From 24a9d14f47fcee18b3f7a31d666383ef93dd8cb9 Mon Sep 17 00:00:00 2001 From: Petr Velycko Date: Sun, 18 May 2025 20:22:35 +0200 Subject: [PATCH] * misto = --- linearni-rovnice.tex | 2 +- skripta.pdf | Bin 227249 -> 227258 bytes 2 files changed, 1 insertion(+), 1 deletion(-) diff --git a/linearni-rovnice.tex b/linearni-rovnice.tex index 540e789..6848bc8 100644 --- a/linearni-rovnice.tex +++ b/linearni-rovnice.tex @@ -134,7 +134,7 @@ Uvedeme si několik poznámek k definici fundamentální matice. Je-li $\Phi(t)$ Dále si uvědomíme, že $\Phi'(t) = A(t)\Phi(t)$, přičemž násobení maticí zleva provádí řádkové úpravy na matici $\Phi(t)$. Konkrétně $\varphi_k^{j\prime}(t) = \sum_{i=1}^n a_{ki}(t)\varphi_i^j(t)$. - Platí $\det D_k = A_{kk}(t) \det \Phi(t)$ (vlastnosti determinantu). Z toho dostáváme, že $w'(t) = \det \Phi(t) \sum_{k=1}^n A_{kk}(t) = w(t) = \tr A(t)$. + Platí $\det D_k = A_{kk}(t) \det \Phi(t)$ (vlastnosti determinantu). Z toho dostáváme, že $w'(t) = \det \Phi(t) \sum_{k=1}^n A_{kk}(t) = w(t) \cdot \tr A(t)$. \end{proof} Pokud $\tr A(t) > 0$, potom wronskián roste, $=0$ množina možných hodnot řešení zachovává objem a pro $\tr A(t) <0$ v průběhu času objem klesá. diff --git a/skripta.pdf b/skripta.pdf index ed11959d0dec34bf0ce8774b216db665fd7e641c..7d50854371f20f8d637f2e3902e0e23f47bbe759 100644 GIT binary patch delta 10900 zcmai$MN^y&qeKaW023S%+=DZ?dvJGmmjHviJh%k+;0f+9xJz(%x8UyX-&=Kmz^&@) z#i?GMRYT8FTFz0b84ut%nOPHA4!}TP2P}h8*EWz-^$;h;F*jr9?MBoax|yOz9@$q_ z+Ck^|;2IayWyr&gpNXvcPpD^`sp($e?bZ3=xaXn>kmC6lPgxcgHeQoco#)23&f#_$fXOS^XjE4|!SJIIC5{J;BbrTCPpXkpjG@duXVM z>aLXUipW=JV3qNb@aUxHMI=!q3a|}{g5zRE7X3FqzM|IqH4rPz?C6uG-Fk!b4;1M8 z%)WWbIQ{BT5y-pl19^~7mn)nMZKlP0U$uJJoiJJ##$FQh3@p2W_iw~xwi=s^P}uO~ z+N|K&jOHBISvlGBv*M^nK>%f5$}-iMmTp7xr8ZoY+KPnSxY4l$ZIMxw%UlYefk04ad6`0mO^^5Rzz&&6NyQ#4E?jzEVvSl@7E5;ZcP~A#-Vb`}7M@0>hX~ z=A7z-(gWLI>V5m7<$x@fokTF5M&G+)7~!T=h`CcSRsn`l!uFNN6s+>p7;ZV&ix}R? zZ&Llop?QN5Bnt9JpS$)LGJ0#sPw;d)H~(d+Vpv-`#Xu-z6pzzO1b+tpCvalP7pb-- zh2rJ3p4O!4E_9c8eZ&B?cIN+rVEhY>r?R8X=f2OOVerTzGb*^;Lo;Wcit=wm?W7U* zqmEV*f@N=O^jDfjDBmYA*u9ZQ9)bBgWO>O4ILKtc`c%Avd)Crq*w znmp)aX5{+@Kh!6he?)o9kj}6n&l^t^V~aSyM6jSipk>@T2Twp1sLf|nD5Rp2*~l(# z*58PtS)wt+{2tyx~F6Z@oIySiy$ zUp`RiHt~0V1FcP^OkkmO;5)(P{*%e>s|FO)7;Het+QNC_pQp*7Imq}^dE7%<7AE?G zm`fIy9BD?u%e&p@8eP`g4U$m9FzN2O(ECBC-}JQf?{I*IE6lIt{4aew`#h=;+6J;= z)%r&`)zACFn;hsq1}pbmPUO3Q;m3n7hauuJnXB#yBFy!FTWU-9RzD{} zY%b$;WSW7Rm`9eRPbfk$Y00Ia$6o~eoV$C!IQ9d6CRMO{ju-6H!BMZLV=5S|#SXWk z%po}vyqGu!Nugk-g_n5zK@v}1453$ym3@yvEkV^}!?j5NSEis-BWCg;pIM-^ivubA zRxkxu7b34}a%RM8w~4pLsyNepvvtC|@FqV%!C?x>UMrs-HFQmP(zrAJ)(wpHMhNM| z^;j7qmoZP%Cs_l>fRs~120n{B#!