_^(jgkb^(unof xTCub`YXdn^T+smbpr[rYZkb`b^aT+ub` • YX[rs^3TIYRYZdb^ s´T7n[rs¡kbsµTCWZ^3^h_YZ[]sT+YX^`UvfVCmnYX[rs´TCp ¸ prYZ^(W_[]ub F y³u!YXdb[rheo(V\u ¸ \kbWXTIYX[]VCu¡² [rYXd¡+TCW_[qTCUnp]^Mugkbs&UF^WeVC«;mndbVCYXVi^(pr^(oYXWZVCubh(\²)^h_YZkb`nf¡YZdb^ [] u xkn^(ubo^VC« Y³²)VmbTCWXTCst^YZ^(W_h(ÇeYXdb^ st^TCuugkbs¡UK^(W VC«%^C^(uvYambdnVCYXVi^(pr^(oYZWZV\unh TCub`2YXdb^ hXT+smbpr[]ub¡«¦W_^(jgkb^ubofC§ db^hZdxT+mF^W)[rh)T CR − RC o[]WZokb[rY(v² [rYXdT¡|+ÈCubh@YX[]st^o(VCubh_YXTCuvY§edb^o(V\ubh_[]`b^WZ^` hZo[]uvYX[rp]pqTIYXV\W `b^oTfYX[rs^}[]heWvÈCunh ¥ÁSg¿ b ª§ 0. c. n. 0. n. c. c. i. .
(152) . . .
(153) . db^OhZ[rs¡kbp]T+YX[rV\ubhTCW_^)[rsmnp]^(st^(uvYZ^(`3² [rYZd N = È\ÈniTWvÈ\Èn+|JCÈ\ÈnC\È\Èni\7|+È\ÈmbdbVCYZV£^p]^(oYXW_V\ubh(§ w[r\kbW_^®TWAh_dbV² h´YXdn^±oV\[]ubo[]`b^uvYtYZ[]st^WZ^hZV\prknYX[rV\u T+hT¯«¦kbuboYX[]VCu¶VC«YXdb^st^TCu»ugkbs¡UK^(WtVC« . 0. Q.
(154) bm dnVCYXVi^(pr^(oYZWZV\u;§ dn^`b[]h_mF^WZhZ[rV\ubh&TCWZ^ ^£mbWZ^hZhZ^`¶[ru h_YXTCub`xT+WZ` `b^i[qT+YZ[]V\u ¥¦hZ[r\s´T\ª T+ub` «¦kbp]p@² []`£YXd°T+Y&dxTCp « YZdb^±sTI£[]s&kbs [ru¶oV\[]ubo[]`b^ubo(^+§Âdb^±WZ^(p]T+YX[rV\uUF^Y³²M^^(u«=² dbs T+ub` h_[]\sT¹«¦V\WtT7K TCkbhZh_[qTCu `b[rh_YZWZ[]UnknYX[rV\u []h √ ¥|\ª f whm = 2 2ln2 ≈ 2.35σ y³uo(VC[]ubo[]`b^ubo(^+b²M^ TC`b`2YXdn^ ^WZW_V\WZh []u2jgkxTC`nWXT+YZkbWZ^+Ç √ √ ¥~vª f whm = 2 2 2ln2 · σ ≈ 3.33σ coinc.
(155) H. . == *. 2. <. H. . % :. "4!
(156) "#. #. H. +. < == J K== & 4
(157) #)% >+# I?. . H. ==
(158) O. ==. (* J==.
(159) # L8N. . "
(160) #
(161) 6!+# (. ( . L. 2.
(162) #5. "%@ (,
(163) *,1 . "# 6
(164) . . CR − RC.
(165)
(166) . :.
(167) (. 3? . J=. ". 2 #5 .
(168) *. 4.
(169) *,. 54 1
(170) # "#5 # . %". N =. #56$ (. A^ oTCuhZ^^ YZdxT+YYZdb^ `b[]h_mF^WZhZ[rV\u2VC« W_^(oV\ubh_YZWZkboYX^`±YX[rs^hhZo(TCp]^hT+h τ /√N §edb[]hYZWZ^(un`±[rh h_[]st[]pqT+W)YXV¤YXdbT+Y}VCUbhZ^W_\^`P«¦V\WYXdn^`b[rhZmK^(W_hZ[]VCu±VC«%YXdb^ hZ[r\uxTCp h UxT+W_fio(^ugYZ^(W¡¥¬hZ^^&h_^(oYZ[]V\uÅ\§ |£§ Tvª§ y³ub`n^(^(`;£T+h «¦V\W YXdb^YZ[]st^T+YeYZdb^UxTCWf£o^(uvYX^W)V+«KYZdb^ hZ[r\uxTCpÁ+YXdn^ YZ[]st^MW_^(o(VCubh_YZWZkboYX^(`Uvf!V\mnYZ[]sTCp ¸ p YX^WZ[]un&[]hOhZ^ubhZ[ YX[ \^}YZV¤TCp]p9mbdbV+YXVi^(p]^oYZWZV\ubha¥¬V\WOYXdb^}pqTCW_\^ugkbs&UF^WVC«YXdnV\hZ^}² dn[]o do(VCugYZWZ[rUbknYX^ YZV¤YZdb^ mFVChZ[rYZ[rC^3p]V\UK^aVC«"YXdb^ h_dxTCmK^(`Ph_[]\ubTCp=ª§. .
(171) . .
(172)
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(174)
(175) . . J&==
(176)
(177) . :. + H. +.
(178) (. . % :. 1 "4 !
(179) "# == . J&=. L. N. (5*. (5.#3*. #5 P
(180) *,.
