From 92e245e9a6ff2202612cd96a8c44130f4ecb664b Mon Sep 17 00:00:00 2001 From: Marco Ammon Date: Thu, 15 Oct 2020 18:44:48 +0200 Subject: [PATCH] =?UTF-8?q?Abstrakte=20Verwendung=20der=20Dualit=C3=A4t?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit --- zusammenfassung.pdf | Bin 438839 -> 441061 bytes zusammenfassung.tex | 24 ++++++++++++++++++++---- 2 files changed, 20 insertions(+), 4 deletions(-) diff --git a/zusammenfassung.pdf b/zusammenfassung.pdf index 54d0c06613be4eb9576feda4755b10a3c6ce82a4..dbb5a37de039631b62479cd9e1b170299c753bcf 100644 GIT binary patch delta 20837 zcmZs?Q*ZIctZ_f+dvnh^R>f|uy>`eY=MfxLH)!qO=9ec4{xm6m4={A__4#0W9)=91 zU)oHeI5t;WMqGy+LQ>m&ewe*8j>B~PGUQnDNd8p8eX2ibXpA6sTIsJ(8ViY z^9ZKw?y1(O;~_q7EbzFhIyKFO5U5YCK7s_J;bN#TS(o$nR@`KUiTBfYSY8|d!xH;1 z1s#)Na@4kiT3#n-WLD|s=Avx-qTV#QZMex+)h~@2fk+8P3}^Kldb*|MSFQwNY-5y4 ziY4|xg7%f!>`(eZtxkY+T_|-YP#$L7U4CuFU5GHx+&}d*4Q;5IUX~`31zDIGAHq`* z>>zlwoY})J2#$my8HS7{Y5W!~+lNQ5^Sn5ZNxsF6n1Os7SbXhF4q)kTBLf6d?$L+c zGKC93o3RWnYNVua|D~NEC2=t`+9*yWaC(fiIhBK!!B85UDz^R_1W&jECfJp9+liXq zUZ)K}%YRH|#Ze&r!c?2j{j?Hs6$S?x1{6XhM9!%qT@N*{^7aOFf+^+=x8%HMA|ul+ z{$=X2)%8{rjH%rSWheol7CiU$Y=<%ozaOt9gbYIMF)JpQnnU5A^uImbRWX*ABO+>I zrc*j;eFtnT3*LNQ{^KkMX3Tt47rWA+7SB%Esl9ah%c93B1f&j@vdz`gIhJroUE5rN zj;(w@BzctwqK4L4`R~2_SxfaYUgrxqE{~7TSpnBhurso}!1Qz^r1v#+LC;`vRv;`7 z>e=IlQ15p+z;IT-=|Pq`E_!nqZ zYX~yMuGfaoqC2Q{R>?ApfyYvZw-&8F{tf5}4;m@7R(i-In{!Gk4Vf>fyy=k?91CVd zmQMzZMc{u{Tkr6JR*t;04-i+p>b}k>d^pTp#;!s;V4w-uGg6C%T*XMA zym3$GE^&dedE;K^N01gLsoQ~=d{K3|KxCP2TLgnZnRjrq3S@HqjulJ0_zSvf9KN}>ky ze|yOPvw1uW?0N)M92@$nX8%k7LrsW0KghQy;!7w>bmOb6rm(89b)F0AQr*+)a4Uhm zr7+eX7A}t>4fiFHjrz@%ys35lorCb@@+>Q#sDUFJfsrdqCC1mjfvDk3NTl_ARSWT4 zRPEHQlzuKR?A~-PPmNtmBNpB0?bn5t)tc$=b)6HS8@;=GOO#&p;jL{@<^Wr}nM%t< zlAtA&Zf|3Xftwy-R$EX|H^9Wbdo#OTd@7^QHTs&a;tOc6pwpg9U4eh{*`QA2nD;U0O%m!V&K^zz_yeFpmq+7?$3& z9i|3iS8fl!EN-&cCtRyt(;r0RJ`zMyc!UF*3%Z4vHZBrz4Zri~1SwR#Uky$45}lu3gn@$}J_o~yRdPy)L`$EB@a+%Yh-G_yf93lTPZo1+6}Vb;ku9?w zdeAbgvhj?j9BfP2FJr#5DR2njaxKh0q!<`X98Oa|al9C#jFy6EU5p<>7L+7hxISa# zfQ~3#k+rK=pNyrjCW|PnV^HXj!C;X()P>n`x(qb}B>OP5v}F+`_Y}b|ki5OL3pCPE z24;kQdyMCPb!JUiL6J}<_>_!IS~Jp{@+-7(q^M4QDdq*_;n3h!0NB@<4Pi}ohB zdU%#g%MK(x<&wio&vm!~`sy^tz$Qn~1Vg{STaih7aQspz37e6kK!tUWSe{@?>$J^o zhM~6igRzEb;QjP^(?J{fgT7-SKF?(G^*(sR>i;7^Sij=*^D#ade0o zwsh@vHtSe~Kb+0b{7R-ko{(l}Vi{vUD0TD^l?3Q15#eqSV(;HU*Q9&!eulLw57fju zAj&Dy+VqY05=M4$=)VYuN*)g9H%uh~bK-e3*a}hz=5QdiJe1_}HZb`QwB_8RP@u;U zAQlNH9PpKDO zNQ5Xd=05mI!b(Y~MB&oY!s`D9_nYJKy9Lm3=frDw1BLOUZw{&Ne5m=m?7~XCHV=@>tIBx#I3dtQvdLPdEk&wWrBb|F9jCdvvBN z1&6!{g?Bu8bJwqkg%?B2N8s~|-%QoBY5h^f^S7y%O0AH9;&LRrnfu;?_78xo!VuTp zTsQKkgLuvuSsQo4iK|E98p$f3d-?nfyd_GCf=Bsmf-tQZY6BFKy>h1r;=ptF`^x4} zX~S|-E8}Ia6y!?ViriyPK9+J^LOA*=W~ngzoZ0gFRuB;t#FUq-_GxOQ{Y=Rx{vPwVYNUgu-jiB714QI75aEJ%KX_L@QyDV@l<_1dObZ%r1g)h z$f@hU(75)@&ApuCGFt(@HGRC9dbMnZ^~(GgEjxz)%3*pr-4Q<84DoUVwvA$)@^0!; zICLHVzKl2n;}yj=uU{e{T{;9=No>-y)?a>$Y~KHXh(@UjQ3#_d;KEidOj&t; zEPMj9$<}+>r4|dp)sK%7RtQocnzS9GAcU@s?+_8!$Zc_gSb=<*Dlx^Bl8+_<5}4!K zcX*2+8E+q%zx+5(J`hi=*deyn_d)5KUp8>)dJ1^BZF<-zBN*F$Ii6XA7Bi308fG4x zCKESzNZLo5PUbS26o1=5g3 zI!yYjL$y!-vDI=bA&cCqh`Jc7sVCkJpNxi#FuwH@r4S5Q@jm{SadQ+y@X`;&t`;uxo_E5QJ!2Yf)kzu($I?rUIg`6J(H_(-&lH>KEIZTzCM*V8}Oaxh#E z9*SRcUs0MVhLY7^F5k$th!(T+7bw7Wdc$AwEswqlu zn{X zEl=!UxT)uFLCv@g4sK}en;hfm4Gemn5e-Ey-@S6D^~57R_y_D={eYhEUE!uSIH7}b zG%KmfApy8Kntz#4Ap&?!74E^ogpE$s4CT1tUp>)iiPiYH>>qT`|S9!XuG8rcDZY?#$|n7 z3O8-P27f9j3@}(fV!W_#ovjE&drpkB8ooh?#E#jly^>7ftkFgidzg>rI?gh;Egn4= zXKEwYgmY8gOA`U2THQeabZ#Pnr%!r>W5ZdZWFv|<;aONg+btNQMu4qQ*gO|eS%0kX zj3!zW-?$aBy9E~486L`WAbL)j3P8jbA#rCL@gq*w0c?6Oao6q=|Lu%jH=J}P{mZzu zuS=Vx{E8j<3MvW1l%t-fg)c;hf}v<7<|le{2G zatBs?6fipaNgW&AHM&R;Qxa^bDM~KH#gbaKDY!(ACLH6CgC-Z+gbqUws~j!_1T!cW z1&YfO4W~N#(omi;6vnE4+|*a|vCqOTfnbX_ph@PH4syLgRbrS`b7v?wYTp<$Jv9cVCOHe z%lG?}oK>93c@&z{=INva#h$(aZ}dtMQ-AcTDhVsHj{);4$V->>tB=hM~A%j=Q(Ip~8_s|!-P7+X!XQ+wRyN&YBHrTOimS zG4)1+s410VtZA{lSuuTlw5z0i8jV#mi%R*1!hDJu;h=0k?8F@Y*nyNayxjO^_I(Jh zUCZ2M?V>ha*}D5S%^!tZ?v*IQ$#W_y={rjRZf7c4S!Je8Qlk(j>Y@T5_+=n zppw>1yC3CsPus75Yas^yiKx+EBg0MAUc)1)sZ;zRixm+m?%_g$#2jO#5&p4qm#Qi) z6u)Z8c141=CB#R)jNqA$Rv9sl;VZB<or-4vQ8H@$hd4gZMlRc39jzx?@MxmvfoR_2jT2e14;Xv24AmVvB!HnJ6rWo-E( zR=@HgIo|7uiF%!