!∀#∃%!∀&∋()∗∗)+∋,
−
!
!
!
.
!
/!!
0#1
!
23,!)∗∗∀#
,#
−
#123)∗∗1
∀4−!
5∀
%∀6,).)7∀)∗∗4∀8.80&9%∗:::;∗<)
=
White Rose Consortium ePrints Repository
http://eprints.whiterose.ac.uk/
This is an author produced version of a chapter published in Parallel
Computational Fluid Dynamics 2001, Practice and Theory : Proceedings of
the Parallel CFD 2001 Conference, Egmond aan Zee, The Netherlands, May
21-23, 2001.
White Rose Repository URL for this paper:
http://eprints.whiterose.ac.uk/1866/
Published paper
Jimack, P.K. and Nadeem, S.A. (2002) A weakly overlapping parallel domain
decomposition preconditioner for the finite element solution of convectiondominated problems in three dimensions. In: Parallel Computational Fluid
Dynamics 2001, Practice and Theory : Proceedings of the Parallel CFD 2001
Conference, Egmond aan Zee, The Netherlands, May 21-23, 2001. Elsevier,
pp. 191-198. ISBN 0444506721
White Rose Consortium ePrints Repository
[email protected]
!"#
$
&%('#)*#+,%-$.$'#)/&'102435'16728.'193"'1$
: '#;3"<>[email protected]
8)/$3C'1
DE3"+'16' :!F '1$.G3"'1HI%('1)/+J3$9K7'#L
$)K0M+
N <2$A%()/$0'10
OPRQSPUTWVYXJZ5[]\;^5_a`Gbaced8^5Tgf4TS^5h?i!Xkjl^5mPIPU\Mban
bporq \Mst8QS^"QS[ qvu ^5w#Oyx?z{W| u [}Q~€d$_a qq w q f orq \;s8t8QS[ u‚ ~€| u [}ƒ5PUT„{…[}Q‡† q fˆPUPIm{U~Jˆ‰dŠY‹ŒZ5?~k|eV
sQST„PIT…Ž PUu_ P;qvQ„u mm[][][}{&\MQ„[sP qv^5u u s{…PI[ PIT“qvT&u Q rq{UX—PQS“mP!PI{„{…[]_I{!QaT„^"[][]‘‘J{!w]P’P^ QS” 8‚ u PP?[•u QSs€PUP^5T„^5TSPU^"w}w]PU[}w]hw]\MPI^"w#Q„P [ u^"qvQlsu˜s{ w]qq [}f™w]_t$^"PUQSQ„^5[ [ q5T„qvu-w}u;[]PUq qT?fEfE _ ^ qvq uuT„`kƒ5q ~™ƒvPU_IPUš›Q„Š$w1[ ~Q‡qvœ" už~q– m [ w]uq PI\Mƒ5Š PU[– wu mŸ^"^"QSm^ PIumm-m¡[}Q„s[} ƒ5T –Pq mŸ‘d$w}T…_aPUPUŒ\M{„&sJ{e^"PUT„[_ u h –
QS^5[•{„ƒv{ PUq w•_I†v[¦X¢^"Q„iPUm¡u ™^5[}w Q„‚ ¡PI‘[}TSQ„^"{Y[]_£s€^5f qTS^"T…\Bw]w]PItwrw]^"[}\;QS[ qvsu¡w}PU\Mq flP u Q„Qa^PQS[ sq5T„u PI_ ^5qvT…u P§m8m[}QS[][{…qv_Uu tPI{…TY{„PU[]m#{¤X/sdT„PIq {„\;P u P§Q„PU_ m¥q \M^ su t8m¢Qa^Q„QS[ P-q5u `"^5PIwr†¢T…[]PU{…{…{„ttw}PIQ„{{
[}^5Q„T„{“Pes ^5q w}{Q„qP u [ QSu []_U^5w}wtf mq PUT“mMs€™^5TS^"[]w]_aw]§PIw#m8[}PU\;\ sqvw}PUu \M{…Q„P TSu ^"QaQ„^PlQSPI[ q5\;u sX [}T„[}_^5w}w}†¨QSP q s8QS[}\£^5w}[}Q‡† q f1QS8P’sT„PI_ qvu m[}Q„[ qvu PITr^ u m
©€ª;«I¬(­¨®§¯¤°±(²7­!«³¯M¬
oq fJr·€tq5[]u m¤ƒ5PU· _Rq QS¥[ q5u$s– T mq [•‘´#w]t8PI\;{„[ q5{IuX¸lPUµGf1t€s^"^5Q„T…[ Q„qv[]u _U{“t8w¦s8^5w¦T^_a†¶€^B^"w]{…w]P[ ‚vuu ‚ [}P&”€Q_UqB^ u o&Q“¹ T qx6w}P’s[TSu ^"_IQSQS[•QSP?[ qv\ u q PUm8T…{PUw][][{uQS‚7qPWfE[]\M^Bs™q [}mT…QSPl^ ƒ"u ^5QT„_[}^5PIQ‡{…† P
™q fT„PU^5T…sPY[}mQS_aP¤_^ q5uu ‚ ƒ5P"PU~_R{…QSt[ q5_a¼u ^5QSPI{™T„{„\º q [}_a{?`Gm { q q \MT™[ ‘ u q ^ tu uQ?m^ ^5u T…m˜†—{ w]^³q †5QSPUT…{UP¤XrT…“PU{„8t8[]w}{WQS[ s€u^5‚ sJ·PUT™q »™[]_w]w#qvu‘Qat^5[]w}[ m—u {?t{„s \;q5u^5w]wsT…T„PIP ƒ‚ [[ qvq ut8{{
f q q TT„QS` qPef^5š m€^"~½Š$s8~QSœ"[•ž€ƒvQP™q ” s8u T [}q Q„PemtPI_Uw]PIPe\;^ P u u PIQ ¾MÀ¹ _U[}z¿P uÁQ¿{ q s€w]^5t8TSQ„^"[ qvw]w]u¤PIw8q m fq _ \£qvu ^5ƒv[ u PI_ImQS[PUqv_ u$q – \;m qs \Mq {…[ [}u QS[^"qvQ„uPUmMÀ x?PUw}xw][]s$ÁEQSs8[]_rT„PUs_ Tqvq u ‘8mw][•PUQS\M[ qv{ u PUq Tf
QSP?f q T…\
ÀÁ
ÂWÃ5Ä ÅSÆYÇ¢È ÉÄ Æ¶ÊË qvu(Ì6Í¥ÎWÏUÐ
™{ q w}t8PUT…QSP&[ qvÑYu Ò {…Q„TSà ^"Ò¨Q„P ÒԂ †¶Ó mÈ PUÓ2{…~_U{„T„t8[}‘‘Õ…PIPUm-_RQ[ u Q q š rž1PI[]w]{Ww – ^5s {&q f{„q PIw}m7w q ‘ ™q {Ut X u m€^"T…†_ q5u m[}Q„[ qvu {UXÖi uBq t8QSw}[ u P q f$QSP¿s€^5T„^5w]w}PUw
XW_¸’q ‘8T„QST…PU^5{„[ us qv^¶u m8” [ u u[•‚(QSPYרPU؀w}PUÙ³\MÚRÛÝP ÜRu ÞpQß+Ù{ Þpq ß w]PUt8T„Q„T [ q qvT“u¼PUq {gfQS[}\£À ^"Á Q„qvPUu{ qv^§u _ QSq 8^5[]T„{“{…P¤\M\;PU{„PI#{„X  q f¿Q„PIQ„TS^5PImTS^^ u m q ‘$Qa^5[ u
Š$X™{…Ot^5‘T…{„Q„PR[}QSQ[ qv_ u>qvu Ì Qa^5[ [ u u [ Q uq¤‚ à ^5‘ {„qt8t8‘Qm Q„q \£P^5{S[ ^5u \M{P_ qQ qT…T„QSPI^5{„w s À qv^"usms[T uq‚á []\;Q q ^"{„Q„tP³Á#‘8PU{„PIT…TQ„q{ T q À f&Q„P u P£_IP¿_ { q q ^5\MT…{„PyP£{…\Mt‘JPUm{…1q \;~EPU^5^5[ _au  {
