合取范式(conjunctive normal form,简称CNF)公式F是线性公式,如果F中任意两个不同子句至多有一个公共变元.如果F中的任意两个不同子句恰好含有一个公共变元,则称F是严格线性的.所有的严格线性公式均是可满足的,而对于线性公式类LCNF,...合取范式(conjunctive normal form,简称CNF)公式F是线性公式,如果F中任意两个不同子句至多有一个公共变元.如果F中的任意两个不同子句恰好含有一个公共变元,则称F是严格线性的.所有的严格线性公式均是可满足的,而对于线性公式类LCNF,对应的判定问题LSAT仍然是NP-完全的.LCNF≥k是子句长度大于或等于k的CNF公式子类,判定问题LSAT≥k的NP-完全性与LCNF≥k中是否含有不可满足公式密切相关.即LSAT≥k的NP-完全性取决于LCNF≥k是否含有不可满足公式.S.Porschen等人用超图和拉丁方的方法构造了LCNF≥3和LCNF≥4中的不可满足公式,并提出公开问题:对于k≥5,LCNF≥k是否含有不可满足公式?将极小不可满足公式应用于公式的归约,引入了一个简单的一般构造方法.证明了对于k≥3,k-LCNF含有不可满足公式,从而证明了一个更强的结果:对于k≥3,k-LSAT是NP-完全的.展开更多
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
Herein, well-dispersed Palladium(Pd) nanoparticles(NPs) with good catalytic activities were prepared using a wood nanomaterial(WNM) as a reductant and a supporting agent. Various factors that influenced the NP morphol...Herein, well-dispersed Palladium(Pd) nanoparticles(NPs) with good catalytic activities were prepared using a wood nanomaterial(WNM) as a reductant and a supporting agent. Various factors that influenced the NP morphologies, including reaction time, temperature, and precursor concentration were studied. The as-prepared Pd NPs/WNM showed good catalytic performance for Suzuki coupling reactions.展开更多
The palladium nanoparticles/carbon nanofibers（Pd NPs/CNFs） catalyst was prepared by the electrospinning method, the hydrazine hydrate solution reduction in an ice bath environment, the high temperature carbonization...The palladium nanoparticles/carbon nanofibers（Pd NPs/CNFs） catalyst was prepared by the electrospinning method, the hydrazine hydrate solution reduction in an ice bath environment, the high temperature carbonization. The catalyst was characterized by X-ray diffraction（XRD）, fieldemission scanning electron microscope（FE-SEM）, and transmission electron microscopy（TEM）. The nanofibers are not cross-linked and arranged in order. The surface of Pd NPs/CNFs is smooth, and it can be observed that a large number of particles were loaded and well-dispersed in carbon fiber matrix, and the particle distribution is uniform. The activity center of catalyst is Pd^（0）. The Pd NPs/CNFs exhibited a high efficiency, good reusability and stability in the Suzuki and Heck reactions. It can be used for at least five consecutive runs without significant loss of its catalytic activity. The good recyclability of Pd NPs/CNFs provides a way to greatly reduce the cost of the catalyst.展开更多
From the SAT physical model, a physical hypothesis named PHHY is proposed. By PHHY, it is proved that there is a universally efficient algorithm for solving SAT problem. Then, by square packing problem, the authors sh...From the SAT physical model, a physical hypothesis named PHHY is proposed. By PHHY, it is proved that there is a universally efficient algorithm for solving SAT problem. Then, by square packing problem, the authors show that there are interesting industrial NP-complete problems which can be solved through SAT algorithms, but each way of solving like this will be much worse than that of a certain direct solving.展开更多
基金Supported by the National Natural Science Foundation of China under Grant Nos.10410638, 60310213 (国家自然科学基金)
文摘合取范式(conjunctive normal form,简称CNF)公式F是线性公式,如果F中任意两个不同子句至多有一个公共变元.如果F中的任意两个不同子句恰好含有一个公共变元,则称F是严格线性的.所有的严格线性公式均是可满足的,而对于线性公式类LCNF,对应的判定问题LSAT仍然是NP-完全的.LCNF≥k是子句长度大于或等于k的CNF公式子类,判定问题LSAT≥k的NP-完全性与LCNF≥k中是否含有不可满足公式密切相关.即LSAT≥k的NP-完全性取决于LCNF≥k是否含有不可满足公式.S.Porschen等人用超图和拉丁方的方法构造了LCNF≥3和LCNF≥4中的不可满足公式,并提出公开问题:对于k≥5,LCNF≥k是否含有不可满足公式?将极小不可满足公式应用于公式的归约,引入了一个简单的一般构造方法.证明了对于k≥3,k-LCNF含有不可满足公式,从而证明了一个更强的结果:对于k≥3,k-LSAT是NP-完全的.
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supported by the Hebei Key Discipline Construction Project
文摘Herein, well-dispersed Palladium(Pd) nanoparticles(NPs) with good catalytic activities were prepared using a wood nanomaterial(WNM) as a reductant and a supporting agent. Various factors that influenced the NP morphologies, including reaction time, temperature, and precursor concentration were studied. The as-prepared Pd NPs/WNM showed good catalytic performance for Suzuki coupling reactions.
基金the support of the National Natural Science Foundation of China(No.21266016)
文摘The palladium nanoparticles/carbon nanofibers（Pd NPs/CNFs） catalyst was prepared by the electrospinning method, the hydrazine hydrate solution reduction in an ice bath environment, the high temperature carbonization. The catalyst was characterized by X-ray diffraction（XRD）, fieldemission scanning electron microscope（FE-SEM）, and transmission electron microscopy（TEM）. The nanofibers are not cross-linked and arranged in order. The surface of Pd NPs/CNFs is smooth, and it can be observed that a large number of particles were loaded and well-dispersed in carbon fiber matrix, and the particle distribution is uniform. The activity center of catalyst is Pd^（0）. The Pd NPs/CNFs exhibited a high efficiency, good reusability and stability in the Suzuki and Heck reactions. It can be used for at least five consecutive runs without significant loss of its catalytic activity. The good recyclability of Pd NPs/CNFs provides a way to greatly reduce the cost of the catalyst.
基金Project supported by the Chinese High-Tech Program, the National Natural Science Foundation of China and the Chinese Science Fou
文摘From the SAT physical model, a physical hypothesis named PHHY is proposed. By PHHY, it is proved that there is a universally efficient algorithm for solving SAT problem. Then, by square packing problem, the authors show that there are interesting industrial NP-complete problems which can be solved through SAT algorithms, but each way of solving like this will be much worse than that of a certain direct solving.