_gO_z9YG|RHfSK{eDz&e&V#;;>vGAs5kIzQ)$Usaft&e(JaJlTB z2=0jG1DB;QObAUauUYecG$PoO>IP13#elBtpM&P^HLGmM1bPH~9x`Y135S~HRWqqo zGHsPKmGoX8gvIFM67L%|1FCu))JVF*w~&+HymQRUB0O?XFN&A1RaR$(gfz*+nWSQC z(yd-6BsIm4h%E^wsX$VWQIZ;FpR&d`R;?rDH(>q>uS9F-buY(L#R(ct17AmcV8c!7 z&izBaqMZ9Q+*7Sp+L`Z>(9>A&kVwtfx|jW|Km@|o?@|(b+N1E1lR_Po#Q1F>Xhqel z%KumCvvTkdGZX(W&Ck#OKW`D_e^Q=}<$ubX(|X&fo2@9oS)(E;+mo<8JaNABIJN{f z$GnwVr<6Z3gx;97X7nmt^fYN9Q=TXk5w6h;=ut`yceTMSzK3iqS_<0%Kg z>y+H1-YLA7T$vS#g!p`{T{X)4|0*1f2Y1>_bKD9y56m;XyCxM*8Na3PtNJgxsUKj0 zuXcndv<9QfhFHfZ%8m_pMfzq%?ez^>IsWIA(=K85dQAV_Di5aNv7vuMsBK&%oRssg z_xA~cPkt-pf3PgD`&7mlv`*id%^~IjYm0E=V0BZ)YFVbEF<{d!B7a!^;Mi!QjL2_> z?7gB*KBBFxJ-+qVj$y@i_5+r#N)AdJ{2Er6*Tt;CHf3vyL~yft%a9qSFpAVj_q&`P zapY?pRIl^8N5|T?ARUz8YhZ{HJ`C(}LgxM~o;SC9(;qv;5{bgGt@u`nZyxvoWp(UH zCEyh{C4USjmdJ@rLv;pzb+45IxD z=5KA!m+b8zm@X6g=*neamvN6enk1hajp+ciX&QlU{V#V_A(MEBKRat%0C-7{i>i|H zi7auCb2?PpVvzxn>RHCCg!w!XV0ZjY!ahCkcC?93Rm38~RdC*vw4Y!570(p1iHE(Z zO#gk&39t3w04u?cv%LqA9#susNU#5B>!K0ruD|q57|=>geCS{HoMi& zmjaR{jt=e+t}W$M*oX`RLid>tYF7j}#6zd7A$$+B&eTBGH!fz}3Va`kW0%CDo9Ryv zZQU`SHd}hys?tW{i+RtW8@9Pmg&X)F2<-M+yzxTX^gj(_lQ~?4*#Q%tpu*7XxV;+j z2`wUU0gDKu8RSejUd>Skj`%8L*QfKmVBeI<@?H6-VlnH$-}n2fqJ$r$-t~bIU$in1 z;6=fYLhQ>*GF-cJJ9h;#Bt|k+&4d#la#S2kyEVA>V5?hs7})oTrWKCU?TYgrs$#w8 znCu21lpm%eY@!wVOft)L3mSUcsrr|NlJ$A%9Ur$`AcFe$Yliqk`3 zghNyAxuSuDb_u9VKxf)4>ptt z*3^hf@bIs9@|a8DPDi~n9amjEEXuLwyVj|u>bQ*~h5HuRXlPl3fo+N&NoK)l?IXS8 zvRyvtTK1BP{!64}d`zfjsbF)JN_&_?iY}8svHJDduaR`KP2$@8pyX0EoN?(`r9Nry zdlb%osUz>-N_|p~8iE7(?(uE=W)6?$MaVgdt?9!KI@laQuZv)$fGB$aceAqFTD`gb zRA7BJ3&hmfyy8 zj0)l|2)O+SYc$TEQ)^CQb9}I4?-vR@p4S3KXSZcGdE8yOY(!@niFy3uCXByRC5$B8 z7R}81f}jz=Y8>o98X>{`%cfK1%mt=VFDj5<3U*O6a#J{AYMg6DXkcu{+Dq~91i>-} z9^5<=GqGzyoovhxKwD!=Nb`q^5PO-R7X^`4%8@1`ye1_9;{T3Qo#sbj)*{XVmBKQ$ zMx7z``CCRs+?@hI)vqwEi-Pg>X{+~)bO^R84$1^djTr_X*FP+f{gE;BZfMD9pPxyM z1ue=DDDor|(1Xq8=YQRQCJMUb8t$!WzP2>NnEt8@x0UxUx?SuYz~Q6p9VA+Di1Q9h zD;eLMH(47@q43Ca5Z(T-hP;cOdnt1}Q9i^waiV6jTrq(5R=S65K22N{=NJtUC{$W` zp~?uf5r=a20j)}+SLmgkFxBeIxu2lW7V+>ZjLNMfagkG9?!TUVRYxxj;MPcR>!H7- zbfY>+!BGytX|Zr``n?<{{6k5I&v32lkC&+?YHXcb(~Mi@&o6$MMB1b6meDi*FIkSd zxF&y?g0{fGPoc+`z#t6}?I-=p8KQ0sKadAh?ze>ctiQj8SWOE#3zD$$69)V3bGl8eE=a@W}9W!=0_akr*=c0wY?k z{%*tW&M4Ug)RHnqu5r_T2#ZOZokGK_2Uc=IOxz&oBl{Ddd$bu;}k>@?o3C zQJYJ@DxFlyt0Q+O(kW5b9v%L}UC1~R6D?CVe~YCgDdcl{KCED&s&KS0X|=Hj zqH-8y#uW%eQcm;U)=jZ}hiVL^5mR`H@Jw@JuXY{F!TGbRgdLGzjO93YUjYCZG>L0} z>)5eSCu>7qto(Gf-;V$$6IVDM74?20EE$QKNI_&&s9cC#g_X^W{vO-pGDw89%!l4E zh2%pg%#|)hN9-N^J>b+;Y~u=?uT#KNE_wu1!D&BgCz_SDEsQ<)Ryl|1Pzy~}5%jO( z$J)l1*>`Op@hS0apDHmnPF4fogS4b?3Qiz_@26H9Y}akJ z_xASH@3CyrlShrpYH29F zlQKxq+yA~uyQmK2FH9TIzlL6%;w3GLa($lw6Z?Dp$YY29{W`q<_7)~5*tF{N4-&=e zONZ6DawWmpRpSMNo-D_ zUC`P=mx(D|kp9>>&7=aK4QC(pE2LlLj@djExKotaKIEiX%z)&Kkzste*zpXT|Fang zt?BzYnYbQO^;Rp(SfVSWj|+A~VS)~lAaNVZP(!NU%~gUp^c43kAk@TF7>s)%$jYMi zt7C>GYL{owb>Rd^I8@gh%#$n#-oO;olnWy2W)GOP{S|@uG!5ehO9-OjKCHQakSF3w zcC6pEcr8aKu%!(ajig4@)yRP2`*z{+SPm(&e{k&uluQFwOKM1>gg%KSU0b`ewMj)8)>g_lCsm;%u)^7hRH*QEM;=HYy(_n6PSTK(>6(zu+?(uZ^AVXvR1@99VJ_py{}s+} zEP~v`tnO`F{)IgoWdk7)?op#RcN>tkNM;F04C<3s7N(LD0+N!1{YEM<0T)RjgMt(R z3w7HcfN4)*sG|Ufl^xW-#SV!;P62U~;Z8;p`ESKZ2C0Zi1#v5r30h<(20bysZt(`M z$eA+BvSaQy<6cIAVNMhW0aYX$nl#HA6@+odmD>pMsp-#33?~9dPReESkwb1TV@E~>0zM&bDFC;GK?tC7=JHNSoJcZ3JZ1EKToq{$(5E3uV5JPgL3_-Z&|=Qq z={ew8a$z*wzi36AjO)mqqoB)z#U8^+O+#G4V35!Fiz_L>Rq*HVvg}|ihQMP?7%Taq zb>4^QlW2aTlFn~Q6+*}fF~AR`lZ5$gw^756LqUpw{?Kb!F_rx~Fz84NBX(ufdY>hz zN55K0C&JQb&;jBcu))p9)KXy~Sz@QyKVzx~bKvt8Q7jV*`^MqV;~<(tD$%kjQKIe*XT?&{Jid6RiQN1tbPgU6~;R(fY9-5noCI#2hZ zZnq(5$-E67TsVl`8s{+U5KAZsxPeQ8FceN!j|@jlYe>f2a8o)s_aJRY5V+hY074%g zvusbls7ImNWw{xYFvv^(~b(rSl>kNIaRm3G>J3YzybY3#Qck3}1MB!M6B>nk+e zB@$BUXp{ig)HC1WWz$__Z;%8Ih)u&zUQyeR^B85~ zHihkX@z@bb6_*QBJSt*YJHZy#v~+1wGr-qzfg%<}lVe{X*ZHcBUA|KP{X%L8Ys z+;ehF9i@(I#y+yMo7##v=Wx3hOU+jw`b*^@Q%AaW{(%i@G5;<3hzn>Rq-J^tUhWs7 zJ_n=PDMtt3UD$K8`VEX@Y$+u3=g_y5cruO4^RP)|Z$4|p`z&^CKq=MUmY3_!{rnI| z(jASUqQwR@%K+uk*Hm~}TTi@f=^1(-pG8*aj+z1Pw%Hb6rCC{jbX9%-%ZdE9a|8B@ zF}BL!LXkfpA3T_Kged;Z%Y0h{V+be=Ruw(GjQ=5S3L&d^@qvw~@p?43$Ty)}bmJF9K@VV9Hr*U@C>wYu*9 zVUa)0vcwqmYa%WMF#IdW%izI+j}dAB@oQs~i?3(Uz&5Qcw2@CkElz$HSWe+qVbHLD z`Mr}bI(^VG-uH7js)|e`FXB%fZqC8>50TJ?_TXV*RDBr7GeC~ibQu0Bksq`Um(IvlWe|&S)btv z1e?