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G=(V,E)表示一个顶点集为V,边集为E的有限简单无向图.若存在映射φ:V(G)→Zk(n)(Zk(n)是由{1,2,…,n}的所有k-元子集构成的集合),满足:(A) uv∈E(G),有φ(u)∩φ(u)=θ,则称φ是G的一个k-重n-顶点染色.本文证明了奇围长至少为5k-7(k=4)或5k-9(k=6)的平面图G... 相似文献
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Temperatures and enthalpies of fusion and solid-to-solid transition of a homologous series of linear alkane-α,ω-diols, HO-(CH2)n-OH where n = (6 to 16), were measured by differential scanning calorimetry (d.s.c.). The enthalpies and temperatures of fusion displayed a marked odd–even effect as a function of the number of methylene groups in the alkyl chains, with even terms showing higher values than odd terms. Thermodynamic parameters of fusion were compared with those of isoelectronic linear alkanes and earlier measured alkane-α,ω-diamines, alkane-α,ω-diamides and alkane-α,ω-dinitriles. Results were discussed with reference to the effects of chain length on crystal structures and packing patterns raised on hydrogen bonding and hydrophobic interaction interplay. The enthalpies of sublimation at T = 298.15 K were obtained from the enthalpies of fusion and the literature enthalpies of vaporisation, both adjusted to 298.15 K. A smoother odd–even pattern was observed for the enthalpies of sublimation. 相似文献
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David Défossez 《Discrete Mathematics》2008,308(11):2265-2268
In this note we prove a long-standing conjecture of Sterboul [P. Duchet, Hypergraphs, in: R. Graham, M. Grötschel, L. Lovász (Eds.), Handbook of Combinatorics, 1995, pp. 381-432 (Chapter 7)], which states that a hypergraph is bicolorable provided it does not contain a specific kind of odd cycle. This is currently the strongest result of its kind, improving on results by Berge [Graphs and Hypergraphs, North-Holland, American Elsevier, Amsterdam, 1973] and Fournier and Las Vergnas [Une classe d’hypergraphes bichromatiques II, Discrete Math. 7 (1974) 99-106; A class of bichromatic hypergraphs, Ann. Discrete Math. 21, in: C. Berge, V. Chvátal (Eds.), Topics on Perfect Graphs, 1984, pp. 21-27]. 相似文献
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It is not known whether or not there exists an odd perfect number. We describe an algorithmic approach for showing that if there is an odd perfect number then it has t distinct prime factors, and we discuss its application towards showing that t9. 相似文献
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Kosuke Ono 《Journal of Mathematical Analysis and Applications》2005,310(2):347-361
Consider the Cauchy problem in odd dimensions for the dissipative wave equation: (□+∂t)u=0 in with (u,∂tu)|t=0=(u0,u1). Because the L2 estimates and the L∞ estimates of the solution u(t) are well known, in this paper we pay attention to the Lp estimates with 1p<2 (in particular, p=1) of the solution u(t) for t0. In order to derive Lp estimates we first give the representation formulas of the solution u(t)=∂tS(t)u0+S(t)(u0+u1) and then we directly estimate the exact solution S(t)g and its derivative ∂tS(t)g of the dissipative wave equation with the initial data (u0,u1)=(0,g). In particular, when p=1 and n1, we get the L1 estimate: u(t)L1Ce−t/4(u0Wn,1+u1Wn−1,1)+C(u0L1+u1L1) for t0. 相似文献
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第Ⅱ类三态叠加多模叠加态光场等幂次2m+1次方Y压缩 总被引:2,自引:0,他引:2
构造了由多模虚相干态|{iZj}>q、多模虚相干态的相反态|{-iZj}>q和多模真空态|{Oj}>q这三种不同的量子光场态的线性叠加所组成的第Ⅱ类三态叠加多模叠加态光场|ψ2(3)>q.利用多模压缩态理论,研究了态|ψ2(3)>q的广义非线性等幂次2m+1次方Y压缩特性.结果发现:在压缩次数N=2m+1(m=0,1,2,3,…,…)的条件下,只要各模的初始相位和态间的初始相位差分别满足一定的取值条件,态|ψ2(3)>q就可呈现出周期性变化的、任意奇数次的广义非线性等幂次N次方Y压缩效应. 相似文献
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