™ƒ"^5[}T…w]w[]PU_ {‰qv{„u [ Qa‚v^"u [ [•u ”€\;_^ ^ u u Q„†¨w}†’\ Q„q T T…q Prt _ ‚ q  ^5q T„t8{…P“Q‰PUQS8w}PUP¿\Mm P q u \£QS{E^5Q„[ u€ÁR^ X‰uBˆq PIQSQsPIT„T {q _I[•f€PU{„QS{q P TE×&â ؀À â Ù³ÚRÛÝÜRÞpß+ÐÙã}ã•Þpã•ßÐ+à PUT…Á1T €q ^TEƒvPUPr{…Q„^e[]\;_ q ^"sGQS† P
qT…PIf” Q„u PIPB\;P P u u Q„Q []T…PBqvu _ w}q † ^"T„[ {„u P7{„\;tPI‘J{„m ˜q \;^ u ^5m¼[ u {…PUâ µGtÀ ^ P uu Q„m¥[¦^5[•w}QSw}{§†[]{ \Mq w}\MƒvP!PUmQS[]^"P QSP ÜRä€u ÛPUßåÞS[ ‚ Ü Gs‘ T q Êq t‘T„w]PI\æqq mktÁR{…çŸ[ u‚ Q„^5Pèm€^5Qa^"s8T Q„‚ [}ƒ5PRPQ
u t\B‘JPUT q fPUw}PU\MP u QS{ qvu P^"_a-sT q _IPU{…{ q TW‘PI[ u‚ Q„P{S^5\MP5X
é„êõëRðì+ìñ³í„í…îñ ï5ëRð"™ñ³ö+ò÷2ðíó¿Eôpõ2ë öR÷2í…ëIìì…ðøýrï2í…ù„ðUú+ö#ûEë üÝëIý&€ôRïGùUþ ÿò½ígîí„ö+ôpñ2ð™î…þ ôIö÷2üpþì+õ2ëRù õ2óI÷lô õ"ôpò½ñ ]í …ôRý îü÷2ëIÿ ôRì+î÷2ò ïGþ
Š
8X“i ‚ w q €
‘ ^5w"” u Py\;PI{„¨[]{mPR” u PUm!Q q ‘PQ„P¿t u [ qvuq fQS8P¿T…PI” u PIm7{…t‘m q \£^"[ u { À ™[}QS¨s q {„{…[]‘w}P
\M[ u8q TY\ q m[•”€_^"Q„[ qvu { u P^"T;{…t‘m q \£^"[ u [ u QSPIT…f^5_IPU{I~rQ q P u {…tT„P—QS^"Q£[•Q¤[]{¤_ q5u f q T„\M[ u8‚ ÁR~
^"w}QS q t ‚ —
 [}Q&[]{ u PRƒvPUTeP á sw}[]_U[•QSw•†£^"{„{„PI\B‘w}PUm1X
X“i6s€^5T„^5w]w}PUw€{ q w}ƒ5PUTy[]{ uq ¥T„PIµt8[]T„PIm;Q q { q w}ƒvP™QS8[]{ym[]{gQST„[}‘t8Q„PUm À ¿PUw]wkw q ^5m – ‘€^5w¦^ u _UPImkÁEsT q ‘ –
w}PU\X
“[}{s€^5sJPUT™[]w]wGmPI{„_IT„[]‘JP“^l{ q w}ƒ5PUT q f€QSP¿f q T„\ T„PIµGt[]T…PUmBf q T‰QSPr” u ^5w{…QSPIsM^5‘ q ƒ5P5~Œ^5w•QS q t ‚ 7Q„P
{ q w}ƒ5PUTr\;^†;^5w]{ q ‘JP’^5s8sw][}PUmM[ u mPIsP u mP u Q„w}† q f1Q„[]{f4TS^5\MPI q T…`JXE“Pl q T„`¤[]{¿^ ‚ P u PITS^5w}[]h^QS[ q5u
^ u m£P á Q„P u {…[ qvu¶q f1sT…PIƒ[ q t8{rT„PI{„PU^5T„_a¶[ u Q‡ q m[}\;P u {„[ qvu {I~#š›Šž~^ u m£[ u Q„T„PIPlm[}\;P u {„[ qvu {I~Jš›œ"žXŽ u
s€^"T…QS[}_Utw]^5TU~f q TQ„P&_U^5{„P q fk[ u QSPUT…PU{gQPUT…P5~v™PIT„P À Á‰[}{_ qvu ƒ5PU_IQ„[ qvu m q \;[ u ^"Q„PUm1~5^’{…Qa^"‘[]w}[]hUPIm ¹ z
\MPIQ„ q m¼[}{?T„PIµt8[]T„PImA^ u m菿PMm8PU\ qvu {…Q„TS^"Q„PBQS€^Q’QSPBQ„PU_a u []µGtP¤[ u QST q m8t_UPImA[ u šŠ~ œ"žE\£^†-{…Q„[]w]w
‘JPB^5s8sw][}PUm{„t_I_UPU{…{…f4tw}w}†5Xe“P¨f q w]w q ™[ u‚ {…PU_IQ„[ qvu(q fQS8[]{™s€^5sJPUTesT q ƒ[]mPI{’^M‘T„[}PIf[ u QST q mt_RQS[ qvu
Ù 5ÜRÞ •×R،ØJßåä m q \;^5[ u
Q q Q„[]{™sT…PU_ q5u m[}Q„[ qvu [ u‚ Q„PU_a u [}µGtP5~J‘€^5{…PUm(t8s qvu ™€^"QW¿P!_U^5w]w
^ Ü„× §
mPI_ q \Ms q {„[•QS[ q5u ~^ u m>d$PI_IQ„[ qvu §sT…PU{„P u QS{!^¶{„\;^5w]w u t8\B‘PIT q fQ‡†s[]_U^5w_ q \;st$Qa^"Q„[ qvu ^"wT…PU{„t8w}QS{IX
“P¨s€^5sJPUT™_ qvu _Uw}tmPI{™™[•QS^¤‘T„[}PIfm[]{…_Ut{…{„[ q5u X
1ª¶­ ¯’® ¨«U¬! °(#¯ "$¶«U¬ °!²¤¯#"%¤ ¯&#«I­!«³¯M¬ ¨® ('
²¤¯M¬-°§«U­¨«2¯M¬)’®
“P{…Qa^ u m€^5T…
m *^5w}PUT„`G[ u§¹ z m8[]{„_IT„PRQS[]hU^"QS[ qvu§q f À Á¿{„PIPU`G{l^ u ^"ssT qá []\;^"Q„[ qvu Æ,+ Q q Æ f4T q \ ^
” u [}QSPPIw]PU\MP u Q™{…s€^5_UP.- + {…t_a-Q„€^"Q
À ŠvÁ
Ã0/2l
1 Ä Æ,™+ ÉÄ 35476 Ç8/91 À È ÉÄ Æ,+ Á 3:476 Ê;/2l1 Ë<354=6
f q T¶^5w]w 3?> - + À m[]{…T„P ‚ ^5T„m8[ u‚ ‘ q t u m€^5T…†/_ qvu m[}Q„[ qvu {Mf q T¶{…[]\Msw][}_U[}Q‡†8ÁpX | u w}PU{„{¶Q„P¼\MPU{„*[}{
{…t8¾M_U[]P u QSw}†£” u P?QS[}{“[]{&` uq  u Q q ‘JP¨t u {…QS^5‘w]P’™8P u Ñ¤Ò Ã ÒÒ Ó È Ó’^ u m—{ q rP¨^5s8sw}†¶^¤\ q T…P
{gQa^5‘w}P ¹ z \MPIQS q m {„t8_a*^5{YQSP—{gQST„PU^5\Mw][ u P – m8[}´t{„[ qvu ^5w ‚vq T„[•QS\ À {…PUP"~¿f q T¤P á ^5\Msw}P5~lAš @žrf q T
mPRQa^5[}w]{SÁRX“[}{T„PUs8w¦^5_IPU{ 3 [ u(À ŠvÁ‘Œ† y
3 ÇCEB È ÉSÄ 3 Q q †[]PIw]m¤QSPWsT q ‘w]PI\ q f#” u m[ u‚ Æ,+> - + {„t_a
Q„€^"Q
/21 Ä Æ,+™ÉÄ À 3?ÇDBEÈ ÉÄ 3 Á 4=6 Ç /21 À È ÉÄ Æ,+ Á À 3?ÇDEB È É³Ä 3 Á 4=6 Ê /91 Ë À 3lÇEBÈ ÉÄ 3 Á 476 À ŒÁ
f q T&^5w]w 3F> - + XŽ u§‚ P u PITS^5w B []{¿_a q {„P u Q q ‘JP’sT q s q TgQS[ qvu ^5w€Q q Q„P’\MPU{…§{„[]hIP.—
G ^ u m§{ q ~€^5{rQ„P
\MPU{…-[}{“T„PI” u PUm1~€Q„PsT q ‘8w]PU\ À ŒÁ&^5s8sT q ^"_aPU{™QSPsT q ‘w}PU\ À ŠvÁRX