-0_*-MWIvmBlSz^aFRx=LiDqKxG^*Vd)8u+}X_+A=@N3O1?+y1zsa_E= zk1Y3Y6G5x(AHt--F%vn`*ldWjZBU4?8jDSfMc&BVCZ;+1WlDVF9nADe2Q}J-zZ3@y zyuqRgnClwr@HG+pgvD(>Aw5N0iGvFjdfrAyf;q|yW6#7>tAQ?G!&)13mw@BB!IKS& zxvzQ6M#tdTR^m+tdLc4-oz~#=Sc*vvk$8 z<)L$|1bW3UUoY&92o7u4Pe%48cv@plhbwq(^rRYCH)X#vxxLOxWZ3SBpif#Z-_WyAWrVOcw_n(PK6C9(>$_|nO0l@jcePFbecthf$0Jxaj z`l2D{VF7GB|78eNNIV?O|MzccgCy!fI5esEBkAtOU76Zd3a{w0o zLR1EQRn@5+5`{uiMz0|Pz(c~vu@TZ%HPD($U}^e!nWxeGLS8e4g9=b~3C{$qsP^9O zm|z*3AuF6AqBwKl-Zn)gW=O;#YOV%lIWJiiVRrMgZVWn79F)84LQ)&UUy1vI9l}p3 zBYHU)M_{%a^{Lp#E5lFCAwE0N-v9+bz|Bk|=0WY42f5+WK(iLa^#=#wt0{zCmVB(v|Xzbe2sEWlLoXq6W6XGmkg#xUDhs*w+3ej zvp?hrgaD-K9z+9Bk{$yBV_nA%3pxj7E4xRly{J7{_9r;!4%UuZiZIAJ)*nOLEea)J zd8TM*vmv zy>bb(Gg}!ReXH>fy#Ja<5<)+=QTb*EvN26a4SQARHfwnF)}1z+0cjGyUWOBe2m@Z~ zbOWm_vACKi4~lg$d43`NtnARoe#8#Des}cd?@cY6`|=pATvlJ&a`uV>lg-8_`SWXq zw&{h?n=c?WJ9a^7>Mox;bLy;*4`BG0nkPev=_34roY{do8pAp*x>{Nd>4KmC62Ac) zZuqg#N7uHSf~qtgz?y}=uR*UMX`{nhp3guf&f47r1Mb$}Tf7o{epk7W+zX?;>8j!$ zS2;|eKR!h!)S3Jd^Dr#b%%|sc#+W1ctzuI^kD3u z*dU1SYq;V>ieLu};HG#2ijvNA$k19KcE&1ef5hi@@ca>5|7$8R#)oz)Lm}f1d^6;l z{N;%mG@i_A6-_bJvDCoy@_oic=Tciwhf(MV8u3gRRcH}*tzBLC%|J1@&x*}P%`i8@ z!4MYy0E5gGG6>Do&5 zyW7ayQbFr`@yD8sAmV0%jeFAkwQ2r6n@EQh7sp6OsFE6yPci&Xzs8Q^qwP8Q%?k@_I zbvWn=Lg{5YMQep=DPo0Gm`}3Q+Jre;@o+Ur1!*YO2Q$%SLnt>{^=Sf7K zNTmv900H4CO2&N_eRq9kBF%Y{0{8+M`N&Xh7`QdW=N7Pb;9&TmFpu2J66&RjhaEwK za2HsCX z5?C-Y1RDw|PiTBxQX~+-G3nhB-VjOySf3;b5Cj96+yOfTnm1OZ2#^@#DH;Jv0qIFd zHcpwv7+V?a6q^Dw1~x@JPDm?<3$K9AUAu+}$`gGD_nS2eI|v6vWdC9Zm4PGA-4tH7 zj*PZ2A1#DFll0j}pNfk@|GBm`-8wC4j>W{X-xDB*Kx+Z_EqFs{vlks3#VAfFtsK1u zj3OWR+H&Oa25iuw?jjQBqCnrpPXk z{En-nY=6XEA1u>YnzVpqV-l!L|0IL(!8xCla@DV#vN~4OH-t2inM9C_VwO1u-f0=b z&6Kr0y4Y8HW{~_o{<6R=FmAImA0_FyOqqsH&4bR(F=r*|$_H17ia>g2Mqi^ZD=LbH z{W|vaA5PYx&Vt#plvB!Z#TlFURmbn8P2TX9`7-z$vR3s4)TDyN+N2*p)Rht={s3B6 z861^{pOP>QxY?!R#hRjhNOHgm6e&>!1?T=ZK@L{dmeH+A3f^XJ=OXtfSb9&!v@#TH zZvl3haTe`9{tlarLq}$tG4;hZ)|NtKGx~^-dgTCt!=uuoYaHB zgBOA`ehGB5mINrjPnb8jb2eZ8kOiJiT*|xdWrB_!E+&^eHdte(GcodjO@_e2+-g7N=Od=CbjYR?@|qp@og_v5iSy%T zvROlJ zp?^QoU&wVq3I{1yCl3z+EECsUH!0S|Zt6kDpn(SqA#T@It{Wx6#pV)@Om@J=#OIAu zX*d52?g{2cj0DXElfrzl9Pe*)H|--eWtUCXZ{3_`t=QExA~BP%il+W%jB7#f+#}ZpPFA?IlowaYM z;}A7=%9HiB&``BJmsn9ZK{edS(cDPGX;zYpMuNutWPan}(u`{*Qd&gN5BqRJq-Bk{ zk)$-Jl4A+SsC1Puoss&OrKl<7yRwAkvmABni3YpTcB8-fB$OtnT@WHMkY$tXx-{EY z)<=u$S82N2%X!xTDU?*)FsW^UQ-Z&c@;}w(Lk|MgZHZQ1_e{pZiSlR5$^#wT7oa@t z#&bfQOO`C!A{2Dv25@LnXLtK4Qx_?z+r&Xp)d=fR9E2ZaRhq5r{`vC(iIpKk-1_yAcqubp3#mU$ zt@X)qLvCF;&M)WgU}wD#oL06He*3lR%#*uOaU(Zu0 zDZok~*w=#t3E(HlO$L_LRACPdZ8NjlMFr3*6?Ky}@6r@9%)8Rg)^Qm>+}UsmsCYlz zv4XQ`VEdA(()v% zW5a6aA7z$I{4K0K!S96S$5oWH$gZ?V!V#<}tPRPtJ=1jhsEbShWv+|Ukjr3QDKtIA z(lBqpKQ(Fgu4=4YDdiJ4+)=jMy$@e~Z?=p@s#Pe;UsfowZZK{DgMI6G{(U~OV^Qm8vrmMFag^(7ny4XQ64Xu;8_4qf~fL zX|S!FWke24)8kOOY;=+dJr$Xq@)y&-ODmzc{ED{}{Q%Wg4 z#rC*3lcv>I*gp@7_&0&NKptVnU~!QmzdbL>u(@g`<)X z!SZbXGH~+fvkEhz!NY7A&T|icB*y*`m7JY1m+Mf97A3rLne7$4rMGCqibKBc)^bvu z+|~k1<=pgy_J~Yp8%MsF4|igqS9BcBGRqce`j|zO|0&hxDg*jUaVYPrcM9B~K9pNz zhd1ju4HfCaG?zGBql4l+$5x!T zbROD-#ly1_G>G4vYuLSPrZOMw@Dn?l^9*voTSl!nM19RdJBHXc=k;w@V$XXJCaO9q z>kl`@9M2I{V!Y44AmE14#ii?!STc8fj(+3ae_I3WRSsX4_uZqiS`yf6P$ z|9wvrI(VA@PZo*CME?8sf4H*vZx|*PolpklHr!gN^p=38n^{2B+YOsW zd`m1QwUb{@aptFPW$|LL^EZ==Xh#-(H4cYbJnly+a~sLMd^;tNLRSd7D{xjr{3Y6{vvxx+ziFG<4S1RQ@XKpj9ADkpA2tR!VoeszauzU6A}zl8uY))d%|IfZ z|AyEU$U`V#>{?79dx*R`uelLAQpz@k@UgxWj#c#gQb# z=`@u_L1$b4frvwYse0J`zRWJjCP2Vx$U*VoQVR&|4fx{B6BnfXNFZ5T@{2KYD|V)N z05#pch3J{Q-4;Z4Rs$27cJsV_kLc!Ra z2QPeY<)_(MPs4O*HJUZNKBk!-!i{=7xb;AzpZk-ew*9y5n>N|au}F8nvtz{4O!UC& z-5BtXT#1su<9Z!%LVpDUzAsELi?2MzTcq>Rzx&J6Xx*mUI$(_U$=DUCyH08f14$u5 zZ7+1HD-DBdeg%<&o_?+7&xrQ(Y~IWjY|B?H<9g`y@c-@jW`_817LEg4#elvO`fpqSV$WLrp$}|cOJ8G^u=M#&%7Fh z`L1Zw_5L05p<4Tq@x{o$y>>8-oBCVLr6{IBSvzw!jXv_b6=K|Rh?O>NbNeLt2{NdM zIPj zgIsEYjxQ{!{HP?n7mb2pN)>;3o9s~!H8HP`bG2r_xu@xIOS%={#aOL*+nrDcr)>4S zjD0PvCvnkQSA+7LxU`56nWZ9u+Qos22aD1hBij>U-M-I9-!PJ56{+jCUbIWesrz>o z@XVWK)1FGSgjqj}JaYDHQ)~8;BK5v5a|PoAaqW;q5j%a$mX24(P(g74j^~>XE|nHu zZLHQzJKv87>!C+S`GFmRxk@kPWE%80Ds|An-TsfOv7prtkKo|-IuSx3D3zjI6!