In this paper,we consider the truncated multiplicity finite range set problem of meromorphic functions on some complex disc.By using the value distribution theory of meromorphic functions,we establish a second main th...In this paper,we consider the truncated multiplicity finite range set problem of meromorphic functions on some complex disc.By using the value distribution theory of meromorphic functions,we establish a second main theorem for meromorphic functions with finite growth index which share meromorphic functions(may not be small functions).As its application,we also extend the result of a finite range set with truncated multiplicity.展开更多
The pinwheel pattern as a suitable and advantageous alternative for the loading implementation of the pallet loading problem （PLP） is identified after a survey on the loading pattern. The definitions, elements, cate...The pinwheel pattern as a suitable and advantageous alternative for the loading implementation of the pallet loading problem （PLP） is identified after a survey on the loading pattern. The definitions, elements, categories, generating algorithms of the pinwheel pattern are discussed and a uniform symmetric pinwheel notation is proposed. Based on the forming geometry of a pinwheel, the pinwheel structure is analyzed in terms of the innate box ratio, the box/block orientation and the box number by combinatorial and geometrical methods. A revised data set for the PLP with an area ratio range from 1 to 76 and a box ratio range from 1 to 10 is proposed. All pinwheel instances with this data set are calculated, and box ratio range is obtained for each possible pinwheel pattern, which can be found for all non-prime numbers of boxes. And a high box ratio makes an optimal pinwheel pattern more likely appear. Results identify the impact of the above pinwheel pattern and the box ratio on the pallet loading problem.展开更多
基金Supported by National Natural Science Foundation of China(12061041)Jiangxi Provincial Natural Science Foundation(20232BAB201003).
文摘In this paper,we consider the truncated multiplicity finite range set problem of meromorphic functions on some complex disc.By using the value distribution theory of meromorphic functions,we establish a second main theorem for meromorphic functions with finite growth index which share meromorphic functions(may not be small functions).As its application,we also extend the result of a finite range set with truncated multiplicity.
基金The National Natural Science Foundation of China(No.70571033,70831002)
文摘The pinwheel pattern as a suitable and advantageous alternative for the loading implementation of the pallet loading problem （PLP） is identified after a survey on the loading pattern. The definitions, elements, categories, generating algorithms of the pinwheel pattern are discussed and a uniform symmetric pinwheel notation is proposed. Based on the forming geometry of a pinwheel, the pinwheel structure is analyzed in terms of the innate box ratio, the box/block orientation and the box number by combinatorial and geometrical methods. A revised data set for the PLP with an area ratio range from 1 to 76 and a box ratio range from 1 to 10 is proposed. All pinwheel instances with this data set are calculated, and box ratio range is obtained for each possible pinwheel pattern, which can be found for all non-prime numbers of boxes. And a high box ratio makes an optimal pinwheel pattern more likely appear. Results identify the impact of the above pinwheel pattern and the box ratio on the pallet loading problem.