#jklXeI+#f?$c;$184F}sg`5suo{NL zaTO1sN8)k5rfsmCA1nB>ftiR-=CEq+x6K;q1rFzg#V!1+Sg5J+&FvPOlA1g*VRTEw zorF^=Tf#>b4$vdZ(@RsagC6r!2bljjWty~^l$6z>0`tQ!Bqf!F%6=yg#8FA%w4`sG zsK`8%ENPn<4xif+Pu=VFV+fr4>)fjWi1h&AT3pvurJAm0GD+*xJH|i+8mAJneYlk7KQ)T6p;QnH+Gg0ol z-RqxdQCYTr`$xkAGSeGRU_lDcFc?*HVYb6Sg zWxsb!Wdr^$S$5ya$~LdZE{6cFo1@T(5v5bvUT`!|xHmMD``FDKN=LFc0b=UQgfMsb zjiUhenAcEY(1o^Ozfu)^Uj$i8qHa!j9D48%m}Ixvr}iTKo_SM(pk^PG_)kt?{NZFf z#keG7&8!!C5?qR!6g;alxD;r*f#KX!W(KKsu2oMA^T)$xZ7rhs?d?z~tyY>14?1>qNlGaAdUSg9PakF4xt<{3Y<9hEmCA~B zMGdbIj*j3EaiV3;Jy#VZG@h$?Bbr6irN`w&c43X#d+{Wc=fh-K>1D+R72mar43`|e zuN{}|T&IiPk8$yFYQP<#3!UTplApBS-5(x@eM))X<$pFG=3BrS`+AGi{we`jZ0DVi z%vueXrptfXka1VJ(z2npkF?uW#fv^ zkEM}%%db-`%Y}X}_}V!tH|oO%$7*tUg3dcZ+EcKLwxJ9hQW`CSdpX;t67M-6AVg@uWHwc+S>((?;{_bod4#D-!)r! zGz6Fy4iizpCs8^}@ZJaLI$UIAowc6q4%Nt}4aej_AXJM^2{sRh>Z)OOJB`$(*)}Lv z^c;6)!-F9dz=BZIFhU^ul+^_$cdd}yEs|Umft~3=Gnz778ZOPx%7Fq+;?q+c(W>SS)gbOJlkShbl<|=i;>W%?Md~@;HC7lI+!-3~ zSb-JSIOQz=Qa`^}67rhEg`ONS$|w*zDN;+Yok`?t1AA=Jb8b6UFji{q?Qv~*#w$vX zux?soM!OcccfQh|{~n|q7+A=NXx`?i?^KQl2hWMF-+HBE^elawaT0tq!Gzq~!WI>- zY|JOvVCIL~)Rz3Car5;Rbi?ILcSq;mP9uU|anX+1YOrXB69Lny?W*=?NK#{amLoxz zWzNDNFh<3?O@oikpx4ZXD0uJ`)!`pc@%~d%1B^Iqz8EMFtZ*USk!|#M&P2dLF@&r> zW}WVR|ISsFOYTTaEW%8)lBZD?r1NA}Qu%Zdf&{T+?m&-^`ve^IhuYQJG1z5rbFKVr zIBk)3FjPUUVb&$>U-;29GEJWGHLf`zCc*Cri08<$2s5f*-2>7|wx%mu=X+;K{F*ue z;loz9H0*}NM{*Fidz4Rw@Mfv`?;J}_WTpZJ9Ij%!DvC4PSv!@KrG&!M$0DL?GGFKB~KH76|nd)osrXpK<=gS z-mPPjHYcRd=ojYB^2||K$n3R#4KQ>>ni#Yg61dT|;C2jyPm~bsaVq{W4VlE{x??-R z-w-3Q57L*26mp1?AVCHq{j8#1E_lLV|Y*o+()cgH>H@A znJb^x-FzLxtJ27zyOATP4aY*R1N(j87dxZ1RfJ{y(N7qjjP%y({ok2q^^bv`ub)|^ z#Xo&b3)b6^Ssp@&?SdUvZi=&Yy+L{T7O*XHm4_3`*fBT<<1iK5h~ZUP(&L%$IOdZS ze(NKf`80HkvKg4kt^SHVgfOfBm5Jc1Ukoe-U8g9c@^li+oMUfPBlxg_%LqF>K# zQ{OE%r$DXbT13V~k7Um2smuau3HNrYio$5(=(p6KUzVQ}9KHnb$s0$>O+DPj`(rq% z36P8199O1c3JGEHaN~CBPhRU{r!Xgd1gr>eR?lVnN0K=@gki%FUwRdQEi+j`Zd@|- zStib2V<$LQ>JILqwGU*(%jdk{gJ46k?yk`Ysd3ng6{`3K_mjn-e>UR^qq@SB$0M2< zqt9$yyZQzrD;^tL=22tWOl&OM*jMs?qVU@VWT;(?-*$qa-<3iwn%N3Eyl`NvMdY?@ zp2TCK;kMb8{}~Y~)QXV-6w0k$Pm$?%mzCzoDxKQOouAZ<(&G89ej(&|x4)RoyIb2I z+=Wg~SVRIo_it-G6IGoLM{lQ{!1Kl4cF&lJ-|h3tyVvy_#L@5*mo`6@=&=T?p@5P- z*S0-{Z5x?r;()4qk9O5#=Dn+Csho)&SVM`C-3fai%F{@IH`@Zxa>+T(=s=n_apEm_ zEE^mvXm3&8IiD~{(2 zYUjb8YNr<;l8Z&=_r^i6#ql*bY>sz+{4|Iz&$Cubl6v)k#=lyX!hOF(7rxC-{K-cQ#2 zOpZ9#SB!|-yhIwfPmaA* z(Tm?!?AE^RDi?i_{(&s^UnThq7U}1Y$*Y)CeszBs>(d61nTMiLm4vSc@BbYN+%aojKvkmI8u7Kl;r|6HIsCk>`-BT6a*$PRJz_ZB{ z74_Mscnr;XUyToNV?f$hQTx6`_KoqY#O%sZZrPmepN^fR5lth-WH5vk*#R|*dR(Ys* z{=P-cJeWency`p~P!y)tP;S?BNTnP-A@A<;FKL@+2if*eO?d8ncupFkH3H8LS4KGT zXFI?