The simultaneous diagonalization by congruence of pairs of Hermitian quaternion matrices is discussed. The problem is reduced to a parallel one on complex matrices by using the complex adjoint matrix related to each q...The simultaneous diagonalization by congruence of pairs of Hermitian quaternion matrices is discussed. The problem is reduced to a parallel one on complex matrices by using the complex adjoint matrix related to each quaternion matrix. It is proved that any two semi-positive definite Hermitian quaternion matrices can be simultaneously diagonalized by congruence.展开更多
Hexagonal and triangular monodisperse Fe3O4 nanosheets have been synthesized via a two-step microemulsion solvothermal approach in which uniform Fe3O4 nanoparticles are first prepared and then these hydrophobic nanocr...Hexagonal and triangular monodisperse Fe3O4 nanosheets have been synthesized via a two-step microemulsion solvothermal approach in which uniform Fe3O4 nanoparticles are first prepared and then these hydrophobic nanocrystals are dispersed in a uniform microemulsion environment as "seeds" for further re-growth through a secondary solvothermal process. The growth of anisotropic morphologies has been explained by the presence and orientation of twin planes in the face-centered cubic Fe3O4 which direct the shape of the growing particles. In particular, reentrant grooves resulting from twin planes are favorable sites for the addition of adatoms, leading to anisotropic growth. Triangular nanosheets are believed to contain one twin face which directs the growth of the primary particles in two dimensions. Hexagonal nanosheets are believed to contain two parallel planes that allow the growth edges to regenerate one another. The growth mechanism is evidenced by the analysis of high-resolution transmission electron microscopy (HRTEM) results and the as-prepared Fe3O4 nanoparticles have been shown to be an effective catalyst in the synthesis of quinoxaline.展开更多
We are going to prove that the Monopole and the Coulomb fields are duals within the unifying structure provided by the Reissner–Nordstr¨om spacetime. This is accomplished when noticing that in order to produce t...We are going to prove that the Monopole and the Coulomb fields are duals within the unifying structure provided by the Reissner–Nordstr¨om spacetime. This is accomplished when noticing that in order to produce the tetrad that locally and covariantly diagonalizes the stress-energy tensor, both the Monopole and the Coulomb fields are necessary in the construction. Without any of them it would be impossible to express the tetrad vectors that locally and covariantly diagonalize the stress-energy tensor. Then, both electromagnetic fields are an integral part of the same structure, the Reissner–Nordstr¨om geometry.展开更多
基金supported by NSFC(No.11371133)the Natural Science Foundation Project of CQ(No.cstc2014jcyjA00041,No.cstc2014jcyjA00054)Chongqing Municipal Education Commission(No.KJ1401106)
文摘The simultaneous diagonalization by congruence of pairs of Hermitian quaternion matrices is discussed. The problem is reduced to a parallel one on complex matrices by using the complex adjoint matrix related to each quaternion matrix. It is proved that any two semi-positive definite Hermitian quaternion matrices can be simultaneously diagonalized by congruence.
基金This work was supported by the National Natural Science Foundation ol: China (Nos. 20901069, 50873093, and 21271156) and the Henan Province Scientific and Technological Research Program (No. 092102210054).
文摘Hexagonal and triangular monodisperse Fe3O4 nanosheets have been synthesized via a two-step microemulsion solvothermal approach in which uniform Fe3O4 nanoparticles are first prepared and then these hydrophobic nanocrystals are dispersed in a uniform microemulsion environment as "seeds" for further re-growth through a secondary solvothermal process. The growth of anisotropic morphologies has been explained by the presence and orientation of twin planes in the face-centered cubic Fe3O4 which direct the shape of the growing particles. In particular, reentrant grooves resulting from twin planes are favorable sites for the addition of adatoms, leading to anisotropic growth. Triangular nanosheets are believed to contain one twin face which directs the growth of the primary particles in two dimensions. Hexagonal nanosheets are believed to contain two parallel planes that allow the growth edges to regenerate one another. The growth mechanism is evidenced by the analysis of high-resolution transmission electron microscopy (HRTEM) results and the as-prepared Fe3O4 nanoparticles have been shown to be an effective catalyst in the synthesis of quinoxaline.
文摘We are going to prove that the Monopole and the Coulomb fields are duals within the unifying structure provided by the Reissner–Nordstr¨om spacetime. This is accomplished when noticing that in order to produce the tetrad that locally and covariantly diagonalizes the stress-energy tensor, both the Monopole and the Coulomb fields are necessary in the construction. Without any of them it would be impossible to express the tetrad vectors that locally and covariantly diagonalize the stress-energy tensor. Then, both electromagnetic fields are an integral part of the same structure, the Reissner–Nordstr¨om geometry.