通过一个适当的归约变换,可以将一个CNF(conjunctive normal form)公式变换为另一个具有某种特殊结构或性质的公式,使两者具有相同的可满足性。带有正则结构的CNF公式的因子图在图论中具有某些良好的性质和结果,可以用于研究公式的可满...通过一个适当的归约变换,可以将一个CNF(conjunctive normal form)公式变换为另一个具有某种特殊结构或性质的公式,使两者具有相同的可满足性。带有正则结构的CNF公式的因子图在图论中具有某些良好的性质和结果,可以用于研究公式的可满足性和计算复杂性。极小不可满足公式具有一个临界特征,公式本身不可满足,从原始公式中删去任意一个子句后得到的公式可满足。借助此临界特性,给出了一个从3-CNF公式到正则(3,4)-CNF公式的多项式归约转换。这里,正则(3,4)-CNF公式是指公式中每个子句的长度恰为3,每个变元出现的次数恰为4。因此,正则(3,4)-SAT问题是一个NP-完全问题,并且MAX(3,4)-SAT是不可近似问题。展开更多
In the present study,a film consisting of TiO_2 doped with copper was prepared for efficiently decomposing 4-nitrophenol(4-NP) by photocatalysis.The preparing process of TiO_2 doped with copper includes two procedures...In the present study,a film consisting of TiO_2 doped with copper was prepared for efficiently decomposing 4-nitrophenol(4-NP) by photocatalysis.The preparing process of TiO_2 doped with copper includes two procedures:preparing Ti(OH)_4 doped with copper and synthesizing anatase and rutile TiO_2 doped with copper.Ti(OH)_4 doped with copper could be achieved by hydrolyzing TiCl_4in the mixed solution containing deionized water and copper oxalate.The Ti(OH)_4 doped with copper can be gained successfully by the following procedures:rinsing,drying and vacuum drying.The Ti(OH)_4 doped with copper could be converted into anatase TiO_2 doped with copper and rutile TiO_2 doped with copper by incineration for 4.5 h at 723 and 1 073 K,respectively.Characterizations of anatase TiO_2 doped with copper and rutile TiO_2 doped with copper were determined by X-ray diffraction(XRD) and energy dispersion of X-ray(EDX).Anatase and rutile TiO_2 doped with copper were dissolved in a mixed solution containing isopropanol and diethylamine.Stainless electrode was submerged into with the solutions,the film of TiO_2 was formed by drying the thin layer at a ramp rate of 3℃/min until 373 K,and this temperature was held for 1 h.The temperature of the oven was subsequently increased to a final temperature of 823 K at a ramp rate of 3℃/min,and was held at this value for 1 h.The stainless steel covered with modified TiO_2 film was utilized as the anode.The stainless steel mesh was used as the cathode.The cathode and anode were connected with the source and immersed into the solution with 100 mg/L 4-NP.The whole reaction on photocatalysis was perfectly carried out after ultraviolet radiation and aerator were run.The experimental results showed that:cracking ratio of 4-NP ring,the removal ratio of chemical oxygen demand(COD) and total organic carbon(TOC) were respectively more than 90%,80% and 80% within 2 h.Degradation of 4-NP implied its potential application in associated wastewater.展开更多
文摘通过一个适当的归约变换,可以将一个CNF(conjunctive normal form)公式变换为另一个具有某种特殊结构或性质的公式,使两者具有相同的可满足性。带有正则结构的CNF公式的因子图在图论中具有某些良好的性质和结果,可以用于研究公式的可满足性和计算复杂性。极小不可满足公式具有一个临界特征,公式本身不可满足,从原始公式中删去任意一个子句后得到的公式可满足。借助此临界特性,给出了一个从3-CNF公式到正则(3,4)-CNF公式的多项式归约转换。这里,正则(3,4)-CNF公式是指公式中每个子句的长度恰为3,每个变元出现的次数恰为4。因此,正则(3,4)-SAT问题是一个NP-完全问题,并且MAX(3,4)-SAT是不可近似问题。
基金Environmental Protection Department of Jiangsu Province,China(No.2013023)Jiangsu Key Laboratory of Industrial Water-Conservation & Emission Reduction,China(No.IWCER201202)
文摘In the present study,a film consisting of TiO_2 doped with copper was prepared for efficiently decomposing 4-nitrophenol(4-NP) by photocatalysis.The preparing process of TiO_2 doped with copper includes two procedures:preparing Ti(OH)_4 doped with copper and synthesizing anatase and rutile TiO_2 doped with copper.Ti(OH)_4 doped with copper could be achieved by hydrolyzing TiCl_4in the mixed solution containing deionized water and copper oxalate.The Ti(OH)_4 doped with copper can be gained successfully by the following procedures:rinsing,drying and vacuum drying.The Ti(OH)_4 doped with copper could be converted into anatase TiO_2 doped with copper and rutile TiO_2 doped with copper by incineration for 4.5 h at 723 and 1 073 K,respectively.Characterizations of anatase TiO_2 doped with copper and rutile TiO_2 doped with copper were determined by X-ray diffraction(XRD) and energy dispersion of X-ray(EDX).Anatase and rutile TiO_2 doped with copper were dissolved in a mixed solution containing isopropanol and diethylamine.Stainless electrode was submerged into with the solutions,the film of TiO_2 was formed by drying the thin layer at a ramp rate of 3℃/min until 373 K,and this temperature was held for 1 h.The temperature of the oven was subsequently increased to a final temperature of 823 K at a ramp rate of 3℃/min,and was held at this value for 1 h.The stainless steel covered with modified TiO_2 film was utilized as the anode.The stainless steel mesh was used as the cathode.The cathode and anode were connected with the source and immersed into the solution with 100 mg/L 4-NP.The whole reaction on photocatalysis was perfectly carried out after ultraviolet radiation and aerator were run.The experimental results showed that:cracking ratio of 4-NP ring,the removal ratio of chemical oxygen demand(COD) and total organic carbon(TOC) were respectively more than 90%,80% and 80% within 2 h.Degradation of 4-NP implied its potential application in associated wastewater.