*3sfAc-|U!>vEUTY)kQbpTx@LQTm)OX8{s7YFG^JG_KLfE!6#x4X^b#Wg57KQ z0g#`#lcsFLaoe#6?9bUMGI(rw{HBLC<;}w|CaqY(!p~k+>SgTo*XxmD;rDjmxR}MM zen6?AcUQ3(87kz%|BrF~AG@sa8bQhrFkd(a<~ITc=Iw#(h#DJO2m?5gT}WnWZq00` zMFJl`HhRy&aJ#bVAh^6TzK;lqjt=o>`eDmnRBpMTNoBOq1UtX@3qdJ5ItOM}epuUH z;a4RYd~OL8873W{4=jMlv6@B%8@_70h1aqlvN3n9v?B@#~uc-arje?^C7=( z^TNz_VJd3+&kf3~1g4L8t})r*ImnqFj8bHK_Btodjl z<$=SJ$b9_9Um2zND>YfKc;fg7zi$6jPJg*26teUohq;rTxx!bf%*Iw#P*>CR<2Ym4={0c>`vY=`93bAV)1N|U!E}lCoVNvs-wJ7!#iF7-PF-~X86-Y&0^_)wWNzD&R zBNhRAt_G*;6g{CXD`QF=vf-^Go&I{4hDxWIHosY?)H{sY0z2_^VTWTI<^YHBCX=%F z#jEr?q|Ysw$a+B)mEUVO&9vV?E+K{ur`0LZ#Sv!yAKMaIqDGoJTB0)U3jA4mOu3o>< zL8kJnu*bLqo_@m;B-=A^o^^c%Q3LMCCAQ?gHex<1m3ADV%QvMj^|3CDe)>`OhfKR~ zxdH|!e`RP$$Vc?iFwuqXpZ0v1tj2~@x>?T@GZV1LSzWc-8?BWwwPirBhs%O~Tx)J0-Yd2{6 zMNTF1f-0IB+r!!E`!uLlH0%uQ?P+FYM4&@N;E zXY%63hxx>P$z*IydZ9WLNO{GK!$H=aVl%O3!Kt3~T>n(0d~Dnv)aJrujrgDorrlTk z0MvBO-+py}jJi(s6(d>C@LzTBw{~tE>@iol8l{MbL>&mo7e+|29puAP-nMg<4EUurG2!a>#JnLh}$ zf1@>7h7i-MqpB7miD*Jh(WH0mpEB|yP8|)eks)st*L_%)q%#1UzjRZeigHt6nI*wl zpYionPr^&VP{&7J-fChc{9A_ovQxg4uGy9)nT3+Y(lSl8{lwTaiKM8R&(iQKO%M0)oZglqWaIVt zR*;GMNRA%UG2EM){dv^5t!!Nq8-@P#88}58S+#@P{pNi*$;VWr{dMF6?oS>2-71%a zj+Vmi9~%$pc7!Qb(Ek>d-9Q1N=XUOTc5;JcCr4frTme`iP2MYc|R3gcEp zJeqr}i{D2#CO1kytdWvsMu`MFoIUtEnJ;4~m9d38?|k9Kyd)prne*3ZUEJC}Fd`)< zQp1FPiNWIoRU)8nemSLSou%r9xgpger(%6p7Iwgehm*E7{=|+NkE;n}!1qaf68MBT zFeQvDd6mnDhsc4M_(^nPT5KthY^hkHMjPWaSOOE}$<>Cd zl5Cw43xkYRxow!eBo337{LC9CLOfzJ=2WpIT`d+fkY8HrrUEk_6-@UVrWYN)Wm;<6 zg|gM{8+(lsX1WRkqC5v6Dxr$eOGQukhm^P=m&zgfv&)~Y@$Zvs#Zkih#RnfV$Y)^# zQ0c3vla&f(gQUO_a&m3fHKbNXvnXGUkBam9Jm=UBWgkuS(c;I7xsbp7-78b%?*f}v ziusyjDw%mohkc{%CT5jb!{}6YPmy$)d>OK*6;ZVp*MU)n8%Tx&h5;H*nf>jBDQS@w z_=dLdMk{nR%V;|6#gHWRaB8yu*#=p>9h|DV!9ze zaFzdX|9kn#Jw`-JUe(RjoDlnzEa-)u#fZ%63W|8==l1-%liN)Xnb8~Skz0oOizPtm zFMar%AX%a9XZ=n-aKjy!q;QKKKJ(FtMspbbd|*-3HE}ty?8zDYKuXJwd<6>!*DT|| z^Ou<$nU_==g|NnC9)vR>K@9_FJSTteMjiX{9&1`(s1Ln=|@DiJs$W{}8VjvDW^0g=U#=c@jJe23!~H=F)4 z*!zN%=3`F%tsUD>T@GY4gKY`d@?qP0jD`14yd?HtpqCNlg7vP~M3h4$y8+3Q$0Ijg ziOOWMj{m;{MDs}`Jz6Q>TDv?OPB240_2l%mk5v$kk2jxp?Vl~sM6h)83S0=H^OHZqGSS=BwJLqkKgKf0#Ct= z5nmImBr4SW$ODb-yXT%oJlvSuyp?0B>{W8w6&FbQ^L9}Lo+9(_4z2gFqOG%~6sc>} z`5*1Zm!_P!@eI%8tEkPpmuiPDyp**jUs-8^?vad5mj)VOa}EgQdh<><&l`w)eaa)A z=ugD78s8U`%G<4})^iDOXPrs8^HeE$9r}ECeB;C!NUK!=rnP1Nh*j&+L@%%-kkOtI zGu1kp5oo~KGF9__dGIHQCR_D3Zv}l69tVLf5bAEGHokx%SYS8zI>OgW+w-2*p9Jr5Mo_!zhw~4S zwe3ciHK<>$b|a8obckhl(9pmFM`fmc98gTR2!^#C_Yj%I;GZi*be5et?cBcFET$yr zbdUA>_;ezEXliXoK_JW&e6@oe%HIGc@OZKPXS%2ZU+v1c6+|a;3X@EH)hZ$$E?