In 2014, Vargas first defined a super-shuffle product and a cut-box coproduct on permutations. In 2020, Aval, Bergeron and Machacek introduced the super-shuffle product and the cut-box coproduct on labeled simple grap...In 2014, Vargas first defined a super-shuffle product and a cut-box coproduct on permutations. In 2020, Aval, Bergeron and Machacek introduced the super-shuffle product and the cut-box coproduct on labeled simple graphs. In this paper, we generalize the super-shuffle product and the cut-box coproduct from labeled simple graphs to (0,1)-matrices. Then we prove that the vector space spanned by (0,1)-matrices with the super-shuffle product is a graded algebra and with the cut-box coproduct is a graded coalgebra.展开更多
In order to evaluate the productivity of reclamation lands in mining districts, field investigation and spatial information technique were adopted to investigate influence factors of land. Based on the collected data ...In order to evaluate the productivity of reclamation lands in mining districts, field investigation and spatial information technique were adopted to investigate influence factors of land. Based on the collected data of each land, membership grade of each factor was obtained based on Fuzzy logic, and combined weight of each factor was got by analytica1 hierarch process and Delphi method. According to membership grades and combined weights of all factors, integrated fertility index (IFI) of every land was calculated to reflect levels of the productivity of reclamation lands in mining districts. Experimental results show that spatial information technique is an efficient method in field data collection, while lack of evaluation data. By means of quantificational analysis of this method, IFI is appropriate to describe the productive capacity level of reclamation lands.展开更多
文摘In 2014, Vargas first defined a super-shuffle product and a cut-box coproduct on permutations. In 2020, Aval, Bergeron and Machacek introduced the super-shuffle product and the cut-box coproduct on labeled simple graphs. In this paper, we generalize the super-shuffle product and the cut-box coproduct from labeled simple graphs to (0,1)-matrices. Then we prove that the vector space spanned by (0,1)-matrices with the super-shuffle product is a graded algebra and with the cut-box coproduct is a graded coalgebra.
基金Project(41061043)supported by the National Natural Science Foundation of ChinaProject(2010CD032)supported by the Natural Science Foundation of Yunnan Province,China
文摘In order to evaluate the productivity of reclamation lands in mining districts, field investigation and spatial information technique were adopted to investigate influence factors of land. Based on the collected data of each land, membership grade of each factor was obtained based on Fuzzy logic, and combined weight of each factor was got by analytica1 hierarch process and Delphi method. According to membership grades and combined weights of all factors, integrated fertility index (IFI) of every land was calculated to reflect levels of the productivity of reclamation lands in mining districts. Experimental results show that spatial information technique is an efficient method in field data collection, while lack of evaluation data. By means of quantificational analysis of this method, IFI is appropriate to describe the productive capacity level of reclamation lands.
