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The Output Least Squares Identifiability of the Diffusion Coefficient from an $H1-Observation in a 2-D Elliptic Equation

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(1)INSTITUT NATIONAL DE RECHERCHE EN INFORMATIQUE ET EN AUTOMATIQUE. The Output Least Squares Identifiability of the –Observation Diffusion Coefficient from an in a 2–D Elliptic Equation . Guy Chavent , Karl Kunisch. N ˚ 4067 December 2000. ISSN 0249-6399. ISRN INRIA/RR--4067--FR+ENG. ` THEME 4. apport de recherche.

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(42) }†ƒ Œ  Œ } ““ oz} ‡} Œ “ ~ˆv‹~ˆv‹†ƒ ½ A³Y~ m o2†y|~€o “ ¡¤wy‡ƒ Œ } “ A³(MOŽ? “Š“ o+‰Š ¤wƒ Œ vxƒ|¥ ~€ŸÛz v vxŽ Œ {‹o*~}†ƒ m t o+y‡p}†“ ƒ‡ƒ¡¤wy‡ƒ } Ž*†ƒ v‚~€v‚wƒ‡‰ o o?°Ãƒ|o~ o v‚{x¡eo ~‰€ ‡}†Ž?o J œ O  J!  J Ž*†ƒ‡‰€2  J`\ _ o q E&M I^ ~ O  J E OO a T  T  E¢ ½E I "  "# J  O T $ T %'& » m o “ oÛvxƒ Ž+}A‰€(o

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(44) Æ ~vx‰<‰€y‡ ¤ ¤w‰ˆo Œ ~ m }~ M ‰Š}~€v‹‰ˆ°¤oq‰ Œ . My_ Ysq10 q .3 2 5O 2

(45) V}†ƒ Œ M¶vx‰¡e†y‡ƒ Œ o Œ }Aƒ Œ Ž?wƒ‡ƒ|oqŽ?~ˆo / E ¢ ½¢ I 2 41O  J E O$O } “ oJ ¤}v “ »<vx‰ˆo Œ vx‰ •–Avxƒ† ~5 ® ƒ  »”o Œ o*°eƒ|o~ m o{‚vxƒ|oq} “ ³´ “ p x ¡w x E  IJ * , K6 7 * 37<; > =  “   : 8 9 m» o “ o K _ xA E&M I O 9 _ xA EB  I O–³´q@ ? “  ‰ˆwp2O oD³´ CFE ¢ _ O ? O _ Æ ™ O  J E OOpO E ¢ ½ B I »<v‹~ m ~ m o} Œ‡Œ v‚~€v‚wƒ‡}{Ž*†ƒ Œ v‹~ˆv‹†ƒ ~ m }~  G G KH7 7 I J œ v±J ³.

(46) J) 5 ?  , 9 >= q  8 t o+ƒ‡Ž*o?³´ “ ~ m »”o Œ o+ƒ‡A~ˆo"¡w Y ~ m o"‰ˆo+~ہA³Á} Œ p"vx‰€‰€vx¡|{‚o ‡} “ }†p2o+~ˆo “ ‰ G ½ l<m o “ o+Ž?vx‰€ozŽ?wƒ Œ v‹~ˆv‹†ƒ‡‰ wm ƒ Y »˜o2¡eo¥AHnv‹ÐAJyoqƒHW ³ y “ ~  m o “Œ ¡eo*{‹`»Œ ½Æ ƒ ¤} “ ~ˆvxŽ*y|{x} “ ~ m o+ »<v‚{‹{$}{‹{‚`» ~€„}†‰€‰€|Ž?vx}~€o~ˆ„o*Іo “ d Gr_ Y ~ o‰€A{xy|~ˆv‹†ƒ _ o*°eƒ|o ¡w G ELK I G H  J x E  I ³´ “ }A{‚{  _  O , $ $ » m v‹Ž m v‹‰~ m oÐ`} “ vx}~ˆv‹†ƒ¤}{ó´ “ pzy|{x}~€v‚wƒ:A³7~ m oo*{‹{‚vx |~€v‹Ž¾oq¯wy¤}~ˆv‹†ƒ M Œ v‹FÐ E?Gz¥ “ } Œ HI<JLK v‹Nƒ M N O HD J œ O<GQP-R J E ¢ ½r I T  T 8 * G P-R J ? P S O HnJ y‡9 ƒ‡Â[ƒ|`»ƒ„Ž?†ƒ¤‰ˆ~Š}Aƒw~†+ ƒ.  O  J E O$OT5   PS Œ HW ³ “ wp x X E M I ~€VU X E&M I z o¾‰ m }A{‚{.¡eoJŽ*†ƒ‡Ž*o “ ƒ|o Œ »<v‹~ m ~ m oJv‹ƒwІo “ ‰ˆv‹†ƒA³~ m o¾p}A ‡ |vxƒ|¥ G iF¥ “ } k ^ m “ vxƒ„~ o{‹o+}†‰ˆ~ˆÇi‰Š¯[y‡} o+‰˜‰€o+ƒ‡‰€o E’ I p"v‹ƒ‡v‹p"v‹¼*Jo &W T ¥ “ } Œ H W D R T %'X & `ÐAo “ GS_ Y O » m o “ 5o Rk_FU X E M I vx‰}¥Av‹ÐAoqƒw¡‡‰ˆo “ Ð`}A~ˆv‹†ƒ ½˜® y “ †¡[•–oqŽ?~€v‚Іov‹‰<~€°eƒ Œ Ž*†ƒ Œ v‹~ˆv‹†ƒ¤‰<†ƒ Y ‰€y¤Ž m ~ m }~ ýYX