@qz z2EE#^I$v)WEQW7>T{62tmzuK6Up)T~nr<{GCQU67|01c}H>22jKus%h%kX_##@K_& z;6?Ldy5cXdjvN*kf>7szxq(Md(|z%y4?6adj@ExL-mIf|Q{1OG z4Yhm}XCx?NlkjJ>(4vevEwJz+#OHUtvZ5(Ol$lA0)DZx>MI+V9SR_9kjH?#@4u|RL zEr{`C*)jaXyrFWNLyBhk9M@|%?@%34sOnsACSG15uuCg;(ZR``%?xMPX|OV^u~C$h zj+#c*m$j`O7iH;G;F;ed@{$9>7ZlH@7??@}77z zBEefUNww{jaqFvGLLsQ_Tm)y-;APap>(+SRMZAs))-s(4#V%Oc;hK3rXB58Ljl8v4 z_?^w~0oQLQC%Y^bfcJCJN?pg}r{nA7Q_s##>-I%?f8nDVdZk0ar#D=UG6R{ zC24;uf1OtR%g{hHga+2x(7!a?zdSrB%DFA?2HiJETBhFI{m!_uVOJ7b=pmYqJZ7Dg1! z;*jDeW``v~S8U^fT;I0yFh;^;nDgRt<@TQcImXYMI~@q5u&00$DG$Y|*_ zo>R>Rds6a3bW7p0ehd7x=2GuTU+kzvZoeI{7Yb!WOuX;SQd0_MNGs|$uIRF|Go<;Y zsnq75Yun}c^84Iwfx)mDZnH0czUnU2F9I@}X>ke%4RQzKGr@ITej{EjxWM@5!$zh| zj;zxLKw#1P?rwWz`HkjqkIb$5l=|$dHM=R}jry$R(suOWr7mb)*IrN}+ONDE5ftyT z+q-eKlc$(`n`L`_*t)uV=#BQMe_!*sU*#%!>r~WUZqMjxaBpc;-TU*sCw3zC9?0&y zowI$a_b7h(%)Nv>hWUr*-~kQWlQ(qf#%3nXZ)z`p&(YPfK~vw^@%oH@DX?Ve?a`i^ zDdv8tollLLgzno@WgJcEYgjH&Q$d8OTc!gLmP>Y}YuE%rQs1Ae&Nk)1??SwM9?yI< z?@yAFe+%XsWOj6mbSrJXPhm&V0GA7)<5^tylL7a|=O#Y-Go*9rc=omCbBC&ro=6*p zQ4!Em&h$0I-wnC#8^7C2&1)(=tF)cxZRXQ!gK8P)D+#U}ajoQPHnPp;lsF|-?L0N} zf`?0W+kK#VsrCb&k^vm9U^k*l^$>_!))tCddhVG$en9%y`@s<_oFI%5psAuc8;u%T z)53wzbVk*~RMx8AF5WKhB}h2ca6rC6XJ1W0XuQ#|POJ|0BvIp7+u&$j-RMKTT~k`q zZ-}vfG!!q%WP818$Zk7+I%`Y0ZeQ7We`OF*KMr?5dro3=Ih|Bbexz-G{6$$@m{X|t zN||t+B%`RUpX|ESu#gV{eoWUTS~kz;SDgkLba=kLESNRMoGiUu(CoKzCX4jDe+qm{ zlYWv`k@apUX>XC8oz+M+Ys|d6xHwoqBPo?T{D4-hJtv6&yW`l({}|Yy7vC<38ZMGL z=!13Ad8OF+cUw}GGEllV1yesVqjQY6K_F;1AE2LfTNQC491|giZlHR>v%qnacyYdJ8_$DoMt+c2ze>IxutQ#i8@d+ z4$L)y7B=zqVspHJaSkViHsJ(kGmQPeVDHh{foQELT?Z^k&x8ZtS(m=nPj3gNvwAEKLw$T_{RAI|S%NMkO!1C9Xh>?lvyi=Z1wxZrI zDY_d0g+$GHO%?m)=VBZ2t9Y$O-z1DR9VKH{eAusf@q(bZl7>NZTZ}1-KK#*sih)h7 z@bm6@u~hB@#J|D?ps7uk_qKu&kK9i7CqYAtIM2oap+D``dR?_W?jTohq&I=d7%Bd1 zYmj4jlTajZazITu$A(9@RS)&U^-YlSAhHRaIe5(9LL`i^CRc{Db;3^c%Fc6)l5#2` zA{tQ^xOU_wo)K3`w6lO^gA-@1tw@t%lQNr9x1pLsrc~@l&J0u)|GBWd!%h{JShS5i zicQN@o5o;q1EfXNG80&u#z?7Gj7=E(VS6%;_dEi>B0b5u8W(*8uT6(OJCHGAdh$+M zd}Yhi%!5e{e_>sTVcb0syJFRgp?9FH{3{Z_(0HQS5_5Q~9c1H3bi}I>d<@mvIi-I- z`6O7j;7kGeJJuw=(}R$4vj9zf6F^B9t4&@-OwG&Q=e&~93kkVd87gx`Ir2>ThnntM zyx#^SuHr^2O#nE}xLm)pA0by%t5LcKvd}1r_eeW-@4?L`oco#7M6@mA*?LXO7*opZ z+>Nkj>(Wd1BONdQ7oO}s9k16nrVGOCA|bI3f1FFqSL5<7iknm@?U?e_m$sh^hq3YY zTXt=tRquVN4_`R*gaV#6I3)Fl6ccn!Q0IZk9P*rQjpAdUFU=HgBKpUr%2ly~LQfJ4 zanDAqM>545t7y-rpmu|a0B%IrHNMDtc2Nh=5q^QDH*$=)e%8%X?0`$AFp$lULH(!0 z9Or`EAUEe{OZI{9Q2!Eln8EotduB|F#Nq33FT?EIA-+M;lzS1*7>X0pk#23G!8uUV zLG;9UkO)MUPjm`iKi)K6qK=8^$>k}Ee_-q`xOvKC=ov5WtTs%fU;(vGZ}iz)f%npSWhr*7x%!iteX9|jFK z=8OZj7dOuSrVp|a4DLE8>=M-Z8NS-dUr!p8}fS(1*aDj(B{r~dY9`GDZ?;^Iy3X*fDj&i+_Y>&!yjV~FvL!%Q zpUJcy`>w-?eZC7j^10Vr-_Enb!