In this paper we use Böcklund transformation to construct soliton solutions for a coupled KdV system.This system was first proposed by Wang in 2010.First we generalize the well-known Bäcklund transformation ...In this paper we use Böcklund transformation to construct soliton solutions for a coupled KdV system.This system was first proposed by Wang in 2010.First we generalize the well-known Bäcklund transformation for the KdV equation to such coupled KdV system.Then from a trivial seed solution,we construct soliton solutions.We also give a nonlinear superposition formula,which allows us to generate multi-soliton solutions.展开更多
We obtain the non-local residual symmetry related to truncated Painlev~ expansion of Burgers equation. In order to localize the residual symmetry, we introduce new variables to prolong the original Burgers equation in...We obtain the non-local residual symmetry related to truncated Painlev~ expansion of Burgers equation. In order to localize the residual symmetry, we introduce new variables to prolong the original Burgers equation into a new system. By using Lie＇s first theorem, we obtain the finite transformation for the localized residual symmetry. More importantly, we also Iocalize the linear superposition of multiple residual symmetries to find the corresponding finite transformations. It is interesting to find that the n-th B^icklund transformation for Burgers equation can be expressed by determinants in a compact way.展开更多
A protocol is presented for genetically engineering loblolly pine (Pinus taeda L.) using particle bombardment. This protocol enabled the routine transformation of loblolly pine plants that were previously difficult to...A protocol is presented for genetically engineering loblolly pine (Pinus taeda L.) using particle bombardment. This protocol enabled the routine transformation of loblolly pine plants that were previously difficult to transform. Mature zygotic embryos were used to be bombarded and to generate organogenic callus and transgenic regenerated plants. Plasmid pB48.215 DNA contained a synthetic Bacillus thuringiensis (B.t.) cryIAc coding sequence flanked by the double cauliflower mosaic virus (CaMV) 35S promoter and nopaline synthase (Nos) terminator sequences, and the selectable marker gene, neomycin phosphotransferase II (nptII) controlled by the promoter of the nopaline synthase gene was introduced into loblolly pine tissues by particle bombardment. The transformed tissues were proliferated and selected by kanamycin resistance conferred by the introduced NPTII gene. Shoot regeneration was induced from the kanamycin-resistant callus, and transgenic plantlets were then produced. The presence of the introduced genes in the transgenic loblolly pine plants was confirmed by polymerase chain reactions (PCR) analysis, by Southern blot analysis, and insect feeding assays. The recovered transgenic plants were acclimatized and then established in soil.展开更多
In the paper, the author generalized the Hardy and Littlewood's theorem toBa space, i.e. for all Pm satisfying 1 < α = infpm≤ β≤ suppm < ∞, m = 1, 2,..., and the following inequalityholds if and on1y if.
基金Supported by the Jiangsu Higher School Undergraduate Innovation and Entrepreneurship Training Program(202311117078Y)。
文摘In this paper we use Böcklund transformation to construct soliton solutions for a coupled KdV system.This system was first proposed by Wang in 2010.First we generalize the well-known Bäcklund transformation for the KdV equation to such coupled KdV system.Then from a trivial seed solution,we construct soliton solutions.We also give a nonlinear superposition formula,which allows us to generate multi-soliton solutions.
基金supported by the National Natural Science Foundation of China(Grant Nos.11347183,11275129,11305106,11365017,and 11405110)the Natural Science Foundation of Zhejiang Province of China(Grant Nos.Y7080455 and LQ13A050001)
文摘We obtain the non-local residual symmetry related to truncated Painlev~ expansion of Burgers equation. In order to localize the residual symmetry, we introduce new variables to prolong the original Burgers equation into a new system. By using Lie＇s first theorem, we obtain the finite transformation for the localized residual symmetry. More importantly, we also Iocalize the linear superposition of multiple residual symmetries to find the corresponding finite transformations. It is interesting to find that the n-th B^icklund transformation for Burgers equation can be expressed by determinants in a compact way.
文摘A protocol is presented for genetically engineering loblolly pine (Pinus taeda L.) using particle bombardment. This protocol enabled the routine transformation of loblolly pine plants that were previously difficult to transform. Mature zygotic embryos were used to be bombarded and to generate organogenic callus and transgenic regenerated plants. Plasmid pB48.215 DNA contained a synthetic Bacillus thuringiensis (B.t.) cryIAc coding sequence flanked by the double cauliflower mosaic virus (CaMV) 35S promoter and nopaline synthase (Nos) terminator sequences, and the selectable marker gene, neomycin phosphotransferase II (nptII) controlled by the promoter of the nopaline synthase gene was introduced into loblolly pine tissues by particle bombardment. The transformed tissues were proliferated and selected by kanamycin resistance conferred by the introduced NPTII gene. Shoot regeneration was induced from the kanamycin-resistant callus, and transgenic plantlets were then produced. The presence of the introduced genes in the transgenic loblolly pine plants was confirmed by polymerase chain reactions (PCR) analysis, by Southern blot analysis, and insect feeding assays. The recovered transgenic plants were acclimatized and then established in soil.
基金Supported by the National Natural Science Foundation of China under Grant 61072145the Scientific Research Project of Beijing Educational Committee(SQKM201211232016)Beijing Excellent Talent Training Project(2013D005007000003)
文摘In the paper, the author generalized the Hardy and Littlewood's theorem toBa space, i.e. for all Pm satisfying 1 < α = infpm≤ β≤ suppm < ∞, m = 1, 2,..., and the following inequalityholds if and on1y if.
