This study sets up two new merit functions,which are minimized for the detection of real eigenvalue and complex eigenvalue to address nonlinear eigenvalue problems.For each eigen-parameter the vector variable is solve...This study sets up two new merit functions,which are minimized for the detection of real eigenvalue and complex eigenvalue to address nonlinear eigenvalue problems.For each eigen-parameter the vector variable is solved from a nonhomogeneous linear system obtained by reducing the number of eigen-equation one less,where one of the nonzero components of the eigenvector is normalized to the unit and moves the column containing that component to the right-hand side as a nonzero input vector.1D and 2D golden section search algorithms are employed to minimize the merit functions to locate real and complex eigenvalues.Simultaneously,the real and complex eigenvectors can be computed very accurately.A simpler approach to the nonlinear eigenvalue problems is proposed,which implements a normalization condition for the uniqueness of the eigenvector into the eigenequation directly.The real eigenvalues can be computed by the fictitious time integration method(FTIM),which saves computational costs compared to the one-dimensional golden section search algorithm(1D GSSA).The simpler method is also combined with the Newton iterationmethod,which is convergent very fast.All the proposed methods are easily programmed to compute the eigenvalue and eigenvector with high accuracy and efficiency.展开更多
Four new species of Elaphoglossum sect. Elaphoglossum are described: E. Amparoanum A. Rojas, E. Chocoense A. Rojas, E. Fayorum A. Rojas and E. Luciae A. Rojas. The first species is related to E. Variolatum Mickel, but...Four new species of Elaphoglossum sect. Elaphoglossum are described: E. Amparoanum A. Rojas, E. Chocoense A. Rojas, E. Fayorum A. Rojas and E. Luciae A. Rojas. The first species is related to E. Variolatum Mickel, but differs from it by having rhizome scales bicolorous and long ciliate margin. The second species is different to E. moranii Mickel by having narrower rhizome, shorter stipe, elliptic blade, attenuate blade base, shorter fertile fronds with blackish costa and present at lower altitudinal distribution. After that, the third species differs from E. lingua (C. Presl) Brack. by pale rhizome scales with long ciliate margin, shorter fronds and blade scales denser and lighter. Finally, the fourth species is related to E. atrosquamatum Mickel, but with relative longer fronds and broader blade. The geographical distributions of E. guatemalense (Klotzsch) T. Moore, E. longicrure Christ, E. minutum (Pohl ex Fée) T. Moore and E. nicaragüense A. Rojas are expanded.展开更多
对特产于湖南省桃源县的桃源野桐Mallotus taoyuanensis C.L.Peng et L.H.Yan的生物生态学特性进行了系统观察与研究,并与世界上自然分布的140余种野桐属植物的分类学特征进行了分析比较与探讨。研究发现:桃源野桐叶互生、羽状叶脉、叶...对特产于湖南省桃源县的桃源野桐Mallotus taoyuanensis C.L.Peng et L.H.Yan的生物生态学特性进行了系统观察与研究,并与世界上自然分布的140余种野桐属植物的分类学特征进行了分析比较与探讨。研究发现:桃源野桐叶互生、羽状叶脉、叶基下延、叶型大小极不一致的组合特征完全不同于野桐属现有组的特征,因此成立一新组桃源野桐组Sect.Qiana C.L.Peng et L.H.Yan,以完善野桐属组一级的分类系统。展开更多
基金the National Science and Tech-nology Council,Taiwan for their financial support(Grant Number NSTC 111-2221-E-019-048).
文摘This study sets up two new merit functions,which are minimized for the detection of real eigenvalue and complex eigenvalue to address nonlinear eigenvalue problems.For each eigen-parameter the vector variable is solved from a nonhomogeneous linear system obtained by reducing the number of eigen-equation one less,where one of the nonzero components of the eigenvector is normalized to the unit and moves the column containing that component to the right-hand side as a nonzero input vector.1D and 2D golden section search algorithms are employed to minimize the merit functions to locate real and complex eigenvalues.Simultaneously,the real and complex eigenvectors can be computed very accurately.A simpler approach to the nonlinear eigenvalue problems is proposed,which implements a normalization condition for the uniqueness of the eigenvector into the eigenequation directly.The real eigenvalues can be computed by the fictitious time integration method(FTIM),which saves computational costs compared to the one-dimensional golden section search algorithm(1D GSSA).The simpler method is also combined with the Newton iterationmethod,which is convergent very fast.All the proposed methods are easily programmed to compute the eigenvalue and eigenvector with high accuracy and efficiency.
基金This work was supported by the Special Foundation for the National Science and Technology Basic Research Program of China(Grant No.SQ2021FY010017)the National Wild Seed Resource Center(Grant No.ZWGX1809).
文摘Four new species of Elaphoglossum sect. Elaphoglossum are described: E. Amparoanum A. Rojas, E. Chocoense A. Rojas, E. Fayorum A. Rojas and E. Luciae A. Rojas. The first species is related to E. Variolatum Mickel, but differs from it by having rhizome scales bicolorous and long ciliate margin. The second species is different to E. moranii Mickel by having narrower rhizome, shorter stipe, elliptic blade, attenuate blade base, shorter fertile fronds with blackish costa and present at lower altitudinal distribution. After that, the third species differs from E. lingua (C. Presl) Brack. by pale rhizome scales with long ciliate margin, shorter fronds and blade scales denser and lighter. Finally, the fourth species is related to E. atrosquamatum Mickel, but with relative longer fronds and broader blade. The geographical distributions of E. guatemalense (Klotzsch) T. Moore, E. longicrure Christ, E. minutum (Pohl ex Fée) T. Moore and E. nicaragüense A. Rojas are expanded.
文摘对特产于湖南省桃源县的桃源野桐Mallotus taoyuanensis C.L.Peng et L.H.Yan的生物生态学特性进行了系统观察与研究,并与世界上自然分布的140余种野桐属植物的分类学特征进行了分析比较与探讨。研究发现:桃源野桐叶互生、羽状叶脉、叶基下延、叶型大小极不一致的组合特征完全不同于野桐属现有组的特征,因此成立一新组桃源野桐组Sect.Qiana C.L.Peng et L.H.Yan,以完善野桐属组一级的分类系统。