^p9 zoB(Sr<>MuIO*z%%@u%7))4ZDNhcTc_#wyh!6Jo+un1Wp&tjWToM;oXUoTwd8r)6jT z8`K$A$UEKlxhQ}6k_kP`dC@&ES_gvLM*$;b`EuN}B|mfZ3BIPUrt@f5iI_g?SQ;P1 zcb=SL!Xn% zwPG;tlGtQ(Cf$+TXhX^6S*^5$=X{#qm8p$yZ0{udV1DXuJ)_iTQ^%SkW8EROu`fIj zwwKvNjfT^tz7AU&U`@w3bBm0!QWh_BHVPB%{dLl5KxW4(W9LG>w)q zi~ApyBB z=r^&q=aG+7xiP{chM9*h;y_syd$z7N`2Q4gUEy#r%vxX3iRfLFjVP;^1X+s+(Gp3p zSfVV#>d_agM9FHOk`TRysH^uLEmrSDuNzjhX!-r;{LeWT=i=PGGtbO3bN61n@63A) zmb16bnN7Ye`czlaJ?~Jj$S~y3b@11aNe7E~rpCgS=(xQ-osZ0t$5f9EYhTPXfHe*6 zem&3j+#F}rIKAdn3@RE_Qi>~uSPr+7+@H?#6mzpHL{?OKhN$wU#8Pk%zE;O>*wYI% z38+iwD$}-7OZ_s(;aA%yR!-h+62I6~DLIwQeRCzPfc6YU{)xA@=n6*!+&d`u@4Bm|~2c#yj4x z&;NN?s#^8Yx%rUhY;l@M-DN{*PL-bjfM8kmfw(a-Osr)d5T5i$_Yg7WEe>#aiZf*T zb6pTYA~rBQ`RKtJYlT=NW@74!QSdbSHm7rI4t;{2d??Ch5lY-M%IQ-mc$U2>P6J>dk6lTaQt7gllhu4d}%DMYhRT%ZvDh@yY zTlObi8?~`qfGLlZli=+T&a*w@g?%n1)?VawV2|jichXReZfbYBe7r{| z)1?Y{D(Zi)!j397<)OP-0J-ipbMkn0# z5pK9d>R|dSKiu2tGjR>Icz}?1K=f+XUKx$TmrFSNS2gsykDg%4yoe$%Lcj5y{TH;K{ zx4P4pDX6y`Q)gudXca|PZ!Fe?FEx_Qb6#yY-)sipLc)?i2+c$EG7sZ-{QfB`cb*#e z4Tn8tQIl(jHYiGb?JR4mhQYLXvMsPr#%|A16KJ%-++By67RdcEG7$SE|GSPO> zwifN`f2uuHu!<-}4E6r)Q&pNjv6FiqgT3!9}$Ub>^bSu>HEBxPC z`l!%|3@5*>Hj|q_wq1)ovrEmZV@UAEe5kyVb4%^+qGcXk<|2X`sd!g4XRPHhTVQpVH*>GO?%UEjL ziaeYyiZeajmfm~}-Tw&(Szq4$Qtfwy=v!a*Izsf^w)#=s9oK5cD``z9{tYIPgG=tb zvj~w9`=jD=u~q+n-9IuCk}0r4vQQFfX=$01?Lso{|3;KWWd9J!NvF{B5wf$&$WVxD z*t@xV@JP!k{Er3*l9f)Re+)!^xm61mWvK!(%du|@R2BKuomA);v?p} zS*YTM^4t+orw7^tRid+)7sr;HbBrlnxoQY>b7e36XO(-Y1W5cUi~l* z4K>~)an{&R$PVvHHObL%5kSWHePzwW`@Ob_4MEi%K{Xt3PHqx3W(rAgUoth9@P1iJ ze~{Wb@lRAbRe^O-NK5BBYclK^oX5p2hD!RdF$={aueUxF`H-#bxO(%Yle>R0F7mE06wRw_gN_+aVnnTQf4onTrHDGe)2bjXIV#`)_&y?e3P^Y1+yV;2TMm$#-^Vt4q=>4#W-sWE|eP$ks+5-kH9xOx@V7 z>o7mBlPlNr5_op{wZv7xO7+Vh87c>E4Fb#@8*XKT8#Pd`AIJ^E6i0MfLkI(Il>v9M zT`8+=8d)H~MtfOd#yxqq*VOmhhRo~tg@-xCVzd8ww@=1u z?X=7sN3pS-YX;o$ZNG*nTMFE70^s5H`9tZ15iF_E1RksS-CgU$W+n68O; zM)@IFM%w6AvJ7p+G0%u z_vWEm2Al=P_|#QP%t2gGvdF`RZHd=P)JpXW36yB0ThGGAkx7~HCd;^G8Fm9K@H$3Y z44GQO8GL8s0kdesp+pMKjZ}0x2N!n&l`&};diw^$>4h;n`!a`53r@nPK|miZOqh)! z-08}APiyFF>rM;11uu2@gQKpUE*IH06(9UXTKUrQBCSPd&7=0nYWtYeIi9j_!eu@- z9`BGGmyR*_d+Q~ALCNU|mW{=Tra`u+dzZG%u5phXS>iw1Q}ai1N?CO#SP_&=2ap-pglSK75 z90FtDw2~j@O6{S|SVEB@&vptYPKlL=eZ5G&8Kqu*MJ@!hDOAd0KYtBe0Qlx~H|LGN zqpOvDC4Z!jyQ8Hq*3&2CjVh_2kzF|_%%HPLH}TD!*=?ngtTlhJr>mrXi@G9L=HI&d z)sxlyH8(JA&9QuTUmg2SDA)1|gReh8Z5#is6XK>+pSQi9*TvxJ#R5TalEj-vAXO)( z2Q5?=-Jg8LRs<1P(hy|4TJdMmiT$9l3ks754{W>9cbuM_e9TdR_zJ< zh*|oAF4V}5Y3-}xZ%E}cywuI%sg^&LJf-hI z+9P%|Z(emSq`$wPsb9$~(}+abQeZq|=CtL?ZLHX3j-%7ZE?d-ZHLoSUy^+2a_2eu) zzvxnMW{rki{p8QTSV@F$h2O>>D`r)*^>){%Yrot+O&t3i;(dkuHU2IxD$(TodKP>Y z{c4iq8(H9MR$xtQ@l7^1Q6?aX$EbhwTs_<0fE(%f2VYRE!tkK33yAb1HMOW0HmX#k2~!e`40H-F?)(^3it zcdom>HRG169PBTq@N0$9_f_P||Ef64C#uOPS_OoPt~m>3+jp zJ&FeWFOyOJ8~*!TPDVm1WxAA%2Pq>VZAKyf!rs@0=N3|kzveLo@ksH2Zj*)xgvV_X zbbDcENFlD}Y>T*!B>xjZcuXIGWFZilCu$%G4LLO#ISCmxd5El(92f+adLsWsUPfA( z=l?CCQNA7YpAS4Bko}(>!eFaI9PGWEAZz=y23r`Csa^Nz74gG;B&CDY<<3x03G5CW>Cc~5{qirW zz-*<52-`c|k&}N~ck*g{#@_30MNP~%o4OAE3QKzr1OWM-#h(+(yGXLH>_<@BF7lIC zDB+(v(P96b2Bn}Eip6iq`{>ZT%~9%}Y74>cfYwYq5!>5eV8P8Ty<;ZAJ=|y&4y62z z%hgJKr)wC$2ciN~ox@t+2?~8nuDP~kwKFW_8_moS>>ZJR=6F(i_qc)@f_oqdb|YCO zPF5ZhP((VoO{^F78-&K1UcA#mj8qUDd0nl%NN)8p6E7eX#78H$UYd!3eDEpkIz9d-_Mq>9R42wT)K{@tA=Yj;3TLSM~W zH~BjqWYi5gsJw>Qo8_xBwNiTxX~_DpPe>N|q#})*8qM|RvZhIIJ}!cdgDp`G>YTuQ z@)*ttEufx$hy1gs9^z`v$H043ick(AqdZP6jzlrf<4;F5G|REfLOK{pJ!c^6?>{oO3Z zNU<2*yG42Jr%%`;?-vA32jd9u0z~VuU#u3hxEUMmJlLee!0%)0Lj=ukz0tt! zCDKz$YbK9l@FdtUTO->xw0@NhI7Qv~YOMN{jwEPfNY} zvsm&A?FB(~^b^e}YC~Tw?AnRD7S&YHoFN(Jl7a}HWDSs(^X60 zQ$zi|;7Z%@d$yVCW}XW3kqvj8kN_ZPL7v3Ao1TZ(FbaH{n;e#|NlN+2dF+A3>4C%A deAuzdWnPkN3QZLm7o~!%B#1&lKwVFR;$JnWsA>QJ delta 18646 zcmZsiQ+%aC)8J!GY}-6>&O{Si6Wg|(6Wg{Yp4hfIv2ELvo%h}SeHXiX)zwdTRo8P< zUHz}_!$kRED@1P}}X0ud3ru9Qx`Fsp9++S7-8x zz?6Y<(}$KCgL#_Fdhlbz`+NJH#OJP>*m*_$*oSJO&5MUPFttCJfrER?$xt2Ih8kg) zBPp1WFqm~FJe_dZ?mZt9y0Drsw|HNm6SAMfIZ>4$kO3fSAVz_51^<_65_P#-tR8>g@vhGf^BJuEYjXxb^M^?q<*NJ9vN{AJ@#UP1*4CXn3h) z7V3t*R#ie?_dlr5lvh0aosEM8#9*FQ#ca<##!FS4P0rULu)QJg+xNI4gVyw@!NJ;Y z^$|VI&m~w-j0W95a@!z1VN>T$EqiSEt+jZ2@2ZhaOYC+Jj-n)3Xk)2gzv)cGDfiOy zbU~c;IpSkFs9Xi2du?