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(50) t†Ç I v Œ o+ƒwŒ ~€v±°e}†¡|m{‹o<†ƒ Y ņv ½ mo ½ ~ ^ m }A~Y~ m oƒ‡†ƒ|{‹v‹ƒ‡o+} “ {‹o+}†‰ˆ~ ‰Š¯[y‡} o+‰ †¡‡{‚oqp E vx‰<¯wy¤} }~€v‹Ž+}{‹{‚QELKÇ »˜o*{‹{‹ e†‰€o vxƒ ~ o‰€o+ƒ‡‰€o¾~ }A~ [ JN\ ¥ “ } ŒnHW _ U X E&M I^ G_ Yba e†Œ‰Š‰€o+‰ŠŒ ‰ˆoq‰} ƒ|o+v‚¥ m ¡¤ “€m [ ZŒ c ‰€y‡Ž m ~ m m }A~m ³´ “ o*m Іo “ U R _ c “ w¡|{‹o+p E ’ I mm }†‰zƒ|º{‚|Ž*}A{˜p"vxƒ|“ vxp"} }†ƒ } p"v‹~€‰}y‡ƒ‡v‹¯[y|oz‰€A{xy|~€v‚wƒ Gà Åe‰Šy‡Ž ~ }A~~ op"}† ‡ |vxƒ|¥R5iG: vx‰<¿ vx ‡‰ŠŽ v‚~€¼Ž?wƒ†~€v‹ƒ[y|wy‡‰˜³ †p U E&M I ~€ x E M I,½  “ ~ m v‹‰ ¤y “ e†‰€o¾»”o “ o+¯[y|v “ o¾~ m }~<~ m o ‡} “ }Ap"o+~ˆo “ ‰¡¤o+{‚wƒ|¥~ˆ~ m o‰€ ‡}†Ž?o X X  J`\ GS_ Y 0 q E M I^ G T  J y‡ƒ‡Â[ƒ|`»ƒ„Ž?†ƒ¤‰ˆ~Š}Aƒw; ~ G  J  J E OO  a O E¢ ½ I oq¯[y|v‹ ¤ ¤o Œ »<v‹~ m ~ m o¾ƒ| “ p "  "

(51)  W ½ l<m o¾‰€o*~˜³À} Œ p"v‹‰Š‰ˆvx¡|{‹oJ ¤} “ }Ap"o*~€o “ ‰ Y vx‰}A‰Š‰€y‡p"o Œ ~ˆ‰€}A~ˆvx‰–³´ ^ Y  \ G _  ^ GfG E I } ½ o ½ v‹ƒ MPO " G "   W fG a O E ¢ ½ I }†ƒ Œ Y vx‰Ž?wƒ†Ð†o?‘}†ƒ Œ Ž*{‚w‰ˆo Œ vxƒ x E M I O E ¢ ½ž I X » m o “ o”œ fŒ G “  Œ ;G  m } x“ oÁ¥†v‚Іo+“ ƒŽ*†ƒ‡m ‰€~€}†“ ƒ†~Š‰ ½ m †~ˆo˜~ mY }A~À~ m oŒ v‹p}¥†Œ oÁvxƒ Y m E m  I A“ ³¤~ m o<p ½}A ¤ |v‹ƒ‡Œ2¥ Rsi Gz  v‹‰ÁŽ?†ƒ¤‰ˆv o o vxƒ~ o I m X Dzƒ| p„Å» o o+}†‰