(If;gnfRGI3nJyXW<#|aX!spkEpUoHxk+RytsO` zXS5D!7KSA<)LN$tPk49z0@?<20n%wHiU`*eDXH)qfw&`-O<3-xcq!Y0 o{Qi;`xY=EaT9g5Qt@hvGI6`bvQ^VciNRhbMK$Mi?iV~pz0sYy3j{pDw delta 10891 zcmai2V{_h((@h#Qc4OPNjW%f9xUp^iVqLLq+i7w|ZEV}N?f*T`7kFlN_RQHiGrN2C z-L_vM*Iy#nF&{y3@v$bd9Weo<%QpTnNFHyOx8F!G%1gZ3Z6{Yi&4z!dl8210D=TWh z6Z#SFkzQ${#K6+@Vm(b>Jz-wFBYu7ezdaj1^==jsUJWJ8_x4)WIXNvb@I<9t{m|hO zB<$XV&#y*v!4RMR81EH%64L9Yc{gdALfIAnxL|qIqD68;Q1m?48c_m@gpLi95>d3D zX;wJ6v_*7KOD%7h%rhJ>E=I=J0ZIcEnwVzZ2G!70vOx^Y zC&?+M*kBY6t!7b&zpNZ)Q^Y?i4>D+s6Q}wLWG7TOmVYI?{hS7@T>1#udqy_wjSz1V zDNl93>X!WN&NN{)`O2kbnG`+KXu(09#e%yXR*&uL>%J)w_obrj#0U4XI)A z@sYy8`LRMECpcq(FE`|Kj%Z3@MH%nn_PD=g6<5*fjOVx8D!=!VCD!V`UJR`qtD@h# zN0!i6ut8iRB+)g{Crj2$Qn)HJP0?G5v;eR4Tt1dhDaILsgef5%O2B{tB@bN~UPn;u zo(MtvhPOBRs(;qFTO7enA^xp$=d)BI#-ZpRJKtQy3>@pQqi2UjK-rNQ(gJ~B0g~I# zxSBT;>)QQb^mrfPSN*}bWKN!bY)b{g9FO@@3H|YSV+kI7GXf#9=;JT_n~#mzQuK~R zutI#7@@tjg&%4B%6Gou1yC}^LeJeDc+Lo?}_pzIn(IcDeck%T>_ozt$9;7FcpR)hW z_lIpsQes#YPMAwym1A22DvtQ(U+4FcQFpY`Vj5HmartSfQZywM800bR9!=4q= za>&2ZPSN2w=EGc7;a|)bQJ`OE!{o>;PE!ZAG7{*|D=59pZn&Qajt-*VsEoT|YLUJE zCd!rDgd#Bo*j@(0-CpwI{)1_Q(40Qfgb;d}p_WJ{)23n`kVP<#OZ+Ul$h~ zUDHoW%8Z0#!Dk0DJp5tTdY~rCE+dO-BuFEX)K$h_nF1r{?2k?<%A7Lu{Fs)k8-F{- zPG&*_XEb8bwyF!d$!?TCLZtgLXyYziJ#hrZJ8q67%3Wvpl>aANqnps z5tX*0k6XvnOBdh8MK+`*<1gzighBI20+mVzO~|qGL3N`K<57LzlB#t(iZdv|6Mph2 z#WQ1}2*-S}?T@`Se)+0)JIG3N@%=|o!CITY9X#;woCxc~YRi@eM4N2t=IhcbuV>R- z9)!vvn)PcrY>B>6tZg0+nzGA-ksA=y@VVnfb?~GqpxJwfA1AJtJjQBO>uzMpmiBLI zQd34MpL=XV6pC>iz16Kp9{r^Kyj@SJLJl_+A76+o?fo(*X=GkSxi_|6yaZ^u$7%$B zmj}dydmK~YqeeN8n@LyTey1Ubq>J#yAI+*JWrfRsX9wx5`!4-<#J^TRe!CBjax(qi zER}nk1&v?c+})G=7nR8}z3B=|SCylNpB^RxPG44QC98T(xYenhr1(adfkFe6tL|cs ztO;G2&W%_<4>9d9$|$`~mBi>^H>9i$?gT(vkdeA4o}F9VCkv$#5HwrR2I;S{dY>c_ zTbf@U29!`IYKzLdBy=@b?(xL@wG1bkS$sldJqF>LEc1bprR78Uwl*}{H}%^yL1WZQb81=@&RzZ zf0~=ex?B40#PRv3K<=)|u)pb^$}looEzIFKDedd4VP$YrIBLzZ&9~}8>gym8ezQ@(`zENG zz61er(}uI1i_hR7*}i>s8cFRzEVJaq8iYIJC6$=iv8y!cWp+*=^CgSZS?|6EwfUcO zCUf)}D-_-Da_lug@DN7n>xj*)?`x9eq3DUS^hWR)K}AsJSc^2QneBN?zy?r~lZPxb zMLrbR$N)(|WKCi6)gw@kYAur-#jYqzRu1-Ug>=XNLo^%Yraa^nV_B0dCOyovzJG;R z&|hjFiP=3&q`#lDfzmB|@ytn?CXBI1jj;kTVvebXK%(njq55$~^Q^0q=kTyz`<|py z^H}I+sK@JUv%{|TisAUf7zNnTXOtOf*VC#R33~?r{lQjB5LKJ&+{>b1B#bQ!DLi_J zb<&*2%O*LBczVH)5%?21Zze{&`?1M-$;-x=HMN#(MzlssqOIW^Jw9Q(qR@9A(MWQE z9ctXShh1a#v{F0Q8Iv;FA@Z5S_mHDZB>SAu5mbAqar+AeQ%cF=g&t6U5z?RuBo*R8 ztmJU;$zkP&VQ^-m@hf1PpQ$s=(aPX!`a^k}JsK9Y(wlUyZY5Byu5tKPWRz#o_~z{P z<6wTA^#=AH%ytlImlorD+)iMInz_zO1L394)pfsWVy^%FIMlMZ_B^!uB{k;9c-zqP z-US410X6L^%kX3u~7*nE`(S|X~+{IjF5fouE^un52O>RhZM z#i;~LTSRRut1eI4Y(R)pKgAvg;5ynS7(+r^(L1rv8O%SnNh+%`SgSeM`#0Jo&3U98 z>}^PX8nt#&lFHFO92@f-wPAP~l{5VWen4x}(omC$iF@AOT$>A$+Wx7H1F7Fi7r(!