¸ u _UP&QS8P“t{„t€^"w€w q _^5w ¹ z˜‘€^5{„[}{[]{m8PI” u PImMf q TEQSP“{…s€^5_IH
P - + ~"QSP“{g†${gQSPI\ À ŒÁ\;^†7‘JP&™T„[•Q„Q„P u
Ã
I
[ u \;^"Q„T„[ á£uq QS^"QS[ qvu ^5{
Æ Ê,È ã
À Á
ŽfQ„P¨m q \;^5[ uÌ [}{Ws^5T…Q„[}QS[ qvu PIm[ u Q q Q‡ q {„t‘Jm q \;^5[ u { À QSP ‚ P u PUT„^5w][}h^"Q„[ qvu Q q¨à {„t‘Jm q \;^5[ u {
[}{M_ qvu {…[]mPIT„PUm¢‘JPUw q eÁp~¿t{…[ u‚ Q„P^5ssT q ^5_a¢mPU{…_UT„[}‘PIm/[ u dPU_IQ„[ qvu
f q TYP á 5^ \Msw}P5~QSP u Q„P
{g†${gQSPI\ À Ár\;^³†¶‘P’™T…[}Q„Q„P u [ u ‘w q _a` – \;^"Q„T„[ á;uq Qa^"Q„[ qvu ^5{
JKL IM Ñ N M RTS KLJ Æ M TR S
I N U Æ U
Ñ
O M O Å IQÅP Æ ÅP
Å
Ê
JKL Ë M TR S
Ë U
Ë ÅP
ã
ÀWV Á
eP{„tI‘JT„mP q Æ \;^5[}{[ u QSâ P™À ⠃vPI_IQ q Ð T Švq ÁÖf#^ t u u m ` uq []{‰u QS” Pyu ƒv[•QSPIP™_IQ PUq w}PUT \Mq f€P ut Qyu `{ q uw}q t8 QS[ u qvu ƒ"^5ƒ"w]^5t8w]PUt{PI^"{yQ‰^"QSQ8QSP uP q umq PUm{ PUq5{yu {…Q„QST„[]_RPrQS[ w•u †YQSPI[ u T…f{…^5[]m_IPP
P
Ê
Æ
‘{…†PR{…Q‡Q„rPUPI\ P u Q„€{…t^"‘Q—m \;q \£^³†K^"[ u‘{IP˜Xe^5“{…{„PIP7\B‘‘w w]q PI_am `G{ À ^ I u m6~ N {…Q ~q T„O PImkÁ¶^ u [ mu mË PIsT…P PUu smT…P PUu {„Q„P w}u † Q?q5QSu P!s8_ T q q \M_UPUs {…q5{ qu TP u â QS{ À âq fQS8P Ð ¹ ŠvzÁRX
Ê
¹ tT…Q„PUT…\ q T…P5~8¿P\£^†§P á sT„PI{„{
IP Ê I P M Ç I P
À œvÁ
^ u m Ë P ÊË P M Ç/Ë P Å Ð
Å
™PUT…P I P ^ u m Ë P ^5T…P™Q„P™_ q \Ms qvu P u Q„{ q f IQP ^ u m Ë P T„PI{„sJPU_RQS[}ƒ5PUw•†BQS€^Q¿\;^†B‘JP™_^5w}_Utw]^"QSPIm
À ^ u “m8P>{gQ q {g†$T…PU{gmkQSPIÁ&\ [ u mÀ VPUsJÁ£P \;u m^P†*u QS‘w•†P˜qv{ qu w}ƒ5sPUT m6q _UtPI{„{„{[ uq Te‚ â…^ X u [•QSPITS^"Q„[}ƒvP-QSPU_a u []µGtP>{„t_a ^5{§sT„PI_ qvu m[}Q„[ qvu PIm
* ezyd À {„PUP¢š Ñ"žef q T£P á ^5\;s8w]P³ÁpX‰TS^5m[•QS[ qvu ^5w™s€^5T„^5w]w}PUwWx?xº{ q w}ƒvPIT„{£Q‡†s[}_^5w}w}† Qa^"`5P qvu P q f
Q‡[ u QSq PIT…f fq ^5T…_I\;P!{It ç?u `PU[}uQ„q PUTu { ^"ssP w}†À P5[ uX ‚ ‚ X‘š V w qž¦ÁR_a~ `(q PITWw][]{ \Mq w•[ƒ$u [ ^"uQS‚ [ qvQ„u P7Q qŸ_ q WÀ \MV ÁlsQw]PRq—QSP7q ‘8{g†QS^5{…QS[ u PI\ ^—WÀ{„VPRQÁW[q u frs€PIµG^"t€TS^5^"w}QSw][PUqvw u À {?P5X f ‚ q XET?š› "QS8ž¦ÁRP X
“^5ssP-w}[]¿_U^"PQS^"[ `qvu7w•† q qfJƒ5QSPU8T…PWw¦^5s8sT„s8ÆPU_[ uqv‚u m^5[•sQS[ sqvT u q PU^5TI_a~v/QSQ„P™€\;^"QM^5[ru P_ q Qa\M^5`"sP(t8[}QS{ ^"QSq [ qvflu QS^5w$P{…QSw¦PI^"sQ…QS{yPIT„T¤PUµGf q tT„[}\T„PIXKm;^ilQs€P^"^5T…_aQ£ f4* T q \WQSzy8d P
[}^5Q„‘ PUqTS^ƒ5QSPY[ q5s€u ^5Tg^5QST„[}Q„P¤[ qv^§u-\;q ^"fQSQST…8[ áGPY– ƒ5\£PU^"_RQQ„qT„[ T?á \B^ ut8mèw}QS[}ƒvsPIw][}_I_Q ^"q Q„T„[ {qvu [}Ql^ []u{’mŸ{gQS^ TS^"u [ ‚ tŒ\BQ„f‘Jq PUT…T rq^5f¿T„mè[ u8Q u q PUT?sPIsT…T f q q m8T…\æt_IQ„‘ {Uq XMQS |e{…q [ fyu‚Q„QSPU8{…PP
qš V sJžÖPU‘GTS†—^QSr[ q5^u † {¿q[ u fQ‡s€ ^5qT„^5Pw]w}á PU^5w\M™s[•QSw]§PI{a^7ÁpX“\M“[ u[]P7\;T…^5PUw€\;^5^5\ [ u q m8t PUu T Q q q fEfÖQ„[ u []QS{WPIT„{„sPIT_IqQ„[ _IqvPUu {„{ QSq T&PI_ T„q PI\;f q T„\7P¨t _ u qv[]u _U^"_IPQS[u qvQSu(T„^"À QS{„PIPI{ P¤qvš u ž ^ q u T
P á s¸’w]t^ uT¨^"{…Q„QS[ ^5qvT…u§Q„[ quf ‚ q s tq T [ uu8Q¨q ƒ5[]PU{w‰Q x?q x ^5{„s{…tT„PI\M_ qvP;u QSm8[}^"QS[QqvurPIP;TUX €^ƒvP£Q‡ q \MPU{…PU{ q frQS8P;{„^5\;PMm q \;^5[ u ™8[]_a
^[5u T„PM{„t‘J[}PUm TSq^"\;T„_a^5[[}u_^5wT„^PRu” m*u PI\;[ u P u[}Q„Q„{£{ []q \Mf&\MQ„PUP£m[]{„^"^5QS\;P P;u PI_ [ q ‚ ^"GT„‘ {„qP;t\;T„ PIq${„q1m X -À ^ uPI{„†/ PUw}PU\M€^"P {7u Q£‘JPU™P u[}_aT„KPI” Qu q PUt8m¡_aPUPU{§^ƒ$QS[}8w}† P
‘™q t []w}u {…m€Q^5\MTg† PU{…q §fkŠ?^W€{„t^5‘J{ym ‘q PI\;P u ^5[ T…u PI” []{‰u mPIm£PI” u PUPU^mBƒ$Q[}w}q †¤‘J[ uP¿[ {…u t‘QSm ^"q QE\£{…^"t[ ‘Ju m Š¨q \;^ u ^5m£[ u [•QS{‰{[]\M[]\M\;\;PIPImm[¦^"[¦^Q„QSP P u u PUPI[ ‚ [ ‚ GG‘ ‘ q q ttT„T…  qq$q q mkm1ÁRX~
ePw¦^†vuPIT?_UP"^"~kQ?Q„PU^5P _aq ˜ƒ5PUw]PRT…ƒvw¦^5PUsw q ‘fPRQ‡QSrPBPIP \Mu PUQ„{…˜PT„[]PRPI” TSu ^5PUT…_am(GT„†5P X ‚ ¹[ qv[ u ‚ {tT…q5P u PU^5{…_a (q ™s{!T q ^ _Iu PU{…P { áq ^5TW\M[]{™sT„w]PIPB{…Q„_ T„q []^5_RT…QS{„PIPYm-\MQ q PU{„^¤#{„~1[ s€u^5‚ Tgw]PQ