(52) ~ oۉˆo+~ “ vx‰$oqƒ `Y »˜½o ‚ »<v‚“ ~ ~ “ oƒ‡m p “ ³ “ †ƒ v‚~€m v‚wƒ E ¢ ½  I oqƒ‡‰€y “ oq‰<~ m }As ~ E K }A‰}¸y¤ƒ|v‹¯[y|o2‰ˆ†{‹y|~€v‚wƒ ³´ }A{‚{ Gn_  o+`ÐAo Å[~ o oq¯[y|v o+p"oqƒ†~<~ }~ G v‹‰z¿ vx ‡‰ŠŽ m v‚~€¼:Ž?wƒ†~€v‹ƒ[y|wy‡‰+Å ~ˆ†¥Ao+~ m o “ »<v‚~ m ~ m o p2 Œ o+{‚{‹vxƒ|¥ ³‰€†y “ Ž?o¸}Aƒ Œ ‰ˆvxƒ‡Â'~€o “ p‰¡w m †{‚oq‰*Å }†ƒ Œ ~ Œ m o Œ “ o*¥wy|{x} “ v‚~²w  m |½ ¤†~£ m oqI,‰ˆ½ oq‰kE ¢ ½ ¢ I Å E ¢ 0 A ½ B I I ³´ “ MJÅ K ÅÀ}†ƒ Œ 9 v‹p |{‹ Œ¤~ Œ m }Œ ~ \ T HW YsT  q &  ^ I Gh_ “ Yba “ v‹‰ ¡e†y¤ƒ o Å E䉀o*o u  Ť |¥ E Œ œ twvxƒ‡Ž*m o  m X E&M vx‰<Ž?wƒw~ˆvxƒwy‡†y‡‰€{‚o+pz¡eo o vxƒw~ˆ E M ³´ o+ÐAo  CFE ¢ Å|~ m o+ƒo*‘[vx‰€~ H @}†ƒ !  ‰Šy‡Ž ~ }A~ H W H “ nŒ H W T % #  K³´ “ }{‹/{ G_ Y 5 E ¢ ½£ I T T "$#  FO T ¥ } l<m o m [ eA~ m o+‰€vx‰~ m }A~z~ m o ‡} “ }†p2o+~ˆo “ ‰‰Š}~€v‹‰ˆ³´h G J G  J y‡ƒ‡Â[ƒ|`»ƒ6Ž?wƒ‡‰€~€}Aƒw~vx‰~ m o ¢ Ç؟ ¥†o+ƒ|“o “ }A{‚v‹¼+}A“ ~ˆv‹†ƒ m ³¾~ m m o m | ¤“ †~ m oq“ ‰ˆvx‰¸Œ ~ m }S~ m G v‹‰¸Ž*†ƒ‡‰€~€}†T ƒw ~¸ †ƒ3‰ˆw“ p"o® ƒ‡o*v‹¥ m Œ ¡¤ “€m w Œ ³¾o+}†Y2Ž {m ŸJw ½'v “ }AÆ Ž ‰€†y Ž*o¸~ˆo p„Å$» vxŽ »˜}†‰ o+¯[y|v o vxƒ6~ o E Ç؟Ž*}A‰€o:~€ o+ƒ¤‰€y o ¿$&t %wv o+ƒw~€v±°e}†¡|v‹{‚v‹~²A u E ~ vx‰¾m }{x‰ˆ„ m |‰ˆvxŽ*}AŒ {‚{‹ “ ƒ|A~J~ˆ“ [ “ o+‰€~ “ vxŽ?~ˆv‹ÐAo†Å }A“ ‰ÛŒ †ƒ|oŽ*m}†ƒ }A‰Š‰Šy‡p"oz~ ½m }~Jl<~ mm o¸‰€v‚¼+oz³ 4  ‰+Å » Œ m vxŽ m p"Œ  Œ o*{ ~ oŒ »”o+{‚{Y¡e†¢ y¤½ ƒ I } “ v‹o+‰+“ Å} o“ ‰ŠŒp}{‹“{$Ž?m†p ‡} Œ o ~€„® ~ o:‰€v‚Œ ¼+o2A³M Ç o¸Ž?wm ƒ†Ð†o?‘|v‹~²}†“ƒ Ž?{‹†m ‰€o ƒ|oq‰€‰ Ž*†ƒ v‚~€v‚wdƒ E ž } o o+¯[y|v o ³´ ~ oJ‰ˆ~Šy "³ ¿