{ z`A*WvV$+`*p9P5-@~;!}8^mJzy>C$|Byk1~12UE3MpV zP!`g3I4gd_cMF^F&8+m5+1s<>Or@k@w=^>oz9nl9-_L7)&XC~wJfh-I8*1fyv`{*` z6Rw7OUs`1#?$=71!%RVosDAHgd=7@NSAQ!t;-#fmThUlM8ex zDx?&gSr|%UVBW8y64SL_Yghi{RU)E0Jz+;V6LTY9=jHpGrW0o+Y$hX2^Vt(S@jBO! zKrYxfr|r#TiBg-MIK6eL;RuO~<35Xlbs(H`)Q7r!C58|gBD$g#CxM5;hJfCn2c;6P zY7MEki-iuAkOV%4in<7@zx$<6---zDxzl(fmv=b+w2I|XJmIn;1j?LnsH)ixHZ;2c z1{QcwNmW~K8}laE`H^|cY!~x{V-xhpVki~A#dJv1Znro)TEO~m^i4}EhaJ?@8E}i= zwk&BzC>0bK!r%`3_p4s+G!CoNp277{1&ml5l1^RN6uj{8BBuNw?W(UA<*Y>u(>nW~ zYh89Hp>o;bwDD&nT!(IQVn1>j=haENSpQZd58#kv%xo#GFV)$$WR@G8N{+V_*n;ga z)>4y#7{{=~ubc5N8k&YmU`*`t3W1_rFO%`oWwKvPtYJNq)Z6 z=uwB9n{|B-556OYaZM!H>};dd#h- ziN$g7fF2@bKAfFgBLW{``;pLu7;bnW6yq!*bm?nHit*yAUiLWGd=6L~ISWX(7BYi3 ztRuwz_*3_tLcv9t9lP;!rgS_*jWU!2%H|LmOiv(7vgywKpL4l zZSO1u9~#X%>zBu3u56teZ6{4hUy!ug5ezbs8)7Uavc4$n(zpz>2Eu zYSl9!+_5&3wRzrY2s(dJTEF&mL<9(a@jM2!z&46W=8S&VPIg2?0$dkg>iPraRpJAr zsL2*v6Wnh8Qq=i7VKGzc5cxuh$Zh?Jdpior2eCMDLFnG?+6L!XpEwX(>T-}!83}D- zl=?aOO8g&d$t~;&AGstz639Fen0kk_=WbG`7{BzbGWd7&ybaN% zIS|WX;j}jHYtt%537m{HLYHNA$cHAILpKzBEcwNzXHELhX&&$-51~u&wQM>F**OY@ zC`_IyyYC#_UQL^OgJ+s0=qH|vlQ3^7IfnOH50(Qdb)~ixRdFd)IlFu*e+Lt)$I4Ex zv|E?-O-@RppbXgK+`VCkP$5zMCBgqH^axJ4b~24-iR&Tz0*KTn@-8Q!qDaF*--D1H z)7C`SBUluj+(pB~9>9u-{M$IntgO!D35^hMEpkQYL;??_PZ^Dvx7a_2UvB29Z$HKq zJX05MxLe{nqUx7#O{vYY#Jh&=%YJuo_CYR%1pBaZ!;MTax|hspUW!9#gvMSlcF4ksDn+b!qXRD-b>=5yrr4YZeK zo9o!ijc)I!=X)H3_3rmady)+wpFdh-wSK^>f&IoN)5Yi(HE7VpV*UF;<=2yQvp3t| zXdV-b8;=t^-czpJ+pdf6$#PZI{Rkr=(lI-N+=p%yK#(@ieyE(C_9!yX8~F?)%?9ZO z_aXeDpM+iEvepgI^*TCPYbx6Amv8wr-dj6t_j*HFT(z2N&uh=uTDm28Hk>|3W384a z^rI0Al0GHVInN0EYgFzG|J&NOdyE;MC>5tgp?|Pmlc~7WLfIAyxgy2avS3(SthhL4 zD^)XjfDr{Z7(J8K2=m77R8eIiZ7Zg4K>7+|phk#~KXRIjdP;pxEAmU?5^3}y)dhJq zCUyG&v^%d7->9Jw@&YZXBaU@8>wmI86y<-l1LUmgq#@n}$S?-MF{P%xkSnL6mn2YR>m< zt9QrRTD#3z;~gHiZtJ1s`9;7wtl%O6Nq5oUb_-vq1}onX({1_0q!bYmO-L{rrmT-p znB{w(tUN-o54k!+i`q^P_QRmI>BZMsGc@A>LADf66Cubh-zTyf5-g1O64lg>I{`?C z(YbjLA{xy!?*F)J`lYd~1hRm`}+Tdd+F%8G-oi)rDi!jBb=2t>`R=?stC6Fp0Iw_VfAqC z%O|h#wdtCA=u+fv<3Qpxv|TEHodH@IYYWV`eyOVm>@T7-#Q8!0lJ@VP;L1LIH+X}F zU2f>@*CWEcxQiP}X-4K*r>wYcJB~rgauN*73Si1cD0|Us;~z%0Zu2+$oxIEEB3M_e z3OQfLz@zANtIdpt`)l6=g$v2%LQS+;P`S4BcNx@t4M`!PpG?`OzI>K8N2E;zXd3=dZnyY@N9FCk4?&Jcu_fCkDxhK2OYT zUvb2SZ`nmgB8c}X^#5vP`Wp6p0i1PbFYl8t0#{2f=aU@DZcP2r#ij`dGIZef%qZPO zS&7~HX~GNZwfk?`ar0b2!