QSqPUw}fEPUP?Q„\M” P P!u u ^5” QSwÖ{Iu X \;^5w‰PI“\;{„PIT {„[]q {Wèt ^M‚ ^  u t q m(u t8[}QSQ£f 8q Q„T…P!\ _[]{;q T…T„PIs€T…” PU^5u{„sJs PIPU\;qvT;u P ¿m8u [ PèQ u‚ ÀT…Q PIq\;” u PIŠYPè{„w]PR^APIƒv{ PIQSw]qvPR{auQSÁ T„^5q s8fT qPUQSm8_UPUTPqv{…{[u u q [}T…‘ŒQ„{ [¦† ^5w‘^\;[]u {…PIPUm¼{„_I Q„Š¤[ uq [ ‚uf @5Q„Pœ ^5¤P7_a*Q„_UPI^5PIQS{„T„m P¨^5‚ ™P¼PIm^ PUTSu T…^5m P w
s€T q ^ mu8t‚ _I[ u[ u‚M‚ uq¡m_aPU{ £[}w]m™T…Pu P uèX u d$PUsJ[ ‚ PUG_I[¦‘ ^5q w~etT„QS[ PIu\;‚ s Q„qPIQST„T„^5^5T…†5~ePImQSTST„^¶^ u ^"{…T„[}P!QS[ qv^"uQlm8PU[}w}´PUPU\MT„PP uu Q’QS{w]PR^5ƒvT…PIPAw]{ ^5q w]{fq T„PRt8” {„u PUPUm6\MQ P q u QU^X’ƒ d$q PI[}m P
š 5 “ž18f qP-T&x?f4tx w}w1smT…PRPUQa_^5q5[}w]u { mq [}f‰Q„[ QSqv8u []PU{“TUs~ T q _IPU{„^m†vt~¿T…P5Q„X€^"QY¿P-t8{„P§™[}Q„8 * Wzyd¡™P u { q w}ƒ[ u‚ À V Á7\;^† ‘JP
mQSPUP{…_U{gT…†$[]‘J{gQSPUPIm˜\ [ u Q„PUT„\M{ q fyQSPY_ q \Mst8Qa^QS[ q5uèq fyQSP¤^5_RQS[ qvu¼q f Ê M à XY¸ u sT q _UPI{„{ q T { q w}ƒ5P
JKL(IM Ñ N M R S JKL M M R S JKL à M R S
Ñ I Å N Å U Å P MM U Ê à Å à Å U Ð
À @5Á
O M O IP
P
Å
^ u m qvu sT q _UPI{„{ q TeŠY{ q w}ƒ5P?QSP{…†{gQSPU\
JKL IM Ñ N M R S JKL M R S JKL M à M R S
Ñ I Å N Å U Å P ÅÅ U Ê à à Å U Ð
À vÁ
O M O IP
P
Å
Å
¹ [ ‚ tT…P Xèi u [ u •[ QS[]^5w\;PI{„ q f(@5œ -Q„PIQST„^5PImTS^5w¿PUw}PU\MP u QS{ À Q q Ÿ
s w]PIfåQaÁ¨T…PI” u PIm¡t u [•f q T„\Mw}†˜[ u Q q
À ‘ q Q„Q q \ w}PIfåQaÁ
‹ V Š-PIw]PU\MP u Q„{ À Q q s¡T„[ ‚ GQaÁ!^ u m QS¶
P _ q T„T…PU{…s qvu m[ u‚ \MPU{…PU{ vq u s8T q _UPU{…{ q T
^ u m-sT q _IPU{…{ q TlŠ À ‘ q Q„Q q \ T…[ ‚ ŒQpÁpX
Q„P u {„PIQ
JKL M R S
U
ÅP
Ê
JKL
MM
RS
M À P M Å Å P Á U
Ç
ã
À ‹ŒÁ
Å
Å
Ž u „Q P?^5‘ q ƒvP uq QS^"QS[ qvu ~ŒQS8P’‘w q _a`G{ I ~ N ^ u m O À T„PI{„s1X I M ~ N M ^ u m O M Áy^5T„PeQSP?^"{„{„PI\B‘w}PUm
_ q \;s qvu P u QS{ q fEQ„P{…QS[•´ u PU{„{W\;^"QST…[ á f Å q T&QSÅ P¨s€^5TgQ Å q fEQS8P¨\MPU{… q5u sT q _IPU{…{ q T À T„PI{„s1XŠvÁrQS^"Q
_ q ƒ5PUT…{E{„t8‘m q \£^5[ u Š À T„PI{„s1X ÁpX“8PU{„Py\;^³†l‘P_ q \;s8t8QSPIm7^ u m¨{gQ q T…PUm™[}Q„ q t8QÖ_ q \;\7t u []_U^"QS[ qvu X
q T„P q ƒ5PUTU~‘JPU_U^5t{…P q fQSPB{…[ u‚ w]P¨w¦^†vPIT q f q ƒvPIT„w¦^"s¼[ u Q„PBT„PR” u PIm¼T„P ‚ [ qvu { q fQSP7\;PI{„PI{U~ IQP
\;^† ‘P-_ q \Mst8Q„PUmK^ u mK{…Q q T„PIm qvu P^5_a/sT q _UPI{„{ q T£™[}Q„ q t8QM_ q \;\Bt u []_U^"QS[ qvu X ¹ [ u ^5w}w}†5~yQ„P
T…PU_IQS^ u‚ t8w¦^5TW\£^QST„[ á M À T„PI{„s1X Á“T„PIsT„PI{„P u Q„{’QSP!T„PU{gQST…[]_IQ„[ qvuq sJPUT„^"Q q T“f4T q \ QSP¨” u P!\;PI{„
À T„PI{„s1X&ŠvÁ Å q5u sT q _UPI{„{ q T
À T…PU{…s1X“ŠvÁYQ q Q„P(_ q ^5T…{„PUT£\;PI{„K_ q ƒ5PUT…[ u‚
_ q ƒ5PUT…[ u‚ {…t‘m q \£^"[ u
À T„PI{„s1X1ŠvÁ qvu sT q _IPU{„{ q TŠ À T„PI{„s1X ÁRXW“[]{e[]{WQSP!t{„t€^"wE[}PUTS^"T„_a[}_^5wÖT„PI{…Q„T„[]_RQS[ qvu
{…t‘m q \£^"[ u
q sJPUT„^"Q q T&QS€^"QW[}{“t{„PIm([ u \ q {gQ™\Btw}Q„[ ‚ T…[]m§^"w ‚vq T…[}Q„\;{ À {…PUP5~f q T“P á ^5\Msw]P;š ‹"žåÁpX
“P ‚ P u PITS^5w}[]h^QS[ q5u¡q flQ„[]{¤[]m8P^¼f4T q \ ŠèQ q—à {…t‘Jm q \;^5[ u {Y[}{¤{…QST„^5[ ‚ GQ…f q T…r^5T…m1X >P§™[]w]w
^5{…{„t\MPYf q T?{„[}\;s8w][]_I[}Q‡†—QS^"Q?QSPIT„PY[}{^ q5u P – Q q"–qvu PY\;^5ss[ u‚ ‘JPIQ‡¿PUP u {„t‘Jm q \;^5[ u {?^ u mAsT q–
_IPU{„{ q T„{IXÔzy^"_a*sT q _UPI{„{ q TU~™âB{S^†5~Ws8T q mt_UPI{§^Ÿ\MPU{…K™[]_aK_ q ƒvPUT…{¶QSP-™ q w]P-m q \;^5[ uÀ Q„P
_ q ^5T„{…P¶\MPU{„€Á¨‘t8QB[]{¨T„PI” u PUm qvu w}†A[ u {„t‘Jm q \;^5[ u â„~ Ì {S^†v~^ u m [}Q„{![}\;\MPUm[]^"QSP u PI[ ‚ G‘ q tT –
 qq m1X!i ‚ ^5[ u ~Q„[]{’\MP^ u {’QS€^Q’QSP q ƒ5PUT„w]^5ss[ u‚ T„P ‚ [ q5u { q fyT„PR” u PI\;P u Q_ qvu {…[]{…Q q f q5u PYw¦^†vPIT
V
q fPUw]PI\;P u QS{W^"QWP^5_a-w]PRƒvPUw q fEQS8P¨\MPU{…1X ¹kq T“P^5_a-sT q _UPI{„{ q TeâQS8P ‚ w q ‘€^5w#{…†{…Q„PU\
™T„[•Q„QSP u ^5{
À Á“\;^†§‘JP
JKL I Ñ N R S JLK Æ R S JKL Ë R S
Ñ I
N
Ð
À ьÁ
Ë
O O I P U Æ Æ P U Ê Ë P U
™PUT…P uq  Æ [}{rQS8PlƒvPI_IQ q T q f” u [}Q„P’PUw}PU\MP u Q“t u ` u8q  u {e{gQST„[}_IQ„w}†M[ u {…[]mP Ì ~ Æ P []{rQ„P’ƒvPI_IQ q T