(53) &t %[v o+ƒw~ˆv‚°e}A¡‡v‚{‹v‚~²"¡w2~ o¥Ao+†p"o*~ vxŽ~ˆoqŽ ƒ|vx¯[y|o+‰ ³´ “ mƒ|†ƒ‡{‚vxƒ|o+“ } “ {‚oq}A‰€~‰€¯[y‡} “ “ Œ oq‰ ® Œ o*ÐAo+{‚wŒ ¤o Œ vxZƒ u Y E w +Å u Y¢ w ½ m ‰<}° ‰€~˜‰€~ˆoq :~ˆ`»} ‰ ¿

(54) &t %[v oqƒw~ˆv‚°e}A¡|v‹{‹v‚~²¸»˜oJ‰ }A{‚{ }Aƒ¤}{‹[‰€ovxƒ„t[o+Ž?~€v‚wƒ B v‹ƒwІo “ ‰ˆoJ‰ˆ~Š}A¡|v‹{‚v‹~² oq‰ˆ~€v‹p}A~ˆo+‰A³7~ m o¾³´ “ p I “ S Œ HW T % & *) T ' Eä¥ “ } nŒ HW D ¥ “ } nŒ H,+I T % & O E²t I T E?G D(' ¥ } ³´ “ ). -Qœ ½ m ‰Û~ m vx‰‰€~€}†¡|“ v‹{‚v‹~² oq‰ˆ~€I v‹p}A~ˆowy|¥ m ~~€ m A{ Œ Y ³´ “ m ¤o m“ ~Šy ““ ¡‡}~€Œ v‚wƒ‡‰ G D' ^ v‹ƒ'}†ƒw Œ v “ oqŽ?~€v‚wƒ ' _ Ň»˜o}~ˆ~€o+p |~<~€: `Іbo E²t †ƒ‡{‚}A~ ¤†v‹ƒw~Š‰ GS_ » v‹Ž } o¾v oqƒw~ˆv‚°e}A¡|{‹o / 1É 03234 © 4 5Í 27698;:   =< $ $ GS_ Y % 2%8"$# &% '( )* s%+#  % 0?>0.9- ' _ A@  %8@ F"=< %+ ? $.*, ?%8.# H + _  ..BDCFE.# 2  H + JyH W %G<4 *,%8 ' J G 5 E ¢ ½H I ê &ù.

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(144) &  i œ³´ “  i  ½ l<m v‹‰¾Ž*†ƒw~ “ } Œ vxŽ?~Š‰ E r ½ ¢ r I }†ƒ Œ Ž*†ƒ‡‰€o?Ç ¯[y|oqƃw~ˆ{‹p E m r ½ E £ I }†‰˜»”o+{‚{ ½. ~m m vx‰ m oqƒ‡Ž?o¸vxp ¤w‰€‰€v‹¡‡{‚o¸~€ m °Ãƒ ŒŒ }Aƒºv‹ƒ|°e“ ƒ|v‹~ˆo ½ Œ l<vxp"m o+ƒ‡‰€v‹†ƒ‡}A{Y‰ˆo+~ Y m »<“ v‹~ Œ m ƒ|wƒ|o+p |~²ºv‹ƒw~ˆo “Œ v‹ “ wƒ » v‹Ž ~ oz“ ‰ˆ~Š}A¡|v‹{‹“ v‚~² o+‰€~ˆvxp"}Am ~ˆo “ †{ ‰y‡ƒ|v‚³´ p"{‚ ½ vx‰p"A~ˆv‹Ð`}~€o+‰<~ o o y‡Ž*~ˆv‹†ƒ„~ˆ°Ãƒ|v‚~€o vxp"o+ƒ[Ç ‰€v‹†ƒ‡}A{. ¤} }Ap"o*~€o ‰€o*~€‰vxƒ„~ o o+p}Av‹ƒ|vxƒ|¥‰ˆoqŽ?~€v‚wƒ‡‰  #*! #& 7P 7( #+)*#, .-L $#*B J 7 z o:~Šy “ ƒÏ~€'~ m o¸°eƒ|v‹~ˆo Œ v‹p"o+ƒ¤‰ˆv‹†ƒ‡}A{”‰€o*~€~ˆvxƒ|¥'³twoqŽ?~ˆv‹†ƒ ¢ »<v‚~ m     q     ‰Š}~€v‹‰ˆ³´[v‹ƒ‡¥ Œ ¢ ½ I,½ z “ m Œ Y J Y