}ZOBZ}oU+dRi2$KHmx81%7wvdZ`q(aoaj-~~YEW++)8Gmfo zVBGwe9x&HkXMC@ah95~TqYP>$vwF)b*n%j4r(N6kT80G>#+yYpkd$3@i3=R?w*P=1 zz$aag>D!Jx5@7*5)W{PD9we{8ZKv37t95gG`$OT){jem(8*=~6vMuBJ!2D;;z<7c9 z45FYmFvaZHZ-F~EZ25ae|2j;Jm z1{-(}{F+S^FvjR_osK(-@9?q^Kqat7vrYTL0;%s%?;N7SHbU`$4y!!ivBP7#URFokBfbn(R^BRk=4{JFKYA!Psh<%>2qF}zCk+3eSCnfGlNj+dOIj0W@ zrgkRIE>5O~w*QgrjjRw@S(Ct(F&c;wOW`5dxEe;Vn!hCtV_`JJlX)Y7vnK8CU^I}h zcp-zc|5yCYuZ4)h3PfO$HMKK$u^?q*191E|{tRht#}Txk`7P`BjU0vSeeA?T1%gE= zmqKgxj=mQBc0|FEppC{a-C=~h0&Ux;w)37A&etDfLBOr)US6E+PjV07IdK*n2+<~! zt_mY*SzGkALP-~3B8wKFRXe02>Icr71YnkCs3kkDIb4$b+9~|CR|sPjoyGJ+=N2m+ z0|Z;rOOA&V(6r+YZ=*QQ!(_$4*Wa}Ftt@dH3IM@YEz~Mh2CZbc;nKTW5XISpSByZM zNcwxn9Z9;p`bK^HOjzjGjv0KW^1xJn$xDLcU^-G*GWPcS&DpZ3A_SX>GKiJ>ew%?@Xvl079tQ z)S(saffJrYNP^)>zn!8+Yk1|cBIdw!Acc4)S-jyVMyQOz{2rGp z-!I_L9cf$}m@6n61D})~RvDiDv0fz_ngNCsXDzh9HD>Av?`i`cWU5GtlQo8nt)N!y zAyUIk2nxJWl^ijW3ETgZs*V+!!<5fC(vA=EInlItSju9|d*YszX7d z(=G?zBbhH=dl81;<2LtaG%dDlhk_neHNF~sJCM#v26#o_J_(m<1TU%w+_!h1tUjN5 zdTjgOrlxwhD<3N_FYTN=-Z24OaMeqK_5!wo|Kf^|Q?*>rhwuG)SQbgMem^hH7?T7u zAoXX}r57~6yCN9A+v&BveT(8VGTAvur}SDXDeS@}-*3k+-fz}#^mA58IjKgL1=RJO zZI5GZ@$KxMrQ`I?p2Y5}LF=ow>)q9vJA*;D=Bxhi`P(9ICi6!3wfl{96fpypm?(ZJ zIu`RxN)c7d>GN&`!Pf(PobSq(_}g$-D_p1*S{rhJW}$zDF!mJWqLs}h9%dfM6Re&R zlROgQn9O}>JXb*51}-Ms87kMj4n)}321hDo;0>#STB`{pCxivRg$C=BfwsW`H~(=u z$ypHtk@yWv8XaB=e_oF<_gSj%REV#gkN7teK026LgSWG&u3YJd>uq#dAxIh9$YU}J zZqW&Q1`=0~7{S;dTFeUE5};ZpDO$jeB96PEX_gg=cF*HOl;YOl5t9U#Bl=S z6<+mdxdnQ9?~ezwjqL8jDsvY{XF%_$@uWj}-M9_c{5PJ^22qXxHq{-;$I$AMB~Qu; z-cW55mj#nDfx$GQA6sq$S%*VH{v{`C;4pk*_d{iDsxORi+8ZC5v(bJK&sG3QlF}IP0*PhqVNs7=y6_AQ4Px)o@y=>z_{xJLc`CgFi0v z@=GZP)=6|`WT*i20lL@ki@B&YvT$j$YW@7U-G8){;_0Q5AxqY$NIY7FdH^OPo~y6N zt#?#z+ilqk>$_?8w5?upxwjOs3|D=9m_E-hUYWJP`zDw*`E_+|%0c?%%yC}idF9Mq zoc`7E*>nNLmd!bRb#RBiJG+UvKSmTRmZQNLgYpjJz=Yu>w!i&omc>UHSJ=-m z?P~Oil=RdO0u}KpLR2`pot}Y@LH|kNtlfI%(CAc!dNS&Kbz0V=g^`}LwkHpD; z@h%p|=&f6|5q5$9^QZekxYRx+KrTQErdG$lDWc>_4g{56Z@;CK{5{arbLl8j7R8&E zEU@Y|bdNOkkYHRVnpkNsf|td*xx1D63}tWQ?3ex{OOL z&DRv^QRladhBp6_97|PP_}x52#9Qk2mnIp%R@jqw2!-i+!iDUv*H7#unpRHAtO(zI z8%Z_5D5%)j3lF2sK2*2N2gax{?E5PB(RqZ?TdjZY(ZZKC&R?jy{oxDz{nRlm()c|&r)Uvg6C>|t#Du>|Rpo}F-YB1RE}rpi#G){* za1k|$*z+b?^)K;EP;$@NoV?OSxQ_%Pugx8C5@=m!b!i)g$0)0~#(4ejR1jG+(fD-T zWwK4h+_o8B!W3;>15$)MZ@0K{{b&rMu~!?G{uFM~BDO1P&^1n7tYLoD2^CAKGu`XD zfEOF2AP&96tqUsmh~<;T+&(}hS7wa`3I5l1nCN?Z{457CdRV~ z5(wroayWQ{oty!eB5&`NPE*`BYxu^ir!c5+Yw3s;F1T%I+p$AYl91X)`fq>sqhOmYiCC@ut9u}lH#-49+@4ve1Zf9JTvc{YDae$!t3gn{Jj=E}q;nXzhnGC2$nYm_30`B-uzJ z?5W1xEe(@|I8t^8liyMf+5Px-iksa!Q-_kn^T}VWCvJwA&xc;4pVo1q?%+bi2#-~q zN?cjENqRbUEbHO0FntQT>GaiR+BWmD0Z-=snceQs1UYE^&7E5JNE6d5vFDepNmkX$ z2<&@SCzN59p4p zl#vW-kS?gty8e>01n4LnpgizI!jKVbj%7HxfKGWOXk^Ay8(pa2wpCa=Ibo~Qo5WcW z8*&oxd(m(?1u-~|1zrK#Tv+J5* z5>cp(|K-74hu_ST>9#r%pj)F&Wfjqq%yvO4h6rkEn%!o%l=F(RJ%TH(Z^9GHnF+UW z=_hkpxrGg=j;xNW) z3dK6!G{+#3#6hSrEGEk0)(qBL7Sth)SrI*U!t5(5BFAB|lIX>ON>qg6?-3_H;t)!_ z3<*jts_@nMhEnBDZhHgB22P^xa=6tN`}38yRd??8%Fb}}N$VQ91!CoI5h5SUyR(P4 zAjiN{l0spz=aNYTnv;R$>mi9QkcB$fbd)z$v_V&oe%1b4QZ zRk6mzrKq!$FVg1wvf#oeo&-FOA5UqK$64pk^xC3dnvE?Ka;oN$6MQG{?2ZKa+>KP% zRI9J1s81KK8_<}bpwf}Jt_-J{_sm!_UM6rG$nex77^{PR!<$x-g;f8ZES2C*1&tH8 z-g8Xs0;2E0`PK4OHr7$tz$)yRPCLL&c$wkU(Z#etypkQmsh@UOy2mo{@VWE#`@mWq zn%^T)^^+`MWYV(_VyFqkI#xT{^MBoRAzT9QclUo}_}$WTkgH-)V4l#3wL}5)=wLQA za&`Nk59LzR^uX!K*U@{_PA&ELL5$AZtgl$vO)IazWYeMw!%>!(*DG#sXNurAev~-j z*ebSuRu~UReSAMrh~#0mm(xMgO8dYxzSm8`6~fEzuSIqcmVk zhm(kU$e7MHDh+e|NHHbnr8yek$YGq?v9%KxSsjDN$3o!h@x1;NR1iAMvV9$k%0m#x zLYYRE>PhLJut2Clx|-4KY$M_e7X6wBF)W*J;HQtt2>;+{j9C@oc;T(=Kr*MM;Gdq! zvzuj1L^&xin}Vw#4G;p?hgn5ApIWp_8PS$8Xe3ByDL~OT8)~#v;GEwY9i`-1K%39Z zP^1J}7_M{cSXt461-Zqfj#7YNl^HX%XU(n2mN zxy{`{{-+IyV%jSYaR9w)>=sY3FwjXT4BhYt(`LZRm$1tGY|WTd1vt zF3DB}DlRDyz4+nN^$%nhZJPbW3n_=}z=m-*=vY-9f)57=@3s8!w~{p)R^id{Fs z=Y6WIaypz}hHP!?P7l}Sax&o)w||eG)y+jR`$#uHqK<>7pM2-sF-P8syyy-{qz~V<9ED4?nDt1pc^P!jf)Zsf3a$!MbhqZ$%hX zzuqc+MKHmPm~(o*#oiI7{XM+s>j_WcY5o5Y4lZ_50O@~N2OnRWbOH&n{*vorxzq#@XYq<0$ThPU@@mt{9+8lU@D>%^B>SQcRf{t z)^A~NRT>;7_g5a7X>Y>mszw=M_{)@9H7F`0%r(mbq}>7xH5#2DhhnkW{#_-~T`a+v ze%>H!bb$~d0J#R@0{|mu_J_6UO%U>Lq~|^SKoHysCD*azWAxxVlJ)^H4md2r(WZY* zKt3FsMht*8vED_<9Ku!