q fyt u ` uq  u { qvu QSP¤[ u Q„PUT…f^"_UP q f Ì ^ u m Æ [}{lQS8P¤ƒ5PU_RQ q T q fyt u ` uq  u { À [ u Q„P ‚ w q ‘€^5w” u P
\;PI{„kÁ q t$QS{„[}mP q fÌ X;d$[]\M[]w]^5T„w•†v~Q„P¤‘w q _a`G{ I ~ N ~ O ^ u m Ë ^5T…P;^"w]w_ q \;s8t8QSPImAf4T q \ QS8P
PUw}PU\MP u QS{ q f‰QS8P¨\MPU{…-[ u {„[}mP?{„t8‘m q \£^5[ u â„~€PIQ„_5X
“8P?^5_IQ„[ qvu;q fQS8P’sT„PI_ qvu m[}Q„[ qvu PIT À Ê M à ÁR~[ u Q„PUT„\M{ q fQSPe_ q \Mst8QS^"QS[ qvu {yT„PUµGt[}T„PIm qvu
P^5_asT q _IPU{„{ q TWâ„~[}{&QSPIT„PIf q T„P!^5{&f q w]w q ™{UX
À [¦Á&d q w•ƒvP
JKL I Ñ N R S JKL R S JKL à R S
Ñ I N Àv Á
U Ê à U ã
U
à P
O O I P P
À [}[åÁ W
PIsw¦^5_IP’P^"_a-P u Q„T…† q f P ™[•QS¶QS8P^³ƒ5PUT„^ ‚ P?ƒ"^5w]tP q ƒ5PUT™^5w}w#_ q T„T…PU{„s qvu m8[ u‚ P u Q„T„[}PU{ q f P
qvu—u PU[ ‚ G‘ q tT„[ u‚ sT q _UPI{„{ q T„{€X
Ž u À 5 Á I ~ N ^ u m O ^5T…P!Q„PB_ q \;s qvu P u Q„{ q fQ„P7{gQS[•´ u PI{„{’\;^"Q„T„[ á f q TeQ„P7\MPU{…è{…Q q T„PIm qvu
sT q _UPI{„{ q Trâ À QS8[]{y[]{ uq QrQ„P ‚ w q ‘€^"w” u P’\MPU{…¶‘t8Q¿QSPe\;PI{„§^5_RQSt€^"w]w}† ‚ P u PITS^"Q„PUm q5u sT q _UPI{„{ q T
â‡Á’™[]_a¡_ q T„T…PU{…s qvu mŸQ qèu8q mPI{ q t$QS{„[}mP q fÌ X“P¶T„PI_IQS^ u‚ tw]^5T¨\£^"Q„T„[ á T…PUsT…PU{…P u QS{YQS8P
[]PITS^5T…_a[]_U^5wET…PU{gQST„[}_IQ„[ qvuèq sPITS^"Q q T’f4T q \ QS8P ‚ w q ‘^5w” u PY\;PI{„ q t8Q„{„[]m8P q fÌ Q q QSPY\MPU{… qvu
sT q _UPI{„{ q T™ây_ q ƒvPUT…[ u‚ QS8P¨T…P ‚ [ qvu—q t8Q„{„[]m8P q fÌ X
“8P>\;^5[ u s€^5TS^"w]w]PIwl[}\;sw}PU\MP u Qa^QS[ q5u []{…{„tP¼Q„€^"Q uq  u PIPUm{—Q q ‘JPA^5mmT…PU{„{…PUm,[]{¶QS^"Q q f
_ q \Mst8Q„[ u‚ Q„PU{…Pe[}PUT„^5T„_a[}_^5w€T…PU{gQST„[}_IQ„[ qvu {I~ à ~GPI¾M_U[}P u QSw•†M^"QyP^5_a;[}QSPITS^"Q„[ qvu X
r
PI_^5t8{„PlPU^5_a
sT q _UPI{„{ q T& q T„`G{“™[}QS—[•QS{ q  u _ q sŒ† q fQ„P?_ q ^"T„{„P?\MPU{… À ™[}_a-[}{&w q _^5w}w}†¤T…PI” u PImkÁ&sT q _UPI{„{ q T
â¿\7t{…QW_ q5u Q„T„[}‘t8QSPQ q QSP¨T„PI{…Q„T„[]_RQS[ qvu-q sPITS^"Q„[ qvu à f q T™P^5_a
 Ê â…~J^ u m(s8T q _UPU{…{ q T¶
\Bt{gQ
 Ê â‡ÁRXE q ^5_a[}PIƒ5P™Q„[]{I~ŒsT q _UPI{„{ q Tâ‰T…PU{gQST„[}_IQ„{
_ qvu Q„T„[]‘8t8QSP&Q q QSP™_^"w]_Ut8w¦^"Q„[ qvuBq f à À f q TP^5_a
[}Q„{&” u P¨\;PI{„-ƒ5PU_RQ q T à À _ q ƒ5PUT„[ u‚¶Ì ÁrQ q QSP¨s€^5TgQ q fEQS8P!\MPU{… qvu sT q _UPI{„{ q TM™[]_a-_ q ƒvPIT„{
[ u ^?{„PRQStsMs€^5{…P³Á^ u m¤{„P u m{QS[}{T„PI{…QST…[]_RQS[ q5u Q q sT q _UPI{„{ q T À f q T
Ì À T…PU_UPI[}ƒ5PUm£[ u [}Q„[¦^5w}w}†’f4T q \¨
P^5_aÊ âÁRXOT q _IPU{„{ q TEâJQSP u T„PI_UPI[}ƒvPI{Ef4T q \ P^5_a q QSPITsT q _IPU{…{ q Tl
Q„PyT„PU{gQST…[]_IQ„[ qvu!q fQ„Py” u P
\;PI{„¶ƒ5PU_IQ q T à À _ q ƒ5PUT„[ u‚MÌ qvu sT q _IPU{…{ q TÁyQ q QSP?s€^"T…Q q fÖQ„P?\;PI{„ qvu sT q _IPU{…{ q T“âE™8[]_a
_ q ƒvPIT„{ Ì Xl“8PU{„P7T„PU_IPU[•ƒvPUm¼ƒ5PU_IQ q T„{’^5T„P¨QSP u _ q \7‘[ u PIm(Q q f q T„\ à ‘JPIf q T…P À v Á“[]{W{ q w•ƒvPUm#X
“P-^³ƒ5PUT„^ ‚ [ u8‚Ÿq feQSP P [ u {…Q„PUs À [][¦ÁB^5‘ q ƒ5P(T…PUµGt[]T…PU{ qvu w•†¡w q _^5w u PU[ ‚ ‘ q tT – Q q"–‡u PI[ ‚ G‘ q tT
_ q \M\Bt u []_^QS[ q5u X
1ª—²¤¯#"%!±­ ¨­¨«2¯¤¬,F® &± ­ &
i w]w q f#QS8PWT…PU{…tw}Q„{ys8T„PU{…P u QSPIm¶[ u QS8[]{{„PI_IQ„[ qvu rPIT„PW_ q \Mst8Q„PUmM™[}QSM^ u i’jld$Ž o []\Msw]PI\;P u QS^ –
e
QS[ qvuq fQS8Pr^5‘ q ƒvPr^5w ‚vq T„[}Q„\ t8{„[ u8‚ QS8P (OŽ_ q \;\7t u []_U^"QS[ qvu w][}‘TS^5Tg†v~$š "ž+~ qvu ^e{„^5T„PImB\;PI\ q T…†
d *»¸’T„[ ‚ [ u Š5ÑvÑvѨ_ q \Mst8Q„PUTUX“P¨je| -i Àuq5u$– t u [}f q T…\ \MPU\ q T…†¶^5_U_IPU{…{aÁ™^5T„_a[•QSPI_IQSt8T„P q f‰QS[}{
\£^"_a[ u P¨\MP^ u {WQS€^QlQS[}\;[ u‚ {“f q Te^ ‚ [•ƒvP u _^5w}_Utw]^"QS[ qvu \;^†—ƒ5^"T…†{„[ ‚vu [}”_^ u QSw•†—‘PRQ‡rPIP u T„t u {
À mPIsP u m[ u‚Bqvu  q ¥Q„P’\MPU\ q T…†¤[}{&^5w}w q _^"Q„PUmkÁp~ŒP u _IP^5w]w€Q„[]\M[ u‚ {µGt q Q„PUm§T…PUsT…PU{„P u QWQ„Pl‘JPU{gQ
QS[}\;PlQ„€^"Q“r^5{e^5_a[]PRƒvPIm q ƒvPIT u t\MPUT q t{™T„PIsPRQS[•QS[ q5u { q f‰QSP{S^"\;P?_ q \;s8t8Qa^"Q„[ qvu X
œ
 ^5‘w}P