(145)  m‡“ m m m t2I mE A{ EAŒ E ‰ ½˜Æ–Œ oqo ƒ†~€v±o+°ÃŽ*}A}A¡|{‚{ v‹{‚~v‹~²„o ³ o?°eGƒ|vxv‹ƒ ~ˆv‹†ƒS v‹pS |{‹v‚oq‰¡w ’”S “ †}† eƒ †‰€v‚‰€~€y‡v‚w ¤ƒ ¤wB ‰ˆ½ o¢ ~ ~ m }w~y|³´¥  “ †}Ay|{‚~<{ ~ G O v‹' ‰_ ‰ˆoqYŽ?~ˆS v‹†»<ƒ„v‚~ ~ m }'s~ J !E G »˜o m }HÐAo Œ H W I J! œ 5  E1E '(D G I ¥ “ } n E ½E I t o+ƒ‡Ž*o»”oŽ+}Aƒ Œ o?°eƒ‡o¾³´ “ o+}†Ž m  _ I “  Œ HWI   J ‰€y¤ T E1E ' D G ¥ } E ½¢ I T  EE '(D G I ¥ “ } SŒ HWI T %'T %'& & 5 S  “ wp ’”“ † e†‰€v‚~€v‚wƒ B ½ ¢ »”o"Â[ƒ|`» ~ m }Ab~ E ½ E I m A{ Œ ‰Û»<v‚~ m 'D G “ o+ |{x}AŽ*o Œ ¡w }Aƒw  _  S Å  J ! œ‡Å }†ƒ Œ m o+ƒ‡Ž*o Œ H W I T% & 5    “  T E ¥ } S W ‰€y¤ Š ‰ ‡ y E ½B I  Œ S  “  &  0 & = q T E ¥ } H W I T %'&  . B. T T.  ". . . .  . . . ê &ù.

(146)

(147) <ƒ$„  . . . . . . o "  W  O &. E.

(148) E.  -Q:  $# 9#k*b #% $@ . ‰ ~ m o³ “ }AŽ*~ˆv‹†ƒ„v‹ƒeE ½ B I v‹m ‰Û}:Ž?wƒ†~€v‹ƒ[y|wy‡‰³ y‡ƒ¤“ Ž?~ˆv‹†ƒ'm ³ ½  }†ƒ Œ Gà ÅÃ}†ƒ Œ ~ m o"‰€y¤ “ oqp}¸} “ o~€}†Âo+ƒ„wƒ Ž*†pJ ‡}†Ž?~‰€o*~€‰v‚~³´†{‚{‹`»½ ‰<½~ ‚ }~ “ S “vx‰°eƒ|v‹~ˆo ³´ o+ }†Ž  tw“ vxƒ‡Ž?o  Ž*†ƒ‡m ‰€v‹‰€~€‰³$Ž?†ƒ¤‰ˆ~Š}Aƒw~³ y‡ƒ‡Ž*~ˆv‹†ƒ‡‰  œ¡w¿ oqpp"}"r E  o*`ÐAo ‰€vxƒ‡Ž?o S  S q Å|³´ }A{‚{  Ň»˜o }HÐAo œ J   q  S  !5 E ½r I  “ wp ~ m oo?‘‡}†p" ‡{‚o}~7~ m o˜o+ƒ Œ A³¤~ m o “ o*Ð[v‹†y‡‰7‰ˆoqŽ?~€v‚wƒ»˜o˜Ž+}Aƒ¥†o+ƒ|o “ }A{‚{‹Jo?‘‡ ¤oqŽ?~

(149) ~ m }~ {‹vxp S J S   ½ ’˜“ w ¤w‰ˆv‹~ˆv‹†ƒr ½ E vxp |{‹v‚oq‰<~ m o¾³´†{‚{‹`»<vxƒ|¥"‰€~€}†¡|v‹{‚v‹~²oq‰ˆ~€v‹p}~€o+‰ ½

(150)  É[Í ª É  8:| B ( E  B  ( E >B  (

(151)  E > B (

(152) 