~Z*&CT61;H|vBj@oN0=x@+yel`FrI=< zDv02wNM0#@a2UK9L2Z}PBV#8Ta~5txjC8<=XdL0ZiU<`^3)V`~)3E4J9Fq&^5z9)a z=@#WMo-f0&8*TO#@1VASxnWAQ6}yXU!SSQK!R*J08?rUIZC`cYdY#7cu0yMOYyK)} zZ{NL7qJt7EPaVw4yp~5yi}fVzw-68iTM#CE>g}L`Zt$ab4cz%rkSPr=ifqnFz_!8$}daJPRzy()ccd&396)6*GM21dQ2-$*{1X?3!6Z?2z3Kkb@1wa7H+@II*T#)eBbG6{o~Zvek; z3F`t;Z^VgYow41O0AfB1nJ3}l4HVkq<<;32c)1TXUE6p02CP)E_tL1qCp+Dpu18+_ z0WceAhvfBdHf9Va&`&ekA4mDx;=D*WHv?0U zOPg|O>%CdbgdMmyW9`U`%NnBZ{!RS3^udYOmE((**6Ej)UEFIm%T}V`0a~{}#_+Ex zNx}$?Zy}p3#WGZ)l5&hgb-JKv%f%e!R9#82$gb&MGoTzPq-VUiORehL%XpY0QH};S z{0c>|JaU@kRJH)7SyoT#tniXgn2w{xsj$RATUj!e<>G&9*E0q_C9nrel$RlY(;qc) zAyV@m^Bh2Hig#8!E1VUU2YH&O(KQx#&A11)`Pr z;g?dnD2Gs`#gk@yuaaWBpj4KKW@;Pd30T_As=r7ys;|owUi)O$8#zn zx@r*p`YFM5+&&;B54w`K7#mV03>90LcvKl~s5Wk2FedJG5^|;Sl1NatnxK0~QT7SU zHhTYYuXOjETSTo6U4TcX8lfhol1u82{l1B42VBRRQUjkcNlIQdP3p;iG)fX2U#xxA z?P+j<-O1h-Ikc&(iJOwPXxMwJ->ZDq2-qat)cSt?)ib-+1lsnxs@q$+q`v&&*cmf9 z^Go@hE2o?$M{99D!+3c$-?bjuQcCJl4htJAT(%uST1v{8zHVB|{3j9iDJ_X4rv{Pa z-N-3@RSf#+xeTV97}F-&Dl+ERW{N8Fi^#Tdd(Ykj%T9zAG~elpJ9{yWO{kmD#m~gC zO!}%i+L%PYTTpv3s+f@D@^Oo>9ucLQI_IX?c!TRKy-awnN@~1P$M^iV`r=-@aXpIt zTtUPq!hRfvn;@q=_v#_f3@%^fE{fg`hd!Xw(#o*1=+x_Op zo3xG{HY=a)-;C(2dv|-m2-t-iVZ`kzfyr4aJ*LcCC$=o<&rEOqPZwwB%?++3OA7g{ znWWQTUa73p^QYGL%Bk7M9ewi_^`uh^V3q>*eox=twfn@_WpT!~LJf}l{pzBeGs9CB zebw*FoLKC=55EsnR(y~qivD&F@ds>kj520Y!7K&@CwrPu0t_`O4>#-oY<28F4&cA7 zjt-UzQ| z9}Jz6KX-mOH2C7o%jB?`U0n{2eocNqoH3&?)NMLs7 zJT2jz)!d$gxR*3JOxnK5<4fV=@z-xG3gMHZT?gATO!&h8aTrFJH`jY==qr-oLIS}f zX%f>@Pn66}ILQPcn9*bjW9qFmp{0w(asfF^JR{Zc>n-V@Ccjy81*r%bI*W>=n(r<} zsn{k&=y73FCvup~TbZ_{9b#qPF18xRkD(4Knn=<*^nYZakW*N!h*V&k1e;_hVF`ru z<=_UP)DvoS%^vt*^C@cfmdrXz3WF4a>-_uD4Ml|;(&J^wmGVsHp@NM>nfr{;8HI|k zEX9eP(QP1{4WLN%^mO3s|D|m(9E1;NGd`iyqLjpgNb&5Plw5o4ivFg6jIM`pD(G}( z6|DM|$TZJ6VSFQ5R)0WUsD|$M`~IG)R8=Ddx(G5)G)H7|cov2U#W^^mNYIMn13g!G zt_eNI{?M=$*7|K@T{=L`(8P`BeLimzC+#SzMs54|Bo2r*&-SY32ISL{Q`IpkrkSA(6`1D0~FIF%Y#^mg}V=0nzA zEAhPP_2j5CnZ|vb)-cri3IbGfS027*h2D2eaI^H`JilBGUwUCd2FX;H<70aliIv(v4kTu8iA%bIj%qo^orp7u4?l{P@rp1}(f+q6F?QziuKb zb2SW2S@CagZEf1;3N6|kPnmW0=;eSknEbS>ua5SO$ees0jTom)m|IX2UXQcxNz|f- z%w&jkX6#9uB>;_wF|k@?YBUB**g!?qfS{#`H5b?l!P4t7f;y=T5tkhS~#=A4UrX7f=DG0$_U zrFB%+wWlvbu6xIurysxF-%7!?qsMJ(GC@n6$3|V*^V0h}%41h^svf3N=%e}1wdkJd zt#6y>`-7j_c$iL|}!?9rCUbAM@P?(NKH;Y)0YPWE#**|ejY{mVT(d+pMJ&t>i! zW|Wi9zgKCipgS*c;bR#JiAkGg>)Wf6=R$(}^j>+HRphA@I4hyLj5uq@2%64!c52J8 zoU-Gh0E{f%DI6nc{JX3yNk|}G@1-Z+UW3f8!R<)Mep;pQz?*tUmnAy28<$-{;lRhq0?Wr#{yZD7NKX>2C(f@Z$`-r65B*T^ruA zH+YcSkT3ss6f}W;i~*SV>)~74s#lcA^EZyWV2DeK-n}+MMmvVTE~X zcX`w1j|WS)j#-U%&7ICJZ$W{Ux8xFsTD?^3i-rkD-s8-o-7D4VqeNsAgsjFmo z=T*d7N8vG|bzaog47M}1fVT9j^=+9TwLWu2xf9x2i~MJmb7FC0#Eb$6Ld=_QYkgmk z@HCa^=|F|qD2OKQ1(W4&L8-In25GIJJ&J=L1oN5(%c6{RMo3k<;ABXU9loq~{)k!-oom$b{`uR$?n>7X6Gpr}=sqTEF|%=Aw1`~J?Vb@6yDL{lsQ z>LYVEM+ek`PRn3%7xZm8VX4^xHFmTck99z-in znUX(&F1il=v+5Ve=W?j}atl99+suHeJnspguysW3wX~&zkIR)LBfoV7493jz_#!%I*win1 zBm@50)Vl!~5Q}~Vza)jFEyxeh71de$<7qprNb84RfY3njSgf%A{Y}DPU{z?dGOvgq zs2B(tBMFR6VD2p{gd=8)mOFkGw&dY=D6}Mg`pGLhSaH6N9NVto;?f>8O`IeWKsk*-f%WY4gW&nsuG zkBEX2vw@xuTP!%RAsy9^?~}D&3K+&00KKll%CW6RgCeNIZa}@O=2KPfnEzN2%s(40 zJ_x~{T7n>v$u}KBsQ2B~fq_*RBudQ2@9nR}ZX|A?fbu&gDDcN44O(FB$&RVR$-zk^ zEEbk%^e~h_;R^!cU&LsU_>2HOI#%RYMOtDZ%ITrK1=v~I1^B%k|6Z(o$^jupX!E-7 zJU3^f@Q{#<;yg7e&2$9}fsORnMj67LJB+EfvtnL=U|MU8w+d966`yHEVdAQV0BDAZJn|T{!X%S`2jK8=mPmD z68K-Z3Y>z{0Ai80^5|3ep9&9WNOCZdqi{$Gk-#IUIk<>IH(-UBT4c9%cNzICX@3GR z_-wvX;^q;Z;$}`L2W{;;=uIMj@3i0wiycd@jNgH*P(`}k1lOi%fmp0esnkkzZxYp@ zr5q3T=HMhFXTgxWyns4#i8*s;aFff{SXgP@Q5|_eo;bdaKVEJ|b3dz$!nWGpdoG$c zeSXQRho^hRYj8T0>sMa2GWB7KRKRBX-2m4Dp`$c@@lS%u=ui{`5F>sB_`BZ>C4;yY zm9JzFmYuNSlVV)|2~S1s!0G^_-LJ3J08Mf4gYm(TTKz>DM}9_;;xyjSmn|sIvmy&9 z^>hl5l<{IxEl0}-pUpkN)h6+#qs3|aBB02q)IdAUmh7OsCE%OYY>=N1mIs{e&H{DF zz-6w-f`nQhfS^4L#1GrNu>J$qyX|bvcy{(FE;}v_M)cRGLUfKZsv#9&lygZ`C@>O- z5J3)Mgfi-WJ4V2QM%!|UM-+j8OPB`thK#il>`*~?vl3p|yS=NibXXY8L<EY5)eX+7zn8|tZ%&SnzPB`R1BluUmz>QP~1U442|U1?uR z+MLmyF9>sFjLcUOJeP?!?d#L1cK{GaAY&iWWY{}CAl5` z#Tx9I`B#7{rD!BIv1-oRPj3BVD1x%yc4cG13Pj6}scRdls~N<%k?(=G?r+yImxk|D zHwiI%-7jKgp!NL+$)4xk(Y`+e0;IR2BgXPPWQrJXGSQQWtVW5XLO_V#v$>Y^XIP8s}1^kk2r9aBl8M4Dj&AL_fd% zE!^slrr7OIrA&afPk{G3h)4(zU#GQqB5L^;7kiT0K*FWzTPSl+JF!h=zhbp#1lQMU z>L{8z$jq(&M5E5SJB%M}#)OjF?g#pAc)=fF*L~`BUqDNyyhwPLe#QoF-Zly-dAQL3 z4Hh-el~k~(&Mb2!kCpg&8DTSC-dQp@_#@_<(sb%Cg6YP|MQe+cf>Cch8ysoOyPxG8 zYFh`98X(qAUZ*~lj2KNOPSYhLNj*5(EefgG%t*T-K9)KBQ;ws`+R4Ax92vCP(G8L4hR8Z*kgQHx7sW3d;-+gwK84AXEk6N5bNm zUlX6ib)Kwx=2f=9FJf*A%SKy?oUUUbbLj3cJCJyo;j&j|e_C&7T~RdQjag0nPl}p0 zHN6MP7_|t#q~?GoD!q7>J9M_8IkL{XrEJc%(#|YJjeuFL+UBSlIjS}uHGPO<)p5mW z^{grVw61DWsb)nKL`L$Y+;}FI&4Zwis9Q(&=_e1ICSk=bh=H=EwFatZDbr^-?