“P¨sJPUT…f q T„\;^ u _UP q fQ„PsT q s q {…PUm-x?x ^5w ‚vq T…[}QS8\ t8{„[ u8‚ Q„P{…Qa^"‘[]w}[]hUPIm ¹
Q„P¶_ q5u ƒ5PU_RQS[ q5u$– m[•´#t8{„[ q5u QSPI{…Q7sT q ‘8w]PU\ºf q T!Q‡ q _a q [}_UPU{ q f à ç7” ‚ t8T„PU{!µGt
u t\B‘JPUT q fE[}Q„PUTS^QS[ q5u {&T„PIµGt[]T…PUm—Q q T„PImt_UPQS8P¨[ u [}Q„[¦^5wJT„PI{„[}mt€^5w1‘Œ†^Bf^5_RQ q T
ÃÊ Ñ Å
Ã?Ê Ñ
zw]PI\;P u QS{" OT q _I{UX
Š
Š
œ
V
V
œ 7
œ
V
‹ V Š
œ
V
V
v‹5 ŒŠ œ
@
V
V @vŠ
œ
z 8m []{„_IT„PRQS[]hU^"QS[ qvu§q f
q QSPIm¡T„PIsT„PI{„P u QYQ„P
q f Ñ UX
Ï
œ
V
@
V
œ
V
V
@
@
^5‘w}P7Š
“[}\;[ u‚ {¿f q TrQSP?s^5TS^5w}w]PIw{ q w]t8Q„[ qvu t{„[ u‚ QSPl{…Qa^"‘[]w}[]hUPIm ¹ z¢m[]{…_UT„PRQS[}h^"Q„[ qvu¶q f‰Q„P’_ qvu ƒvPU_RQS[ qvu$–
m[•´#t8{„[ q5u Q„PU{…QlsT q ‘w]PI\ f q T™Q‡ q _a q []_IPU{ q f à ç¿Q„P¨{ q w}t8QS[ qvu Q„[]\MPU{W^5T…P¨µGt q QSPUm([ u {„PU_ qvu m{’^ u m
Q„P{„sJPUPUm – ts{l^5T„P?T…PUw]^"QS[•ƒvP’Q q Q„P‘PI{…Qe{„PUµGtP u QS[¦^"w{ q w}t8QS[ qvu QS[}\;P"X
ÃÊ Ñ Å
ÃÊ Ñ Ï
OT q _IPU{„{ q T„{
Š
œ
Š
œ
d q w]t$QS[ q5u “[]\MP @[email protected]Ñ$X œ V
X V @X œ ŠvŠ $X v‹ vœ8X @5‹ œ 8X Š 7 Š$X 7Š @ @$X @
[email protected]$X œ Ñ $X @ V
V Xœ
d$sJPUPIm – |Ws
Xœ
ŠX½Š
$X
Xœ
Š$X V
8X @
œ$X ŸPM‘P ‚ [ u ™[•QS>^mPI\ q5u {…Q„TS^"Q„[ qvuAq fyQSPMµGt€^5w][•Q‡† q f¿QSPY¿P^5`Gw}† q ƒvPIT„w]^5ss[ u‚ x?x sT…PU_ q5u$–
m[•QS[ qvu PUTe™P u ^5ssw}[]PImèQ q ^¶_ qvu ƒ5PU_IQ„[ qvu– m q \M[ u ^"QSPIm˜Q„PU{gQ!s8T q ‘w}PU\ q fyQSPBf q T…\ À ÁRXB^5‘w}P
{… q ™{MQ„P u t\B‘JPUT q fesT…PU_ q5u m[}Q„[ qvu PUmD*
ezydŸ[•QSPUT„^"QS[ qvu {¨QS€^"QM^"T„P¶T…PUµGt[]T…PUm¡Q q { q w}ƒ5P¶QS[}{
PIµt^"QS[ qvu ™8P u È —Ê À Ð Ñ Ð ÑŒÁ¿^ u m Ë [}{“_a q {…P u { q ^"{™Q q sPIT„\M[}Q&Q„PP á ^5_IQe{ q w]t8Q„[ qvu
Æ—Ê 6¶Â
Š À  Á
À  Á À  ŒÁ
À Â Å Á
À Š5Á
vq u QS8PWm q \£^"[ u¤Ì Ê À Ñ Ð Š5
Á À Ñ Ð Á À Ñ Ð ÁRXE& q m[}´PUT…P u Qƒ"^5w]tPI{ q f à ^5T„P™t{…PUm1~T„PR·€PU_RQS[ u8‚ Q„P
™[}m8QS q fÖQS8P’‘ q t u m€^5Tg†¶w]^³†5PUT“[ u QSP’{ q w]t$QS[ q5u [ u Q„P?T„P ‚ [ qvu£q f 6—Ê Š$X ¹€q TyQSPI{„P_^"w]_Ut8w¦^"Q„[ qvu {
Q„P&[ u [}QS[]^5w ‚ T…[]m q f<@5œ ™QSPIQ„TS^58PUmT„^5w8PIw]PU\MP u Q„{E{„ q  u [ uB¹ [ ‚ tT„P À Q q sBw}PIfåQaÁÖ[}{ET„PR” u PImYt u [}f q T„\Mw}†
‘Œ†¨ts!Q q f q tTÖw]PIƒ5PUw}{U~2Q q sT q mt_IPr^™{„PIµt8P u _IP q f\MPU{…PU{‰_ qvu QS^5[ u [ u‚ ‘PRQ‡rPIP u œ 7 ^ u mB V @ vŠ
PIw]PU\MP u Q„{UX
ŽQ![}{_Uw]PU^5T’QS^"Q~‰^5{?QS8PM” u [}QSP¤PIw]PU\MP u Q\MPU{…Ÿ[]{?T…PI” u PUm q TQ„P u t\B‘JPUT q fr{…t‘Jm q \;^5[ u {?[}{
[ u _UT…P^5{…PUm1~JQSP u t\B‘JPUT q f[}Q„PUT„^"QS[ qvu {“T„PIµGt[]T…PUm ‚ T q ™{eP á Q„T„PI\;PIw}†—{„w q ™w}†vX““8[]{W[]{W^ u PI{„{…P u QS[]^5w
sT q sJPUT…Q‡† q fk^ u PI¾M_U[}P u QsT…PU_ qvu m[•QS[ q5u PUTIXŽ u f^"_IQ~QSP¿[}Q„PUTS^QS[ q5u _ q t u QS{ q f€E^"‘w]P {„t ‚v‚ PU{gQQS^"Q
Q„PrsT…PU_ qvu m[•QS[ q5u PUTÖ\;^³†[ u f^"_IQ‘P q s8Q„[]\;^5w À [XP"X‰Q„Pr_ qvu m[•QS[ qvuu t8\B‘PIT q fQSPysT…PU_ q5u m[}Q„[ qvu PUm
{g†${gQSPI\ []{¤‘ q t u m8PUm*^5{MQSP\MPU{„/[]{¤T„PR” u PUm q TMQ„P u t\7‘PIT q f’{„t‘Jm q \;^5[ u {;[}{M[ u _UT…P^5{…PUmkÁp~
 q ¿PIƒ5PUT¤rP§^"T„P¶_ItT„T…P u QSw•† t u ^"‘w]PMQ q sT…PU{„P u QM^ u † \;^"QSPI\£^QS[]_U^5w_ q5u ”€T„\;^"Q„[ qvu q f“QS[}{UX¼Ž u
^5‘w}PlŠl¿Pes8T„PU{…P u QyQS[]\M[ u8‚ {f q TQ„P™_ q \Msw}PIQSP ¹ z>_^"w]_Ut8w¦^"Q„[ qvu {Qa^5‘t8w¦^"Q„PUmM^5‘ q ƒ5P qvu Q„P“” u PI{…Q
\MPU{…1~™[}Q„( V @vŠ 7Q„PIQ„TS^5PImTS^"wPUw]PI\;P u QS{UX
@
¹ [ ‚ tT„P£Š$X¼i u [}w]w]t8{…QST„^"QS[ qvu˜q “
f QS8P§s€^5T…Q„[}Q„[ qvu [ u‚ …{ Q„TS^"Q„P ‚ †5~y‘^5{„PIm¢t8s qvu T…PU_ItT„{…[}ƒvP§_ q$q T„m[ u ^"QSP
‘[]{…PU_RQS[ q5u ~t{…PUm—Q qMq ‘8Qa^"[ u Š$~ ~ M^ u m œ¤{…t‘Jm q \;5^ [ u {“[ u—q tT&QSPI{…QWsT q ‘w]PI\-X
2& & &#«³¯M¬
Öª£°§« ²7±
 8PUT„P^"T„P’^ u t8\B‘PIT q ff4PU^"QStT…PU{&_ qvu _IPUT u [ u‚ Q„P’s€^"TS^5w}w]PUw€Q„[]\M[ u‚ {[ u ^5‘w]P’Š¨QS^"Qrr^5T„T„^ u Q
“
f4tT…Q„PUT¨m[}{„_Ut8{„{„[ qvu X§O‰PUT…€^5s{7Q„PM\ q {gQ¨[]\Ms q TgQa^ u Q q frQSPI{„P£[}{?QS€^"Q¨QS8P£^5w ‚ PU‘8TS^5[}_;^"_IQS[ qvu˜q f
