First of all, we investigate whether the transformation of Lemaître inevitably leads from the static de Sitter cosmos to an expanding cosmos. A Lorentz transformation which can be assigned to the Lema&ic...First of all, we investigate whether the transformation of Lemaître inevitably leads from the static de Sitter cosmos to an expanding cosmos. A Lorentz transformation which can be assigned to the Lemaître transformation results in a frame of reference that moves relatively to the static dS system. Because of the homogeneity of space, this applies to every point in the space which does not itself undergo any change. We interpret the “expansion” of the cosmos Milne-like. It is not the space that expands, but the mesh of the Lemaître coordinate system. The velocity parameter of the associated Lorentz transformation is geometrically based and shows that the joined observer systems are moving in free fall. We also discuss the question of whether the speed of light for free-falling observers in the universe can be reached or can be exceeded, respectively. We raise the question of whether the model can be extended in such a way that the motions take place with a velocity that is lower than the one of the free fall. We believe that the method we have derived can be generalized to models with genuine expansion.展开更多
In this paper,an approach of square coordinate transformation is proposed to approximate the spectral abscissa for continuous-time switched linear systems.By applying elementary transformations iteratively,a series of...In this paper,an approach of square coordinate transformation is proposed to approximate the spectral abscissa for continuous-time switched linear systems.By applying elementary transformations iteratively,a series of minimums of least μ1 matrix set measures are obtained,which are utilized to approximate the spectral abscissa of the switched system.The approach is developed into tractable numerical algorithms that provide upper bound estimates of the spectral abscissa.Numerical simulations show the effectiveness of the proposed method.展开更多
Elastic properties are important in fundamental understanding of multiferroic materials. However, up to now, there is no work about anisotropy of elastic properties in orthorhombic Ca_3Mn_2O_7. In this study, using co...Elastic properties are important in fundamental understanding of multiferroic materials. However, up to now, there is no work about anisotropy of elastic properties in orthorhombic Ca_3Mn_2O_7. In this study, using coordinate transformation method, we investigated basic elastic parameters(elastic constants c'_(ij)) and engineering elastic parameters(Young's modulus E, Poisson's ratio v, and the rigidity modulus G') of orthorhombic Ca_3Mn_2O_7 along arbitrary orientations. The detailed anisotropic characteristics of these parameters were presented. The results reveal the orientation related elastic properties in mm2 point group orthorhombic Ca_3Mn_2O_7.展开更多
In this paper of the series, the equations of motion for the spatial circular restricted three-body problem in sidereal spherical coordinates system were established. Initial value procedure that can be used to comput...In this paper of the series, the equations of motion for the spatial circular restricted three-body problem in sidereal spherical coordinates system were established. Initial value procedure that can be used to compute both the spherical and Cartesian sidereal coordinates and velocities was also developed. The application of the procedure was illustrated by numerical example and graphical representations of the variations of the two sidereal coordinate systems.展开更多
文摘First of all, we investigate whether the transformation of Lemaître inevitably leads from the static de Sitter cosmos to an expanding cosmos. A Lorentz transformation which can be assigned to the Lemaître transformation results in a frame of reference that moves relatively to the static dS system. Because of the homogeneity of space, this applies to every point in the space which does not itself undergo any change. We interpret the “expansion” of the cosmos Milne-like. It is not the space that expands, but the mesh of the Lemaître coordinate system. The velocity parameter of the associated Lorentz transformation is geometrically based and shows that the joined observer systems are moving in free fall. We also discuss the question of whether the speed of light for free-falling observers in the universe can be reached or can be exceeded, respectively. We raise the question of whether the model can be extended in such a way that the motions take place with a velocity that is lower than the one of the free fall. We believe that the method we have derived can be generalized to models with genuine expansion.
基金supported by the National Key Basic Research Program(973 Plan)under Grant No.2014CB845302the National Natural Science Foundation of China under Grant No.61273121
文摘In this paper,an approach of square coordinate transformation is proposed to approximate the spectral abscissa for continuous-time switched linear systems.By applying elementary transformations iteratively,a series of minimums of least μ1 matrix set measures are obtained,which are utilized to approximate the spectral abscissa of the switched system.The approach is developed into tractable numerical algorithms that provide upper bound estimates of the spectral abscissa.Numerical simulations show the effectiveness of the proposed method.
文摘Elastic properties are important in fundamental understanding of multiferroic materials. However, up to now, there is no work about anisotropy of elastic properties in orthorhombic Ca_3Mn_2O_7. In this study, using coordinate transformation method, we investigated basic elastic parameters(elastic constants c'_(ij)) and engineering elastic parameters(Young's modulus E, Poisson's ratio v, and the rigidity modulus G') of orthorhombic Ca_3Mn_2O_7 along arbitrary orientations. The detailed anisotropic characteristics of these parameters were presented. The results reveal the orientation related elastic properties in mm2 point group orthorhombic Ca_3Mn_2O_7.
文摘In this paper of the series, the equations of motion for the spatial circular restricted three-body problem in sidereal spherical coordinates system were established. Initial value procedure that can be used to compute both the spherical and Cartesian sidereal coordinates and velocities was also developed. The application of the procedure was illustrated by numerical example and graphical representations of the variations of the two sidereal coordinate systems.