$f|XHcInqf@xv7<#!^Nxz z=Z!&aVsN0fnG(XY-jgC@I1-2*x9R(cJzD|WUiQYEO6|UXG zqp7RPMu7%~iJurt0U^KsJVjPDT)xg~`u4^1KH++p+q-^Al<_{E_aOU6ire0NaDq;0 zyP9PQ$9(gf_biS|(WWX%ck@-@t1BB%2gf1o;FHib#%=YvR+uxToA3I6&?K)nFIkP+ z4sA#)Ec))}FFg4?e~i9n3J5p-VP0o$`I%TfyQS9w4{92FUSpG}UY{CjO|^uasH;f$ z)MzLPNEy}ze)nAS`Qv45cA3!3e*=Q3OemzzrT7&>(&eGTNZs=oTo;P(yv|m0G(&V4p z&#;Qp9ub{CMmc_P0})2Z7YxSs770)!i=?-ioJGgJ>YfPbo47=5J%!X=f3ZNL{I}b)+#_+BgDD=$R}Hu!-sKj)D4Y+XAZnU<3<~!8AN=Rf$??wfMaye3O}2W8a7rhh z->l~YgGxwXX9yYQTIvPzP?2`{Zxd454`h9I%NzYic~0us|MCzdG(q_#8TbX^Q_Yz1 z7JMuf=MiLGetp3%eqoTPXgU)+3g&#Wkmrwt{J*f81Hh4L0fX7H%?S>p4-QECGKax# z`A7y=kcR;9r1>90V73_UgOgf-v!;RjLSwb0$w07q{Of=YA+TDu2O#puAXqtC{>^*i z`}g&qHdaeKIpiD$1nd9NcISfhqXuXDk2Yotf-a;8>c7r^wT*2dg=78|vj4k&#~UQ7 z#=nvOTG;&wMX3Y9_J1r8)IjyPfV2N^3)d9TXqstboZwh3SiaC?I%$W=|3sNpXa(mq znSF5VmReaDd4jY6nSbtKSin#trHu{z6XjiDh|tpf{^PWNC`>m3BnN=?KfrFnK`{SBUUasu-{`D{2*C%%}u(I!dM$ z!sFmk8V938J=wsuuqX^kq3C0p!ybdC3YEg8;9>pqvpGcAMP#72 zJ^kkm;|P{kEA08N-YoQShsD&@1b@SoK<%4&HVrB`Njm0~z~E$QB&Ns#4oR7qb6_AL zh^o=x5|qrU1H;AR9#lYOBY?i*&xua&Prwcwt#RNA`4#}A9b%4mC`n)#@&u==sHIZU z3aGaTMkg5F8w98v1jbMblwwn>d3<}>yCOr5(ku!Hayi@VRP!0{RHEWHG#)q;bVdTR8t;3yv`t7)^#45m;4&1dKjSTsPK4FonC0p$A$@tNYJ z{+U5w7yU^v%M>bU^^L(KoU$yA@Uy(P5b<~qQk)liQzDCKhKm^*B9bGkk6Cs;y%zw>}gkv4W5h z`$WNOydHptx&^My$V!UL|@1li4h&}svucYB{4z&){xFkQ75Qv?t{ zXsh7;gP*>^w1UPdQzQD!ZvqMGLl!I3-bsz!KaTC+Ov=|7endiQe5CzC?9c8fY^_GB zmDyLB){R+L0GaABd?;twe^`~`^k26p!i5iQa{egYfMY-fL#%wXok`}Uff51>@8p!M z*~K>9fy-YO*=-uOMn$}p{a~M=Jh2Y*@$CutzK2FxLR-@F)4v@<;OoxB#N< z>hK#11^FYvu{?=>TBkuqaVJ>?x?_Fu)uKgLR_&l9)uM}AkK008`)gqwnn81k1&AWS zrF~1!&wtlXm?Qxnm5?wGS!RKF&=ZTvT2*1Uy!{gd|v129hg(eLXHZhe!4y6eO*8e?LX($ z=yg{Y7>FoZ1VbommJ?yN2SD7VLm@D^1(COC=eN=}j5+yy{?<^4syVOd5)HIr)x&0Y zUvJu&!bE67!Hfgx`F!X9Dhh7C6#mTNXsf4mxXfufk$a6#_j#3)ZyF?F?f4&e~CZ@`rIZ z=l6MVl_&Mt{Kq(;#oY6S`BUX@DKnCnYT}-k{VCIL-S=al#*g!YlTZ|=X9R)VF99D3 zH<}OBE}}Y-1Jo8Ie{>IvZWO*51^sTHC$t?PLCtmUUmctVRbZa&JV0_DoJ@8V`rt&X z0j_`#hBok6^3WHd{ z%1g2RtBEX7NrT=?^SA0zABSGh9%)$`ZtE-Z{jOg49p(_o+ zX1l%u_A^b^=laFDi-5k`*MOO!ysZywmE~$+#r-W2lJ{G^AL;+$tM&Ax|;&=vk&v0sk{63p(eY>OV_)~eWyXd zgrq?sol+LZecuLx_~Na4vicYd&7#$U6`|fUl6>kh z;+KCmuSq^w%t|9+A)$INf@z^a$r^y-pFMKmuLY)oi$|l$qy>J;s&}X_IX>;3-H%z; zYc+_-I<&D&p)~4EHPh}pD-KA13bb!LeE$h*Q0XEcs#vU;qsgmpMqOu^^LT$+TpS8( z{(L(At)lh@&dVO1wuZ)%dA`+&1^#}dN})-)&Y=6Uzj=82x_=VRmK}b_XYx}6r!-lt z+*3dEh5#s>68yHX!CQ7b-It%`rO8|2Je%^(fik|cN6H7Ae!5t&AdgSBbO_&9v#k^4 z*ZTE6mfcmhgfM-QXN4V)NxeZNYmR=y(KEq zN)aTO@oZs?{GMi`bLf<7HKtc^G4u|aFTJiVoL{d^1t1!~s0C`z{XtJTTCeUH0GA&F zHw8k9-PD!eblfqC5`?+CMn1wnQKNbfMMvSpZFklL;3DHl{PBc3KYN(gGVv)$v-JpEfK^!{S^dy;dLUxE1ZxayANbKR>0Be}>iPFzUh{JB z68iwUCO&QY`_#7h*3)si5D5_~lGheVzx{p>z6MwCj<;CjvidQLpsqODRMbXkC^Zy^ z-NN?I0a`1WCS%WEL=zRL&7A%q-RH2%8s6X{U2-L@q?b9R=3VcQ`1`aOV%;6f6DK}x zq%`3a8Md1y(r&U6od@%uZX<6baV?^mQ;}0gbSHd3SYKqc5(>_jwP~0uE^A|68ZhRS zk%aE%I9&?fZHD}uE^oi5J4(v7w4N)P`_m;S%7%l{#mJkf?xlpWA4~5bZ&=8=YoXj; zc^xwc^yuFOr(RV%#ckPN4|ZOiI@ABk35n++jVN$FnH+d5S@eo3kmEbU{BT)V&ry#x zSO?)lGfqvRyi@?>5fnig;JeoJ_#=xu+-*zAy>=D7|DmcJPt{f&PURzC2a7o>wAs+_ zN=6U5k5met-iH!;X_E;M#K7#CVc@;sqydj!56;A*N9NUo-tOz_>FH3Z`l-CVl)(;| zMaa9u0J`l0_><-n3D^jO%Ew}hH|mTnYN*KyGHkYeha`S8t(Z}bgQwHu#bHt$9lG`( zEWT$Ay4wj{pG{kog1a+CMH|&gqGbCz#_K331e82~Zqr1n+T(?zXF(qq^AW1& ziIk_O^Zf?LFy^Wl)F{04)Q(r1Ny_x@(A%zfQjfb`wACpZuGvMt??0H3SNl<3^Bj2m z9HOhDU)7AB`d-0oh(6I$y>Nuka()ZB+s1INx1ACkRbc@O8qQF2a(ou9-=9}kAG(*P z<6+~udY8pR@1$mjRM)05ZxzECteq0(tXng;dWpd<8MskzPTUszlxLGJzM&XaH27Oz zRC!~^=~^62vz3*;qAy{Wt(XMmCEDz`QYRu&R`d|+Kzzs{I?J)`2ov7j839QqjY_9Q zMp{hm>V!rE;uT%{4i6EQ%}=&wc071w0{J%;LSMYk4pJ z4tDAZ%-HVA$xn98_w6bc?y7bt(v7+6c?8Z~w5-AlRM0Jf`PdY;MxIzC?d2sao$o*$ z#x8^C_ET9_A<6Z!s5$o_DPGq`V)?jm^GWJ}KY!exG6C4X)aFo#Rn7YdF<5rdr43fM zR0G!YW8AI_wpYum0hv#2n4u3P=Tpn=Azmkh{w{3_5&ma#*w~uuEp@RQ&Aw`Yf}0nA z-hsvyD9L3~uipI7scD!J);WLP(L$M8Vm0i}%(tb#2KRGT+T!`s!yKKPa zKnV6W>agJg^{y!{($bZ9)(>_X7ae5bc^5!y2PoMu0<>~E{zQE*Nk1I=+~_VCZIPJMgtH6}-p z-g03CpWxsUa_53=RI?$X@FNuXM@t9f=+aki6I13^p`)XVdKl{OFHUo94&Do47n5%f zsELm~Fg9Vua_r%{jNK&VB8mLLCZE>_Yl*hF;7Pvu89^3WGv4LRI$68^k6JW>!8)K3 z$JS-t7zaM&U4rU?6}esJ;g%t*Wd2-`;0|vK+Cy5kJcBUAV?