QSPsT…PU_ qvu m[•QS[ q5u PUT“QS^"Q™rP¨€^ƒvP7^5ssw}[]PUm—mPIsP u m{ uq Q qvu w•† qvu QSP u t\B‘JPUT q f{…t‘Jm q \;^5[ u {
à ~‘t$QY^5w}{ qèqvu QSP ‚ P q \MPIQ„T„[]_MsT q sPIT…Q„[]PU{ q f“QS8PU{„P§{…t‘Jm q \;^5[ u {IX(Ž u PU^5_a _^5{…P£QS8P¶s€^5T„^5w]w}PUw
[]\Msw]PI\;P u Qa^"Q„[ qvu¨q fkQSPI{„PW^5w ‚vq T„[•QS\M{‰\£^†B‘JP&ƒvPIT…†YPR¾M_U[]P u Q¿‘8t8Q[}f€Q„P™^5w ‚5q T„[•QS\ [}Q„{„PIw}fk[]{{…t_a
QS€^Q’[}Q„{l{…PUµGtP u Q„[¦^5wP á PU_Ut$QS[ q5u QS[]\MP¨[]{ ‚ T„P^QSPUTeQS€^ u Q„€^"Q q fQSP!f^5{…Q„PU{…Q¨^ƒ"^5[}w¦^5‘w}P{„PUµGtP u QS[¦^"w
^5w ‚5q T„[•QS\ À f q T“Q„[]{“ q T„`§¿P7t{…P¶š Ñ"ž¦Á“Q„P u QSP¨{„sJPUPIm – t8s(™[]w}w1‘P!^5m8ƒ5PUT…{„PUw•†-^"´#PI_IQ„PUm1X“Ž u ^ u
PI´ q T…QyQ q \;[ u []\M[]hIPrQS[}{rs€^"T…QS[}_Utw]^5Ts€^5T„^5w]w}PUw q ƒvPIT„PU^5m§rP’^³ƒ5P’{„PIw]PI_IQSPIm—^7{„[}\;s8w]P™s€^5TgQS[}Q„[ qvu [ u‚
{…Q„TS^"Q„P ‚ †˜‘€^"{„PUmŸts q5u T„PI_UtT…{„[•ƒvP£_ q$q T„m[ u ^"QSP¤‘[}{„PI_IQS[ qvu X§“[}{!{gQST„^"QSP ‚ †v~[]w]w}t{…Q„TS^"Q„PUm˜[ u>¹ [ ‚ tT„P
Š$~w}PUm§Q q QSP‘JPU{gQe{ q w]t$QS[ q5u Q„[]\MPU{rQ„€^"Q™¿P¨¿PUT…P7^5‘8w]P’Q q ^5_a8[]PIƒ5P![ u sTS^5_RQS[}_UP À f4T q \ Q„P{„\;^5w]w
u t\B‘JPUT q fys€^5TgQS[•QS[ q5u [ u‚ QSPI_a u []µGtPI{!{ q f^5T’_ q5u {„[}mPUT…PUmkÁpX ¹ tT…Q„PUT…\ q T…P5~[ u P á ^5_RQ{ q w}t8QS[ qvu {eQ q
QSP§{g†{…QSPI\;{ À 5 Á!€^ƒvP‘JPUP u t{…PUm1ç—T„PImt_I[ u‚ QS8PT…PU{…[]mt€^"w&‘Œ† ^èf^5_IQ q T q fՅt{…Q ј^"Q¤PU^5_a
^5ssT qá [}\£^QSP“{ q w}ƒvP À ^ ‚ ^5[ u t{…[ u‚ š Ñ"ž¦ÁRX ¥[}w]{gQyQ„[]{_U^ u €^ƒ5PWQ„PePR´#PI_IQ q f1{…w][ ‚ GQ„w}†7[ u _IT„P^"{„[ u8‚
QSP—Q q Qa^5w u t\B‘JPUT q f’[•QSPUT„^"QS[ qvu {¤T„PIµGt[]T…PUm/f q TM_ q5u ƒ5PUT ‚ P u _IPè[}Q£^5ssJP^"T„{¤Q q †[}PUw]m¢QSP—f^5{gQSPU{gQ
q ƒvPUT„^5w]w#{ q w}t8QS[ qvu QS[}\;P"X
“8P?\£^5[ u ^5m8ƒ"^ u QS^ ‚ P q fQ„P?s€^5TgQS[•QS[ q5u {¿[}w]w}t{…Q„TS^"Q„PUm¶[ u§¹ [ ‚ tT„P’Š7[]{rQ„€^"QrQ„P?{„t8T…f^5_IP – ^"T„P^7Q q
ƒ q w}t\MPlTS^QS[ q7q fQSP?{…t‘Jm q \;^5[ u {¿[]{&{…\£^"w]w+X‰“[}{“\;PU^ u {rQ„€^"Q“‘ q QS;QSP^5\ q t u Q q f^5mm[•QS[ q5u ^5w
T„PR” u PU\MP u Q¿^ u m¤QS8PeµGt€^ u Q„[}Q‡† q f u PU[ ‚ G‘ q tT – Q q"–u PU[ ‚ G‘ q t8T_ q \M\Bt u []_^QS[ q5u []{T…PUw¦^QS[}ƒ5PUw•†B{„\;^5w}w+~
\£^"`[ u‚ Q„P_ q {gQ q fEPU^5_a-[•QSPITS^"Q„[ qvu ^5{“w q ^5{™s q {„{…[]‘w}P5X ¹€q T“_ qvu ƒvPI_IQS[ qvu$– m q \M[ u ^"Q„PUm—sT q ‘w]PI\;{
 q rPRƒvPIT¿QS8P u t\7‘PIT q f#sT…PU_ qvu m[•QS[ q5u PUm¤[}Q„PUT„^"QS[ qvu {T„PIµGt[]T…PUm¤Q q _ qvu ƒ5PUT ‚ PeQ q Q„P™{ q w}t8QS[ qvu \£^†
‘P—mPI_UT…P^5{…PUm f4T q \ Q„ q {„P ‚ [•ƒvP u [ u ^5‘w}P
‘Œ†¡{…PUw]PI_IQ„[ u‚ ^¼s€^5T…Q„[}Q„[ qvu ™[}_a _ qvu Qa^5[ u {¤w qvu8‚
Q„[ u {„t‘Jm q \;^5[ u {QS€^"Q¿^5T…PW^5w][ ‚vu PUmY™[•QSYQSPW_ q5u ƒ5PU_RQS[ q5u m[}T„PU_RQS[ qvu XE“8[]{QSTS^"mP –q ´¶QS^"QyP á []{gQS{
‘JPIQ‡¿PUP u \M[ u []\M[]hU[ u‚ QS8P u t\B‘JPUT q f™[}Q„PUTS^QS[ q5u {T„PUµGt[}T„PIm ^ u m \M[ u [}\;[}hU[ u‚ QS8P£_ q {…Q q f&P^5_a
[•QSPUT„^"QS[ qvu []{™^ u [}\;s q T…QS^ u Q&[}{„{„t8PQ„€^"QW[]{& q TgQSŒ† q f‰f4tT…Q„PUT™[ u ƒ5PU{…Q„[ ‚ ^QS[ q5u X
Ž u ^5mm[•QS[ qvu Q q QS8P7s€^5TgQS[}_Utw]^5T™µt8PU{…Q„[ qvu(q f{„t‘Jm q \;^5[ u {…€^5sJPY^ u m(Q„P7\ q T…P ‚ P u PUT„^5w‰[]{„{…tP
q f“Q„P q ƒ5PUTS^"w]ws€^5TgQS[}Q„[ qvu [ u‚ {…Q„TS^"Q„P ‚ †˜Q„PUT…P¶^5T…P¶^ u t\7‘PIT q f&f4t8T…QS8PUT7w}[ u PI{ q f“T„PI{„P^"T„_a QS^"Q
u PIPUm Q q ‘JP§t u mPIT…Qa^"`5P u X ¥P u ^ uqvu w}[ u PU^5T7PIw]w][}s8QS[}_£Ox?z [}{B{ q w}ƒvPIm¡f q TYP á ^5\Msw]P"~QSP ¹ z
m[}{„_IT„PIQ„[]hU^"QS[ qvu w]PU^5m{?Q q ^ uqvu w}[ u PU^5T?^5w ‚ PU‘8TS^5[}_B{…†{…Q„PU\º™[}_a>\;^†è‘JP¤{ q w•ƒvPUmAt{…[ u‚ ^§µGt€^5{„[ –
jWPI“Q q5u \;PRQS q m1X6i&Q¶P^"_a uqvu w}[ u PU^5T;[•QSPITS^"Q„[ qvu ^>w}[ u PU^5T;Zv^5_ q ‘8[¦^ u {g†{…QSPI\ \Bt8{…Q¶‘JP(m8P^5w•Q
™[•QS1~#^ u m(Q„PYZv^5_ q ‘[]^ u \;^"QST…[ á [•QS{„PIw}fE\£^†‘P!s€^5TgQS[}Q„[ qvu PUmè^ u m¼^5{…{„PU\7‘w]PImè[ u s€^5TS^"w]w]PIwt{„[ u‚
