Báo cáo toán học: " Envy-free cake divisions cannot be found by ﬁnite protocols"

Báo cáo toán học: " Envy-free cake divisions cannot be found by ﬁnite protocols" pps

... replacingthe knives with a ﬁnite bidding or trimming process. So these procedures cannot be called ﬁnite, either. By contrast, there is a simple ﬁnite protocol for dividing a cake between two people—“Icut, ... an explicit sequence of divisions is constructed,with the actual envy-free division as its limit. Because it requires convergence, it is not a ﬁnite protocol.Other non -ﬁnite procedures are available ... this paper, a ﬁnite protocol is one in which only ﬁnitely many marks are made onthe cake. Formally, a mark is a real number x ∈ [0, 1]; informally, it is a physical markon the cake that is visible...

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Báo cáo toán học: " Synthesis and characterization of CuO nanowires by a simple wet chemical method" pdf

... Acknowledgements This work was supported by the Korea Science and Engineering Foundation (KOSEF) and the National Research Foundation of Korea (NRF) grants funded by the Korean government (KRF-2006-311-C00050), ... characterization of CuO nanorods by thermal decomposition of CuC2O4 precursor. Mater Res Bull 2002, 37:2365-2372. 19. Jiang XC, Herricks T, Xia YN: CuO nanowires can be synthesized by heating copper substrates ... HR, Hertel T, Avouris P: Single-and multi-wall carbon nanotube field-effect transistors. Appl Phys Lett 1998, 73:2447-2449. 6. Marabelli F, Parravicini GB, Salghetti-Drioli F: Optical gap of...