Some mathematical aspects of the Lie groups SU (2) and in realization by two pairs of boson annihilation and creation operators and in the parametrization by the vector parameter instead of the Euler angles and ...Some mathematical aspects of the Lie groups SU (2) and in realization by two pairs of boson annihilation and creation operators and in the parametrization by the vector parameter instead of the Euler angles and the vector parameter c of Fyodorov are developed. The one-dimensional root scheme of SU (2) is embedded in two-dimensional root schemes of some higher Lie groups, in particular, in inhomogeneous Lie groups and is represented in text and figures. The two-dimensional fundamental representation of SU (2) is calculated and from it the composition law for the product of two transformations and the most important decompositions of general transformations in special ones are derived. Then the transition from representation of SU (2) to of is made where in addition to the parametrization by vector the convenient parametrization by vector c is considered and the connections are established. The measures for invariant integration are derived for and for SU (2) . The relations between 3D-rotations of a unit sphere to fractional linear transformations of a plane by stereographic projection are discussed. All derivations and representations are tried to make in coordinate-invariant way.展开更多
In seasonal frozen soil region,the engineering geological properties of loess-like soil will be deteriorated after freeze-thaw cycles.Through the freeze-thaw cycle experiment of remolded loess-like soil,under differen...In seasonal frozen soil region,the engineering geological properties of loess-like soil will be deteriorated after freeze-thaw cycles.Through the freeze-thaw cycle experiment of remolded loess-like soil,under different freezing temperatures,the authors carried out freeze-thaw cycle tests for 3 times and 20 times,respectively.With mercury intrusion porosimetry and granulometric analysis,from the micro-structure,the authors studied the law that freeze-thaw cycle times and frozen temperature effect on the variation of microscopic pore of loesslike soil.This result can provide theoretical basis for comprehensive treatment of problems in the construction of the project in seasonal frozen loess-like soil region.展开更多
文摘Some mathematical aspects of the Lie groups SU (2) and in realization by two pairs of boson annihilation and creation operators and in the parametrization by the vector parameter instead of the Euler angles and the vector parameter c of Fyodorov are developed. The one-dimensional root scheme of SU (2) is embedded in two-dimensional root schemes of some higher Lie groups, in particular, in inhomogeneous Lie groups and is represented in text and figures. The two-dimensional fundamental representation of SU (2) is calculated and from it the composition law for the product of two transformations and the most important decompositions of general transformations in special ones are derived. Then the transition from representation of SU (2) to of is made where in addition to the parametrization by vector the convenient parametrization by vector c is considered and the connections are established. The measures for invariant integration are derived for and for SU (2) . The relations between 3D-rotations of a unit sphere to fractional linear transformations of a plane by stereographic projection are discussed. All derivations and representations are tried to make in coordinate-invariant way.
文摘In seasonal frozen soil region,the engineering geological properties of loess-like soil will be deteriorated after freeze-thaw cycles.Through the freeze-thaw cycle experiment of remolded loess-like soil,under different freezing temperatures,the authors carried out freeze-thaw cycle tests for 3 times and 20 times,respectively.With mercury intrusion porosimetry and granulometric analysis,from the micro-structure,the authors studied the law that freeze-thaw cycle times and frozen temperature effect on the variation of microscopic pore of loesslike soil.This result can provide theoretical basis for comprehensive treatment of problems in the construction of the project in seasonal frozen loess-like soil region.