Q„P-‘8w q _a`Ÿs€^"Q…QSPIT u/q f À ьÁRX “PI{„Pw][ u P^5T7{…†{…Q„PU\M{£\;^³†>QSP u ‘JP—{ q w•ƒvPUm¢t{…[ u‚ QSP§¿P^5`Gw•†
q ƒvPIT„w]^5ss[ u‚ s8T„PU_ qvu m[•QS[ qvu PUT?Q q-q ‘$Qa^5[ u ^—s€^5T„^5w]w}PUw u8qvu w][ u P^"Tx?x ^5w ‚vq T…[}QS8\-XY“PMP á Q„P u {…[ qvu
Q q w}[ u PU^5T“^ u m uq5u w][ u P^5T“{g†{…QSPI\;{ q fEOx?z{™\;^†£QS8P u ‘Pt u m8PUT…QS^5`5P u ^ u m^5{…{„PI{„{„PIm1X
®
H’®?¬¼²5&
&^ u `k~Xz™X•~ q w]{gQ~ >X•ç“i»jWPI OE^5T„^5m[ ‚ \ f q TeOE^5T„^5w]w}PUwilm^5s8QS[•ƒvP -PU{…[ u‚ ilw ‚5q T„[•QS\M{UX
d$Ž‡i Z8X qvu d$_U[X orq \Ms1X , À Š"ÑvÑvьÁ
vJ 8X
Š$X &^ u `k~¨Xz“X}~yZ5[}\£^"_a`J~OXV¤X•çMi jePR O^5TS^5w}w]PIw¿x q \£^5[ u x’PI_ q \Ms q {„[}Q„[ qvu -PRQS q m f q T7Q„P
ilm€^5s$QS[}ƒ5P ¹ [ u [}QSP!zw]PI\;P u Q?d q w}t8QS[ qvu(q fyzw}w][]s$QS[]_¨O^5T…Q„[¦^5wx’[}´PUT…P u QS[]^5w‰zµGt€^QS[ q5u {UX orq5u _UtT –
T„P u _I†^ u m orq \Mst8QS^"QS[ qvu çOTS^"_IQS[}_UP¨^ u mz á sPIT„[}P u _IP5~ © À Š5Ñ5Ñ Ár ŒŠ @ V Ñ$X
À ‹v‹ Á
8X o €^ u ~k?X•~ (^"QS8PI~€?X•ç¿x q \£^5[ u x’PU_ q \Ms q {…[}Q„[ qvu iew ‚vq T„[}Q„\M{UXil_IQS^;jWt\MPUT„[}_^
œ J 8X
X *T q ss1~
XxBX}~‰V?PI†5PU{U~xBXz™X•ç¨OE^5T„^5w]w}PUwEOPUTgf q T„\;^ u _IP q f“x q \;^5[ u$– x’PI_ q \Ms q {„PUm(OT„PU_ qvu m[ –
QS[ q5u PUmV?T…†w q ƒ -PIQ„ q m8{™f q T™Oyx?z{“™[}Q„ˆ q _^"w]w}†;| u [}f q T…\ ™PI” u PU\MP u QXJd$Ž‡i Z8X qvu d$_U[X
orq \;s#X © À ‹5‹ŒŠvÁ Š J V X
V X q m ‚ { q5u ~8xBX o X•~8Z5[}\£^"_a`J~O‰X VYX•çi x q \£^5[ u x’PU_ q \;s q {…[}QS[ qvu OT„PI_ qvu m8[}QS[ qvu PITf q T¿^¨OE^"TS^5w}w]PUw
¹ [ u [•QSP¼zw}PU\MP u Qd q w•ƒvPIT qvu x’[]{…Q„T„[}‘t8QSPIm¥| u {gQST…t_IQ„tT„PIm *?T„[}m{UX“O^5TS^"w]w]PIw orq \;st$QS[ u8‚ À ‹v7‹ [email protected] Á v V @ Jv X
œ8X Z5[]\;^5_a`k~€OXVYX}~€je^5mPIPU\~kdX›i7X•çyi >P^"`w•†—¸lƒvPIT„w]^5ss[ u‚ OE^5T„^5w]w}PUw#x q \£^"[ u x’PI_ q \Ms q {„[•QS[ q5u
OT…PU_ qvu m[•QS[ q5u PUT&f q T&Q„P ¹ [ u [}Q„P?zw]PU\MP u Qed q w]t8Q„[ qvu¶q fzw]w}[]s8Q„[]_lOT q ‘w}PU\M{&[ u “T…PUP¨x’[]\MP u$–
{„[ q5u {UX‰Ž u ilT„^5‘ u []^8~ !X ¨X À PIm1X½ÁpçYOT q _UPIPUm[ u‚ { q f&QSP¶Š5ÑvÑvю u QSPUT u ^"Q„[ qvu ^"w orq5u f4PUT…P u _IP qvu
OE^5T„^5w]w}PUw^ u m7x’[]{…Q„T„[}‘t8QSPImBOT q _UPI{„{…[ u‚ ‰PU_a u []µGtPI{^ u mBiessw}[]_^QS[ q5u { À Ox?Oi Š5Ñ5ÑvьÁR~ q w –
t\;PŽ…Ž„Ža~ o d Wzi OT…PU{„{I~J|’d$i À Š"ÑvÑvьÁ V @ J V Š5 8X
@$X Z q  u { qvu ~ o X•çjet\MPUT…[]_^"wd q w}t8QS[ qvu { q f‰OE^5TgQS[]^5w1x’[•´#PIT„P u Q„[¦^5wzµt^"QS[ qvu {&‘Œ†£Q„P ¹ [ u [}Q„P’zw]P –
\;P u Q -PRQS q m1X o ^5\7‘T„[}m ‚ P| u [}ƒvPIT„{…[}Q‡†—OT„PI{„{ À ‹ [email protected]ÁRX
8X -PU{…{S^ ‚ PMO^5{„{…[ u‚ Ž u QSPIT…f^5_IP ¹€q T„t\ç (OŽaç1i -PI{„{„^ ‚ P – OE^5{…{„[ u‚ Ž u Q„PUTgf^5_UPMdQS^ u m€^"T„m1XŽ u QUX
Z8XJd$tsJPUT„_ q \Mst8QSPIT™ilssw
X À ‹v‹ Á u8q X€ X
‹8X ¸?{g&^"w]m1~O‰X}ç -tw•QS[]w}PIƒ5PUw ¹ [ u [}Q„P¼zw]PI\;P u QiessT qá []\;^"Q„[ qvu 硍“8P q Tg†6^ u m iessw}[]_^QS[ q5u {UX
PIt‘ u PIT’d$`GT…[]s8Q„P u hUtTWjet8\;PIT„[]`k~ eX *YX€PIt‘ u PIT À ‹v‹ ÁRX
Ñ$X‰d8^v^5m1~ BX}çyd$Oi ed8V?Ž‡?çki &^5{„[}_? qq wV?[•Q&f q TWd$s€^"T„{„
P (^QST„[ áorq \Mst8QS^"QS[ qvu {I~ PUT…{„[ q5u ŠX
PI_a u []_U^5
w ™PUs q TgQ~ o P u QSPUT¿f q T“d$t8sPIT„_ q \;st$QS[ u8‚ ™PU{„PU^5T„_a—^ u m—x’PIƒ5PUw q s\;P u Q~$| u [•ƒvPUT…{„[•Q‡†
q fEŽ‡w}w][ uq []{r^"QW|eT…‘€^ u ^ –go €^5\Ms€^5[ ‚vu ~8|eT„‘^ u ^8~€ŽÝˆ~k|’di À ‹v‹ ÁRX
v X‰d$sPU^5T„PI{U~ X}~ ¿PUT„hI[ u {I~ >X}çi¥ – x¥| u {…Q„T„t_RQStT…PUm PU{„Milm^5s8Qa^QS[ q5u ilw ‚5q T„[•QS\ f q T“[}\;P –
x’PUsJP u mP u Qed$ q _a`¶x q \M[ u ^QSPUm£OT q ‘w}PU\M{UXŽ u QX€Z8Xf q T&jWt\MPUTUX -PIQ„1X8[ u§¹ w}t[]m{ À ‹v=‹ @5Á
J Ñ X
X

Прайс лист "на складе"

Многоквартирный жилой дом по пер. Инструментальному, 11а;pdf

;docx

Рекомендации по обслуживанию книг Digma R60G, E605, E625

Мойки и раковины из камня GetaCore