=J+XdbBI4=;(u_`?Hr3=rerH9(;mZh>H4aO#gN{zSD8| zS*{{cPOcP4QB~u^9_K_`W*6RFRwo6bwvrfKRi3tkNq76O>1{J%o2fMW(;>dhQqE!y z4AT^gSeP#n0ruH75TJNqqM!4XgDbc#^zIMr7CUR(>^D&k_USet?ZBY~wyw`JEFaMQ z>W}|x=NO?5U&~VGr!!yet0@yyj3rXGXCFtbhh4*pmVeU>eym0AQ~-#Xc#kJ-Vz@c8 z-)#ww_zg=F{d7_gs)UXaV&*7x{A-1n`X7(-z zx5M&-(VzMN1?Ev86H#ekh%2}xYRrZ7@SbC^*Isb*L)u_w)a(`$znN1$pgNtQ()wq< zi23h-;T*ZagUQ$Mw+#u1_nvxsK@T0-ct@op9Qtb)3pq|7*8ip`#b%e9UK$Qav8rUu63lemsNQrhGLpw}A6( z!fTM-bboB-`ZJ>>*+PHxzj^nl2REQC%53T~pp>YDWxSWe;~2`#o|$R4y)& ze1(9Pr}iuM@gJAU9R+O?eT1D64ZlzWN1d%2(4q@d$>_Td>-44JdCTIOZFT7uNLF|( zDQEFVxwl0nQ1Jt_jfo1}1?W#G$oghizeqBlH^z{*4(wDNHIpx>TDd#imgS;ZW*Z+y zUsd(gqdFn_`c$XN4x4_;Os_(n?CnIpd_DtY@X<7$Oa-7=@9_J<|6Y5(foF*mSAIU6 z2l<*rj%03?0-P=HwjX-CRl*lK!V$3V=er)SsI;O6HQSI3(XI|!&21X?t!(%LuhB+~ zb9S8kOBts#AlXJ08`B2c`Gb2ik%AmEiwRX8ebc3Ot3`U)yoQRdaUb6vomTq?h+2S? zCNMJEUdYo=O^&SoMq+hqV1*w!Y{T+1>C{nuWg=P4mauc_4$hJo49l``9)N;0wW=9h zkdk8PE{KEFd1b^Qx~JJ+UN>E%lvZnY33}u z`=?(?nV!mhGBVW$M--IH3J$|qMgoX4^k)Y-*K74QLI+xxwIz1l`Mh_6KQb;+%JLi( zV_`bIwq&cgq>?>?Ne|cpN1IVB+QtlAW`6x{UJi!E%j)`G?#d{dpTX zww#_YEjqj_?q8e>e&~pXixrA?AJ-res@k=`(D7x;hDTfXqw+A(1GlS2CIMS&D)(iq zqmy6>tHMf4AItYu_FK<1r6sg6hBhJD;jN!dqj^_d@P-KghB~e^+XIkKbkhUScXTTQ z4jy#Dzc>UJqQqFd?am?SF52$v4@|1~gsxobB}4Rq9B*NVBp}`4V%$H*c*~oZ@!KT2 zJFJV0LuQRQ3TFc{nNRz75@5A{6QufsVn>}0r<5Xen&Qg2m}0Y!HM_+>{`mB0FKQv) z*>obBsP7H=y&8WC8ROqDtt8xG3@WW=2@zy7e-N*Xem(^{%Z|K0vPCn9NjL@tmV8Ex z3SDPAt-f%}YYR<(I;P==tvHe>Y9N&nc_Rr7beJ-0TpzZX=q_4>Bhak%)5c`V*x!K= zIoOesr9Cm=Ck2}&>m8#)5)*Dhv=wFMw`oNS%IQ3V)B!Pe@^jaU=Oq~GnZP1QbMbBb z9X)n*baKr8O8GG}hw)Bp|>&TnEi4gb&)c9iL@zAXL`#i73-gkFyxfpdw8RIH;DXF@xw zyYW(iH*Mz(pGz3(>&v7@41|?l|BYS}!>^sCDU{fi#IkUYwjAZv`;*M3>!lBBjs4*J zoF+A-R7$FgYy!p^neiOaHG!+Sr{vf1+_w~R&U=j_7&I;iT|OZ1EzGFUMc9uho3cpf z_bA8%1S{scP$upO9$6zKqU&X1z_jEq3F8$9laoubJeCXWlQylAo91OF;cZDash5SK ze~W~gs12W8izmOq_eo@UE;BeTl$k#MN2*#H_cR%lXfDQ#-?76zo-8<4giIj8G~81gQJbhmn-vT13auX(i`*zIy9XphHM%{^vfn`FzzH$_IDR*NI_}V zkt4=)g>oy{zm)Q`!YJ=>vzBnSV7c?T*efI@L@Zm5EDm5D?lA2|{a&=GAVY``#+?m% zN-otSmsI|de01esMZOM+@<0l}Jlypl8jjKxlZ_>`*) zdE(#+LOXL#YlH&X%U3eZK~p#oimimr2~3f+mx~i;J6raBqvN$WHI@?N3@g8Ax+W{Q zKyNABcMAxcZJQ0(Mf(AQ&^{_+g`HXFmqBj`6qK!@?UzgX5hul$(}p-zu3#vxldUOE zkn4>$E(=1lHl3*-%E#W3E>g*k`|g^!Qh4##NU~!5NWP;4?F$__|F;ut&K^}sYP|sY zvD~;}O*iqGAKRM!MG)Kyj@)?!tT_vWg_!uBl4OAV*$f1Wu@WP<8pWPvW?X6zO$EFu zIjq9yEW2Eg5oysfoK!|i{|Vn#?SU5Q0W z(Y&>{+(Aik^z?PuL2-T4Pm6JMweWbJQCOgpm?h@Row6T+5 zK^9>)_kEv+9QOfRx05B<{A({5XaDJi`hNM<<=s$Fdt<7wTh=N!$4q!S?I7aLg3scKq&EWHF~m3!Gm`_$MvF$_5Gp&q!=EE`yJ8 zJ4ZX{j!X*)m|jU@H*$S+9Vtjqn7B!JtMjGoBd~R3Kob`AB>~tv5+JKQn0y3_e4uyQ zB}$+4`=@Br-HClPb|&gx)s&H&=ns;2z3Cn9X(M-;(P@&&2jPy&Ki8=6*sHLhPvSb> zRYYu-)87FaIYXkQ`}L9^S5q^EUHlrlm<)!gLo*6~nq|QXWq;Q5ogQA7L9?mfI36JL z6AZj-^2zreMf)p-%Sa8&#X=PIzX0^tsi-2v^u8yRVpJq8m3icIC_j(Mx*61hm--?