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不含4-圈和9-圈的平面图是(2,0,0)-可染的
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作者 陈敏 戴立峰 +2 位作者 聂静方 王应前 俞伟强 《中国科学:数学》 CSCD 北大核心 2020年第2期317-338,共22页
设d1,d2,...dk为尼个非负整数.若图G的顶点集V可划分成k个子集合V1,V2…,Vk,使得对于任意的i∈{1,2,...,k},由Vi导出的子图G[Vi]的最大度至多为di,则称图G是(d1,d2,...,dk)-可染的.1976年,Steinberg猜想:不含4-圈和5-圈的平面图是(0,0,... 设d1,d2,...dk为尼个非负整数.若图G的顶点集V可划分成k个子集合V1,V2…,Vk,使得对于任意的i∈{1,2,...,k},由Vi导出的子图G[Vi]的最大度至多为di,则称图G是(d1,d2,...,dk)-可染的.1976年,Steinberg猜想:不含4-圈和5-圈的平面图是(0,0,0)-可染的.在Steinberg猜想的驱动下,人们证明了以下三个结论:(1)对每一个i∈{5,6,7,8,9},不含4-圈和i-圈的平面图是列表(1,1,1)-可染的;(2)对每一个i∈{5,6,7,8,9},不含4-圈和i-圈的平面图是(1,1,0)-可染的;(3)对每一个i∈{5,6,7,8},不含4-圈和i-圈的平面图是(2,0,0)-可染的.为使结论(3)更加完整,本文证明不含4-圈和9-圈的平面图是(2,0,0)-可染的. 展开更多
关键词 平面图 Steinberg猜想 后Steinberg猜想 (2 0 0)-染色 可约构型 权转移
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Control of membrane fouling during hyperhaline municipal wastewater treatment using a pilot-scale anoxic/aerobic-membrane bioreactor system 被引量:1
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作者 Jingmei Sun Jiangxiu Rong +2 位作者 lifeng dai Baoshan Liu Wenting Zhu 《Journal of Environmental Sciences》 SCIE EI CAS CSCD 2011年第10期1619-1625,共7页
Membrane fouling limits the effects of long-term stable operation of membrane bioreactor (MBR). Control of membrane fouling can extend the membrane life and reduce water treatment cost effectively. A pilot scale ano... Membrane fouling limits the effects of long-term stable operation of membrane bioreactor (MBR). Control of membrane fouling can extend the membrane life and reduce water treatment cost effectively. A pilot scale anoxic/aerobic-membrane bioreactor (A/O- MBR, 40 L/hr) was used to treat the hyperhaline municipal sewage from a processing zone of Tianjin, China. Impact factors including mixed liquid sludge suspension (MLSS), sludge viscosity (Ix), microorganisms, extracellular polymeric substances (EPS), aeration intensity and suction/suspended time on membrane fouling and pollution control were studied. The relationships among various factors associated with membrane fouling were analyzed. Results showed that there was a positive correlation among MLSS, sludge viscosity and trans-membrane pressure (TMP). Considering water treatment efficiency and stable operation of the membrane module, MLSS of 5 g/L was suggested for the process. There was a same trend among EPS, sludge viscosity and TMP. Numbers and species of microorganisms affected membrane fouling. Either too high or too low aeration intensity was not conducive to membrane fouling control. Aeration intensity of 1.0 m3/hr (gas/water ratio of 25:1) is suggested for the process. A long suction time caused a rapid increase in membrane resistance. However, long suspended time cannot prevent the increase of membrane resistance effectively even though a suspended time was necessary for scale off particles from the membrane surface. The suction/suspended time of 12 min/3 rain was selected for the process. The interaction of various environmental factors and operation conditions must be considered synthetically. 展开更多
关键词 hyperhaline municipal sewage anoxic/oxic membrane bioreactor membrane fouling control relationship of variousfactors
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