In this paper, the definition of three-order form invariance is given. Then the relation between the three-order form invariance and the three-order Lie symmetry is discussed and the sufficient and necessary condition...In this paper, the definition of three-order form invariance is given. Then the relation between the three-order form invariance and the three-order Lie symmetry is discussed and the sufficient and necessary condition of Lie symmetry, which comes from the three-order form invariance, is obtained. Finally a three-order Hojman conserved quantity is studied and an example is given to illustrate the application of the obtained results.展开更多
Based on the infinitesimal and one parameter transformation, the problem of Lie symmetry of three-order Lagrangian equations has been studied. Under Lie transformation, the sufficient and necessary condition which kee...Based on the infinitesimal and one parameter transformation, the problem of Lie symmetry of three-order Lagrangian equations has been studied. Under Lie transformation, the sufficient and necessary condition which keeps three-order Lagrangian equations to be unchanged and the invariant are obtained in this paper.展开更多
Based on the three-order Lagrangian equation, pseudo-Hamilton actoon I^＊ is defined and the three-order Hamilton＇s principle and the conditions are obtained in the paper. Then, the Noether symmetry about three-order...Based on the three-order Lagrangian equation, pseudo-Hamilton actoon I^＊ is defined and the three-order Hamilton＇s principle and the conditions are obtained in the paper. Then, the Noether symmetry about three-order Lagrangian equations is deduced. Finally, an example is given to illustrate the application of the result.展开更多
Based on the three-order Lagrangian equations, Hamilton＇s function of acceleration H^＊ and generalized acceleration momentum P^＊α are defined, and pseudo-Hamilton canonical equations corresponding to three-order L...Based on the three-order Lagrangian equations, Hamilton＇s function of acceleration H^＊ and generalized acceleration momentum P^＊α are defined, and pseudo-Hamilton canonical equations corresponding to three-order Lagrangian equations are obtained. The equations are similar to Hamilton＇s canonical equations of analytical mechanics in form.展开更多
A new layered yttrium iodate[Y(IO3)3(H2O)2]n(1)has been prepared from the hydrothermal reaction of Y(NO3)3?6H2O with I2O5 at 170℃,and its structure was determined by X-ray single-crystal diffraction method.It belongs...A new layered yttrium iodate[Y(IO3)3(H2O)2]n(1)has been prepared from the hydrothermal reaction of Y(NO3)3?6H2O with I2O5 at 170℃,and its structure was determined by X-ray single-crystal diffraction method.It belongs to the triclinic system,space group P1 with a=7.355(5),b=7.515(5),c=9.413(7)?,α=79.65(2)o,β=85.18(3)o,γ=71.870(19)o,Z=2,V=486.2(6)?3.1 was further characterized by FTIR,powder X-ray diffraction(PXRD)and UV-Vis spectra.In 1,the Y centers in a monocapped trigonal prism environment are bound by IO-3 anion and unique circle-shaped I4O12 polyiodate anion to generate a wave-like 2-D layer.The adjacent layers are further linked with each other by hydrogen bonds to form a quasi-3-D supramolecular network.1 exhibits a reverse saturation absorption and a self-defocusing effect with the nonlinear absorption coefficientβbeing–0.66×10-5 mW-1,which stems mainly from the electron transition from O-2p to I-5p orbital within iodates upon theoretical calculation.展开更多
文摘In this paper, the definition of three-order form invariance is given. Then the relation between the three-order form invariance and the three-order Lie symmetry is discussed and the sufficient and necessary condition of Lie symmetry, which comes from the three-order form invariance, is obtained. Finally a three-order Hojman conserved quantity is studied and an example is given to illustrate the application of the obtained results.
文摘Based on the infinitesimal and one parameter transformation, the problem of Lie symmetry of three-order Lagrangian equations has been studied. Under Lie transformation, the sufficient and necessary condition which keeps three-order Lagrangian equations to be unchanged and the invariant are obtained in this paper.
文摘Based on the three-order Lagrangian equation, pseudo-Hamilton actoon I^＊ is defined and the three-order Hamilton＇s principle and the conditions are obtained in the paper. Then, the Noether symmetry about three-order Lagrangian equations is deduced. Finally, an example is given to illustrate the application of the result.
文摘Based on the three-order Lagrangian equations, Hamilton＇s function of acceleration H^＊ and generalized acceleration momentum P^＊α are defined, and pseudo-Hamilton canonical equations corresponding to three-order Lagrangian equations are obtained. The equations are similar to Hamilton＇s canonical equations of analytical mechanics in form.
文摘A new layered yttrium iodate[Y(IO3)3(H2O)2]n(1)has been prepared from the hydrothermal reaction of Y(NO3)3?6H2O with I2O5 at 170℃,and its structure was determined by X-ray single-crystal diffraction method.It belongs to the triclinic system,space group P1 with a=7.355(5),b=7.515(5),c=9.413(7)?,α=79.65(2)o,β=85.18(3)o,γ=71.870(19)o,Z=2,V=486.2(6)?3.1 was further characterized by FTIR,powder X-ray diffraction(PXRD)and UV-Vis spectra.In 1,the Y centers in a monocapped trigonal prism environment are bound by IO-3 anion and unique circle-shaped I4O12 polyiodate anion to generate a wave-like 2-D layer.The adjacent layers are further linked with each other by hydrogen bonds to form a quasi-3-D supramolecular network.1 exhibits a reverse saturation absorption and a self-defocusing effect with the nonlinear absorption coefficientβbeing–0.66×10-5 mW-1,which stems mainly from the electron transition from O-2p to I-5p orbital within iodates upon theoretical calculation.
