Extracting approximate symmetry planes is a challenge due to the difficulty of accurately measuring numerical values. Introducing the approximate symmetry planes of a 3D point set, this paper presents a new method by ...Extracting approximate symmetry planes is a challenge due to the difficulty of accurately measuring numerical values. Introducing the approximate symmetry planes of a 3D point set, this paper presents a new method by gathering normal vectors of potential of the planes, clustering the high probability ones, and then testing and verifying the planes. An experiment showed that the method is effective, robust and universal for extracting the complete approximate planes of symmetry of a random 3D point set.展开更多
This paper studies the symmetry, with respect to the real axis, of the point spectrum of the upper triangular infinite dimensional Hamiltonian operator H. Note that the point spectrum of H can be described as σp（H）...This paper studies the symmetry, with respect to the real axis, of the point spectrum of the upper triangular infinite dimensional Hamiltonian operator H. Note that the point spectrum of H can be described as σp（H） = σp （A） U σp1 （-A＊）. Using the characteristic of the set σp1（-A＊）, we divide the point spectrum σp （d） of A into three disjoint parts. Then, a necessary and sufficient condition is obtained under which σp1（-A＊） and one part of σp（A） are symmetric with respect to the real axis each other. Based on this result, the symmetry of σp（H） is completely given. Moreover, the above result is applied to thin plates on elastic foundation, plane elasticity problems and harmonic equations.展开更多
In three-dimensional noncentrosymmetric materials two-fold screw rotation symmetry forces electron＇s energy bands to have Weyl points at which two bands touch. This is illustrated for space groups No. 19 （P212121 ）...In three-dimensional noncentrosymmetric materials two-fold screw rotation symmetry forces electron＇s energy bands to have Weyl points at which two bands touch. This is illustrated for space groups No. 19 （P212121 ） and No. 198 （P213）, which have three orthogonal screw rotation axes. In the case of space groups No. 61 （Pbca） and No. 205 （Pa-3） that have extra inversion symmetry, Weyl points are promoted to four-fold degenerate line nodes in glide-invariant planes. The three-fold rotation symmetry present in the space groups No. 198 and No. 205 allows Weyl and Dirac points, respectively, to appear along its rotation axes in the Brillouin zone and generates four-fold and six-fold degeneracy at the F point and R point, respectively.展开更多
The braided geometry structures are analyzed with point groups and space groups for which the continuous yarn of the braided preforms is segmented and expressed in some special symbols. All structures of braided mater...The braided geometry structures are analyzed with point groups and space groups for which the continuous yarn of the braided preforms is segmented and expressed in some special symbols. All structures of braided material are described and classified with group theory, and new braiding methods are found. The group theory analysis lays the theo-retical foundation for optimizing material performance.展开更多
文摘Extracting approximate symmetry planes is a challenge due to the difficulty of accurately measuring numerical values. Introducing the approximate symmetry planes of a 3D point set, this paper presents a new method by gathering normal vectors of potential of the planes, clustering the high probability ones, and then testing and verifying the planes. An experiment showed that the method is effective, robust and universal for extracting the complete approximate planes of symmetry of a random 3D point set.
基金Supported by the National Natural Science Foundation of China (No. 11061019, 10962004, 11101200)the Chunhui Program of Ministry of Education of China (No. Z2009-1-01010)+1 种基金the Natural Science Foundation of Inner Mongolia (No. 2010MS0110, 2009BS0101)the Cultivation of Innovative Talent of ‘211 Project’ of Inner Mongolia University
文摘This paper studies the symmetry, with respect to the real axis, of the point spectrum of the upper triangular infinite dimensional Hamiltonian operator H. Note that the point spectrum of H can be described as σp（H） = σp （A） U σp1 （-A＊）. Using the characteristic of the set σp1（-A＊）, we divide the point spectrum σp （d） of A into three disjoint parts. Then, a necessary and sufficient condition is obtained under which σp1（-A＊） and one part of σp（A） are symmetric with respect to the real axis each other. Based on this result, the symmetry of σp（H） is completely given. Moreover, the above result is applied to thin plates on elastic foundation, plane elasticity problems and harmonic equations.
基金supported by JSPS Kakenhi(No.15K05141)from Japan Society for the Promotion of Science
文摘In three-dimensional noncentrosymmetric materials two-fold screw rotation symmetry forces electron＇s energy bands to have Weyl points at which two bands touch. This is illustrated for space groups No. 19 （P212121 ） and No. 198 （P213）, which have three orthogonal screw rotation axes. In the case of space groups No. 61 （Pbca） and No. 205 （Pa-3） that have extra inversion symmetry, Weyl points are promoted to four-fold degenerate line nodes in glide-invariant planes. The three-fold rotation symmetry present in the space groups No. 198 and No. 205 allows Weyl and Dirac points, respectively, to appear along its rotation axes in the Brillouin zone and generates four-fold and six-fold degeneracy at the F point and R point, respectively.
文摘The braided geometry structures are analyzed with point groups and space groups for which the continuous yarn of the braided preforms is segmented and expressed in some special symbols. All structures of braided material are described and classified with group theory, and new braiding methods are found. The group theory analysis lays the theo-retical foundation for optimizing material performance.