(153) En9# B  Eb .*

(154) ( # 0.9b$-  _ I   H W 7 Iq  " H + D  " H W I T % & O T E '(D G T % & `E E X5T ' E SX m. . . . . . . '. 0.59*+* G O _ Y S. >@. . . . S. B (  E (. % 5"?'# %+#. . l<m vx‰~ m o* “ oqp ¥†v‚Іo+‰ } “ v‚¥† “ †y‡‰†•ˆy‡‰€~ˆv‚°eŽ*}A~ˆv‹†ƒJ~ˆ<~ m oÁƒ[y‡p"o “ vxŽ*}{A†¡‡‰€o “ Ð`}~ˆv‹†ƒku ¿ w Å7u ‚ w Å u v‚ w ~ m }~Û~ m o‰€o+m ƒ‡‰€mv‚~€v‚Ð[m v‹~² A³Y“ ~ m o"vxƒ†Ð†“ o “ ‰ˆv‹†ƒ„A³Y~ m Œok½ Gnl<i m HW p"}†“ ‡ |vxƒ|¥vx‰J} Œ o+m Ž “ oq“ }A‰€v‹ƒ‡¥¸m ³ y‡m ƒ‡Ž*~ˆv‹†ƒ'A³Y~ m o ‰ŠŽ*}A{‚o}~¾» vxŽ ~ o¸ ‡} }†p2o+~ˆo vx‰¾o+‰€~ˆvxp}~ˆo v‹‰¾w¡‡‰€o ÐH}A~ˆv‹†ƒ ~ˆA¥†o*~ o »<v‹~ ~ o¸}Aƒ¤}{‹[‰€vx‰ÛA³ ~ m o“ ƒ|Œ wƒ|{‚vxƒ|oq} “ v‚~²¸A³7~ m op}A ‡ |vxƒ|¥ G i HW Ň~€“ :¡¤om ¥†v‚Іo+ƒv‹ƒ„“ ~ m oƒ|o?“ ‘|~‰€o+Ž?~€v‚wƒ Å m }† ‰<p"w A~ˆv‹Ð`w ½}~€o Œ ~ m o vxƒw~ z  y‡Ž?~€v‚wƒAm ³

(155) ‰Šy‡Ž+Ž?o+‰Š‰ˆ³ y|{‚{p2m y|{‹~ˆvx‰€Ž+}{‹o¾}† ‡ †}†Ž o+‰˜~ˆ¸ ‡m } }†p"o*~ˆo m o+‰€“ ~ˆvxp"t2}AI~ˆv‹†ƒhu ¿ ÅŒu ¿ “ oŽ?{‹†‰€oÛ~ o‰€o+Ž?~€v‚wƒ»<v‹~ }Aƒ o+‰€~ˆvxp}~€oJA³ S v‹ƒ„~ oŽ*}A‰€o¾» o o E vx‰‰Š}~€v‹‰ˆ°¤o ¡w:Ð[v ~€y|o A³ l<m o+ “ o+p ¢ ½ E ½

(156)  É[Í ª É  8 6` B ( E $B ( E > B (

(157)  E > B (

(158) 

(159) E4 .*

(160) ># 4 " .$    + 7- .9  $ . 0s . . < (.    

(161) 9s$9 &% +'l. (.  $#. . @. >. S.  W Š‰ y‡ . ‰Šy‡ . &  0 & =  . . . . . S. . E?G O I O.  _  S >  J! œ   I<J ¢ GG   q  X T  &W "  E &W HI H W W T p2vxƒ  E O Y  E?G O  T T.   0. GS_ Y 9# S . S. T.   " H W T.    HW T T. .9. 5. E. ½ I. ª ÍÍ?8  m [w‰ˆvxƒ|¥ kJ & RW T ¥ “ } Œ E & RW I T % & q †ƒ"~ m o “ v‚¥ m ~ m }Aƒ Œ ‰€v Œ o³.~ m oo+¯[y‡}{‹v‹~²2}A¡e`ÐAoEär ½ E r I »˜o¾†¡|~Š}vxƒ ¡w l<m o* “ oqp ¢ ½ E }†ƒ Œ ¿ oqp"p} ¢ ½ ¢ & “ ŒSH W T %X & E T W W

(162) & ¥ } Œ H W I  E ¥ “ }  T T% & ¢ T ¥ “ } Œ E & RW I T %'& }†ƒ Œ m o+ƒ‡Ž*o G q X T &W ¥ “ } ŒSH W T$T  ¥ “ } ŒSH W T Œ H W I  E ¥ “ }  T T% & “ Œ &HWI 5 ¢ G q X T¥ } E W . . ýYX

(163) ý .

(164) Ež. 

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