From 93c1055de8b2ac3316858bac50f5d3ff3c86322b Mon Sep 17 00:00:00 2001 From: Yu Cong Date: Mon, 28 Apr 2025 11:37:26 +0800 Subject: [PATCH] =?UTF-8?q?add=20=CE=BB=5Fi=20properties?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit --- main.pdf | Bin 261874 -> 263332 bytes main.tex | 6 ++++++ 2 files changed, 6 insertions(+) diff --git a/main.pdf b/main.pdf index daa8cd3cfa225a65a16349e0eb66e6b71fb3818e..2dc929500fc4c119ebad1a8980d089bbd7bb7f3d 100644 GIT binary patch delta 25137 zcmV)3K+C`K{STyx5U|)u12#D|lkqhuf9+gba~ro6e%G(y<8sDCalg!@=`?Pfwn^Kx zQ74^I{6I--iM2>6Bo*8J^*sl`Ua$m~)V1=Y54M)O02Vknm+xG#baFAFlW&gb;O|$* zN56T)sG2ZFoKk#p{BA;tv+$5k*hFcfotPLS2$%41IXS70FYD=yD^p$HY!}P=9yE9}%x1bTB_m<5vp2DRx3f2dbermO2M&PJ;0 z^wa1hoFQ7t{3Ngw%nuqciJc7e<`bB;ag*b7-;j#fusBK1I1zfV%lEh|7E*WNOMC-1c`o4~=oG)`Sb04ml=RtRPs>up8YF zD(qyIwCsj7$sB(!a_tLn6n~(&|-pmS4$$QT6cQ0R$M8eF?X%P1y>C zANv1w%4EW$^C<_R+<=6SajFCg3!LbooLVvg$>_VB`sLl(6!e30f0G#}%E>UulTtn9 z0IybLenwtRVe3 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a/main.tex +++ b/main.tex @@ -257,6 +257,12 @@ I believe the previous conjecture is not likely to be true. \paragraph{The optimal $\lambda$} Denote by $\lambda^*$ the optimal $\lambda$ that maximizes $L(\lambda)$. From the previous argument on the first segment of $L(\lambda)$ we know that $\lambda^* \geq \min \frac{w(C\setminus F)}{B-c(F)}$. Now assume $\lambda^* > \min_{c(F)\leq b} \frac{w(C\setminus F)}{b-c(F)}$. We have $\min w(C\setminus F)-\lambda^*(b-c(F))