}3xNIW~up7T#e&DWkS z&7Cjbx1R3Uk3)Cr{6tS;`kRG-((1RRug8(>?W_SBwBWY}c*CuLKK&l%Bf*}~9=CPE zPJ85|mT&;Ehy4f?MFLH#;S{|A+KpLf)X3|Am)3NA%skAqV2V8I!oTKs^)cw!-&spc zr@9pS#B%mdVir*v3tL55k1^`{s>jke2Y#WdU^=W!l?S?ec#ZyV+!Zy8skNRo%3UIS z4Rc$vl}Ch-9^=t3Ssa$Fn?jM!VmXg7W9G2fBxXcj^&riR*DtWqg73pJJ;#BkoEa;hY~(0Qii-im*<;TFq3;+CSvY z|69LZIZ=E+1233)?kg2W-N@@CFdfUKlatDNG8idS3QO!WdD1N$G=pz#U=xlb=TiHK zrMt7Z0%N->E=J_xdP-_r6;NS!25?XNJ1_o4N1`KPgd~-#^bNb2OjgAf(pq5^7m0`? zlW$IF4U6Dz82|2{FAD+cX~;)0oCk$jYco0Sr=YD9kUZ>CpG~1W$Kp;!>rTPM6se1+ zEyrYuxUvFz$;B*)-ON>lsiQn6d~%K1YEBWwl8-%NN%co4VR404`=J`fBV*d?8X#Q? zsVJ9HcGVDfGCfqwRXObNNOz&WfS3)D`lnump-Q0Y1Q7?KnFhP5749RYpY&!ytn6}0 zZzFMW>^!BJ1rE#N4Z28YqQxc!j=jemHVe`HPhG82f*5s>S-ciiqD!%qEazLz0cp)3 z{`bS5F`TqqqYMfjuB*SS7IfCg^w@;7T@S=%xujVZNoz!HRny={hoKI3@J;K*S52ek z{*H*w;6u8GWtqzjj|87BjnrPVvGzy@DgOn(Ftm#Lmc0p zK(V547zm~q|M#0&4sO;o#@{f(G;BatE(QP_4FEtxhrl9dZz5{wVoFLY`kf8H24DrS zaS&VONa0T+P3i{GI<^ z^5f!I$T6ppKm>vbInk{(iX~-75^jjXAs+bVyCHu*uNIh?(*5)U@=4mejppbg(`5qj ztS0{sd7e7IY^Z$^&^DnwWx^fP@sSh)OqkhaTfDaLGfxKNdBf9`hVR;glh2 zUw_v>aP@k>xf{2?>B05I=lywed)$(?4@&DYOeFu}n(^z3cJFEBPqyksAje{W%2srQ zlUxXgP4xF!A@UR4%wevq`gT2VH54VihG`%h|CkIunx8-`392flB3&#)EXL=AOSELN z9c!sPE;{)PU(3b*!fCKNY}<&CR?G4 zNlUcRTjbvBl8*aIAVX&_xL!7F(|*0QGuKhb(Eh3BnT-5$bJl(CW8ITDrOCE) zj1^iN$3>IC z3N#`vsi<%KLvm5y+p8d^r?nh&@SDk0^5DA3)UO5SCW3>U>dt9;?NdKhRKS2tC#BD+ z8H8;%!Sne6<9z-Gf>A?*fB)@kr0+zj2CliYSoZrTmoAAtP10W3+($WG(%p*yGH~dR zi8IZVn?9Ub+c$T`bYLRP0IT`KWHxU6dG>bo}D zvvB)?q(x?8++wxi#>@|K}M@}TJ4b(VHIKT?qb-d&_ zDe@UAui)CCLxGJdRb)y87$9w25+m^mCIAI#;^MjbNs^p>)(hab?c0}#an z5eQcCoif786W$xqv{ri*c`3-mE>JEyP*&$Jv_Yey%3XDO5L)^nfZx^Z$V?fQbwO*3 z72HUAQ>x)|-6X}S-6@&wkM!2EPuj#n*~`fh3IJBr6LX&Is2gURA3m&@i#~)LD6JzY z=mT1_hzS~%a;qZ81l>w`oJjwI!GUZ9FFGM7iQv)@f^Vq=Iztlu-W5M@%1kCNj=IZy z%Ru8_)0Mwv{y-sgqBUXi()=M}`gytrk5l!(%x)4Op&yqWl0Pp$PlS|z~cJ5}?%?pLB!oQ`c zyG*-jTRc0`t(NJIs}@eUQx@`t(1JQ8qt3ONyo=3N!(?wQcgj*j#JWs39XT!8jXU4R z&JDi=^gqt2?zks3Nv-Z&8kFUElGP(+BIjJpx z797!U*i7XHHP?l5DIw{#uf)7Kkp}PAg1Snlt#abmKc>Co(zB0@!>7d+_0-`dmJl5L zywoRVyTE)h_Pov8TFgs&Jb;MFp=Rel^ujYH<#xQ>pt?X817^M0G7#f%W90^Vs4l0t zaL<6@+4@+!y*||INvo(mBUr{0xh9Mnv`jTh{f#daV`J)JS%b{GU+*sn%n9*XPq$pOgyOGU#ZZEn z`8{pJ8H6YF@xK20JwF16SlNz~<6medPmKsgAhQYID})9ROw;r$Y9+C#8q(j>1!u-3 zl?=qBSimc!x#7mhZ<07{=+0M|8fYP8YrdE30(0ZEHqO5E+yFTqOZ}jYWroa#1qHEJ zwuP3I_9WNf@iQf`KS1nb3yb#|$KiT9!Q(Nny~&Q)&!s=suhgpcTYtabIJOdcpTRk> zBeKWNl+w2 0 &\Rightarrow \row_j\left[A\right]\cdot\vec{x} = b_j\\ - x_i > 0 &\Rightarrow \row_i\left[\transposed{A}\right] \cdot \vec{y} = c_i - \end{align*} + \begin{align} + y_j > 0 &\Rightarrow \row_j\left[A\right]\cdot\vec{x} = b_j\label{eq:primaler-schlupf}\\ + x_i > 0 &\Rightarrow \row_i\left[\transposed{A}\right] \cdot \vec{y} = c_i \label{eq:dualer-schlupf} + \end{align} formuliert werden. + Für Approximationsalgorithmen ist vor allem die zweite Aussage wichtig. \end{satz} \begin{satz} @@ -1071,4 +1073,18 @@ Beträgt der Schlupf 0, so ist die Nebenbedingung scharf. \zeta(\vec{y}) \le \opt(Y_\rel) = \opt(X_\rel) \le \opt(X) = \opt(I) \le z(\vec{x}) \end{equation*} \end{satz} + +\subsection{Verwendung der Dualität für Approximationsalgorithmen} +\subsubsection{Entwurf neuer Algorithmen mittels Dual Fitting} +Beim Dual-Fitting wird allgemein versucht, \Cref{eq:dualer-schlupf} zu erfüllen. +Zunächst wird dazu eine zulässige Lösung $\vec{y}$ des Duals bestimmt, bei der einige Nebenbedingungen scharf sind. +Die den scharfen Nebenbedingungen entsprechenden Variablen $x_i$ des Primals werden dann als Approximation auf 1 gesetzt, die anderen auf 0. +Das so entstandene $\vec{x}$ gibt mit $z(\vec{x})$ eine obere Schranke an. +Die Qualität der Lösung hängt dabei stark von der Qualität des ursprünglich bestimmten $\vec{y}$ ab. + +\subsubsection{Analyse bestehender Algorithmen} +Ein bestehender Algorithmus, der eine 0-1-Lösung des ursprünglichen ILPs $X$ berechnet, wird so erweitert, dass er gleichzeitig eine zulässige Lösung $\vec{y}$ für $Y_\rel$ konstruiert. +Da $\vec{x}$ und $\vec{y}$ von einander abhängen, hängt auch $z(\vec{x})$ von $\vec{y}$ ab. +Kann daraus der Wert $\zeta(\vec{y})$ isoliert werden, kann eine obere Schranke des Wertes der Lösung zu $I$ berechnet werden. + \end{document} \ No newline at end of file