(181) #. "
(182) #
(183) 6!+# "#.
(184) *) "#5 6. +"&%. "#5 #> L. 2. (" "3+4 "#5 . N. . "&% (5. +#> . 3?
(185) . " 2. JK==. 4 4 +
(186) #%".
(187) * L. N. (0 ( 2.
(188) #9
(189) . + H F = = CR − RC. M02 M !$ ('y@T*A . % 9. . .
(190) . db^2hZTCsmnp][]unP«¦WZ^jikn^(ubof[]h!hZ^Y¤YXVÈ\Èv½±ºVU2TCub`YXdn^uikns¡UF^W¤VC«}mndbVCYXVi^(pr^(oYXWZVCubh![]ht|JCÈ\Èn§ db^2h_o([]uvYZ[]p]p]T+YX[rV\uAYZ[]st^o(V\unh_Y T+ugY[]h!hYX[rp]p W\ÈCubh(§ £[rs¡kbpqTIYX[]VCubh¡TCW_^2mF^W_«¦V\W_s^`² [ YXdhZdbTCmb[]un YZ[]st^3o(V\ubhY TCuvYZh3TC`#%_kbhYX^`±«¦V\WRmF^(TC¼g[]ub¤YX[rs^3YZVUK^!|CÈ+ubh( CÈCunh("È\ÈCubhTCub`A!CÈCunh(§ w[r\kbWZ^! h_dbV² h)YXdn^oV\[]ubo[]`b^uvYOYZ[]st^WZ^hZV\prknYX[rV\u!«¦V\W CR − RC TCub` CR − RC hZdxTCmn[]ub ² [rYZd`b[ ¢;^WZ^ugY mK^TC¼g[rub!YX[]st^C§ A^&unVCYX[ro(^3YXdxTIY}W_^(hZVCp]knYZ[]V\u[]stmbWZVC^(h ² db^(u¹mK^T+¼i[rubYZ[]st^ `b^(oWZ^T+hZ^(h;kbuvYZ[]p"To^(W_YXTC[]uV\m£ YZ[]s¡kbs§ A^ mbWZV\mKV\h_^ YZdb^3«¦V\p]prV² []ub![rugYZ^(W_mbWZ^Y T+YZ[]V\uÇ YZdb^ `bkbWZT+YX[rV\u VC«%YZdb^ mFV\h_[rYZ[r\^3prV\UK^Cn² db[ro d T [rhOYZdb^}V\unprf¤mxTCWYMV+«YXdb^hZ[]CuxTCp9mbWZVio(^hZh_^(`Uvf´VCmnYX[rs´TCp ¸ prYZ^(WZ[rubbg[]uno(WZ^(TChZ^hM² [rYZd´h_dxTCmb[rubYZ[]st^C§ lMV\unhZ^(jgkb^uvYXprfCnYXdn^}mbdbV+YXVi^(p]^oYZWZV\ubhMTCWZW_[ri[]un ² [ YXdT `b^(p]Tftp]TCWZ\^WOYZdxTCu T T+«=YZ^(W@YXdb^ ¸ WZhYV\ub^ `bVunVCYa[r u xkb^ubo(^¡YZdb^¡WZ^o(V\unh_YXW_kboYZ^(`¯YX[rs^+§ £V YXdbT+YaYXdn^¡`bkbWZT+YX[rV\u¹VC«@YXdn^¡mFVChZ[rYZ[rC^&p]VCUF^&TCoYZh TCh T¤o(k£YRYZ[]st^¤¥ l)«)\§ |£§¨U9ª§ wxV\WO\^W_fhZdbV\WYmK^TC¼g[]unYX[rs^h(gYXdb^}WZ^(h_V\p]k£YX[]VCu´`b^\WXTC`n^(hUK^(o(TCkbhZ^YXdb^augkbs&UF^WVC«hZTCsmnp]^(h [ru YXdb^ WZ[rhZ[rub!^(`bC^UK^(oV\s^h []ubh_k to([]^uvY§ 2. +. +. . .
(191) . zRV7² \YZdb^hZTCsmnp][]un«¦WZ^jgkb^(ubof![]h%hZ^YeYXV |CÈ\È\½PºVUT+ub`¡YXdb^Muikns¡UF^WeVC«9mbdbV+YXVi^(p]^oYZWZV\ubh[]h@|JCÈ\Èn§ db^)hZo[]uvYX[rp]pqTIYX[]VCuaYX[]st^Oo(V\ubhY TCuvY[]h"h_YX[rp]pRWvÈCunh(§ei[]s¡kbp]T+YX[rV\ubhTCW_^MmK^(W«¦V\WZst^(` ² [rYXdhZdxT+mb[]ubRYX[rs^ oV\ubh_YXTCuvYXhT+#` %_kbh_YZ^(` «¦V\WOmK^TC¼g[]unYX[rs^ YXVUF^a|CÈCubh CÈ+ubh(FÈ\ÈCubhMTCub`¹ CÈCubh§ew[]CkbWZ^ 7 h_dbV² h . ".
(192)
(193) . . . 1 "4 !
(194) "#. CR − RC #6 ==. . #56. CR −. (E#3*. % :. (*.
(195) #. "
(196) #
(197) 6!+# . +. "#. H H (
(198) # :
(199) ( RC 2 2 J&= = + "&% ( " "3+4 "#5
(200) # N 2.
(201) *, "#5 16. . ( H. +. #5 == = 2 (E +#>
(202) . .
(203) #5. J&K==. L.
(204) *) LN. 3? (. " 2. 4 4 +
(205) #.
(206) *. * 2. 4
(207) #. #. %". % >+# +?.
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