% zi5P&7my7k&Anmx-Tm@;=0IYTC$amr*Qs2`M1gCUuHAgIU!S_3mUjn(>BnD+QR_NnS zKLEqBPG42n&pEyG-y$^E+4VE%n*T0-EerTLUR`_iBLYJ`Gm7?9pEbe701lIM7{4}F zaccna1Hxl3W{Up%eEp2P{XX-t?SCF@lk-S`_QAdT@7u43=A~S2#I#LAZcYr{3~k@U zA49R{WqCGV^0_AGQ~WxQzPN9FYw4Rav+w9f0ul`@%Ag zdq#Zf1^?hpuO0w#q{ zf$Z}%y{n+Sh~tY^DJY%j_nn+-awaG&!~{#P;fm0Y@*WG@a9f_R-)f2V=now`<0|EW&zWXrMZaBSul&HNz?(0}U}IBXVPw*VFDGgw zL;W-o_-I#WASk(A5#sJ6Z*ADFT%_?Xt)=+g9(6=Kmh6$rFbtvD;9?fN5yd~-RIt{c zESsIkj*l2g0^lo-9Ghz0))7*u?%N4N<@dk$7wFc|-+i6WU>MkO;WpSvnlh{S2U*Bg z`TeAAyGFGKgknm)w}x_wJ&Fg;{la_;gG*}`&4nU4mH=bVaJFsWPkSC3ND;pWRxNApgb>&*umqF8I{`{V$5QdXzi0qB*Z$qRq z!}rNW=!zKA9y<7Q^heC*+x5-;uo8{^qf-0UQEOP?GY#(zH^%99A8Cp8%UAg%4XLCaYQlO&oOJn-eo4um1%1&eY-JC19lS-mD;W(9! z>&HvZ{KN8KuO`dJ40)ZU%s7cvy{jGwsCG$)KMuAV4c6yWkVQOetttgwA9lp~z5dgh zUAB8&4C*wu7wM`xk4>;6Hu}2ix5M0h8Ua2Ac4`PF2cjmG1dclI4~*xI21g?E(Bw1~ z-p@02cN~)sx8E)0+oysikW$ zUSa?W8|n5>9G_xD&j^b76pb%6PE+XS&OXMmRkR}3#4-1t=fdH+>`Gut%Q(;dbi3K{ z$Xx?VxZdQ87hEDl6s!QWFEpzwWcAGz_k(}EpsOsKsgK;AyFX8eC+2QG3mb!4yMu0O z0T)VLZQDx8F4y+`c5Ez#zu^D|V0*OY>5NL`5&ObCu*ik1Qk{Oyt)r1GoSd6__1>R` zTWM9e{0?Kqu=0w$QmIY7n(>&yW!`C4%_qQnYINSt27m$vC|}RzG>}c5IpOz z3a@wU*xwr3b>?;ER*MdM(QQG@H`O<=0{_q-Y){XX=Mx^q)MwxI8b{yt&VFtp&##-F zKBauBCynsUve=&vgKI7)tob&<@9&$FGpfxoaF2CLd=iT&dg|%9GnuhkfmSb;Bl8C2 zZHnc0N%QJjskYt{Q{@A1U*R4Ay5P zEu9y+LDtWGvGT04B1ZlRCPY3W>%OH+7{`>!_X>XmsB8wOQ!yQ(n8Z!EOt{UsdAPVu z`Tj!=E~EblhY33?uQ3OkA-kcmu;BlvNDXv^k_GsLg%O-xoJqaV zFV|(1)p|U|mBmcZ#IU&f(P`A6(b3UmBq1Fk=FniU90$+|e~SHdt{_Yp;cVg@Pad^v zw_KL8b}e2wDQK?;VQ0SsB6fbKT9ba0hK*sDJ_ES3D<`;~_UsO9FI#47;r+kDR~-=T z1_4weP>9Yw}|1jgR)Ya!kaEEj`89=NevY*l|T-@c)?VJpox zQRIHx-CO3cRGLjc3nH?Zh!==F&M~3!J$@g`u4_ySckymQlmREW4v;|ARi-VGoSX1a zgCo+>jWaJeg@%QGI4-*=6}BRA)NzEA zW{>Kts0FCxr~_oUQDnSoW95x*!bzUlgrSDGiksocMs{k;&v5wfIkIezx3(f#!byZ7 z6s-8h4n=8)sAoQmx7&Nly!g8gNHP76PmnP}8w&r4*!B_AJ0E5HYm6PjF3qs7oPi=Egm%X!w# z3X>y;-*z(-=D?I>SFuTy$7D%ZHOa)vpxc8BP@GfE0h?B+wX) z_in)MNN2XquFI^l`4C+7+Yj553aI%vpB8N`d4aw9On7h@x46SU_RSO9*8C=Ix-vfY zRLW2LcPzF8XL<)D&kprkRLC#NoA&eJMOXRSN$j=A)t`&?7;7=bC@rG(`JtuhB?+^ODAj5EGJsRlfF%IO2c;czCt)F3A1{`+8p2bp? z9d_sHMhg6#e1m918m$lfASEuC{wzp1VC94O@A@xRH}F+rdfu)Fj5)oCcQV(w3Q+oz zdOuuVFWeYX52rN`11q74j*3K#TOR-kA@%UlViBo&wi= zegW&pr$0Zz#AOW6o=z;fKuq)<&XB?qfopax&DU+xx#k+k`TWiNeUP zLesAaA)^j3og3LwX)*26$L}LORArU3OdSe^mlLuX0(z@6R{%_m2L z@aN0e;nZfYS%zzxOresLaLwQsFJDFOt>1G7ODw~GaRVieFLyOL^UEgB@m{{}@z0f3 z=6sMnTl)mZ9ydS3cK3JPF+IVN%sxu2Dc4yG_&t*sPSZGJw(fdb!%Os9aAD(0Qw25v&Vt*4#(5zth=;$#ONg#GrQQ=C zywI+#<=&%)xKR>p7`+Y{F@3aA1H6PGyN*aPy%A;LROq?&jEixzU6-r~xwLR+He^?x z;@4s|$H3inbGp4~>m!E6I{wA0O+=n2Vqxf-f zKS$Yl<7q#pp53jS{m1&jm+PXj*5?8qkyg*3M<(3g&fhM2p*-L!uW5+~RXt!&uLKuB erL%06dY+8{