The Stokes shift response function, which is related to the time dependent solvation energy, is calculated with the dielectric response function and a novel expression of nonequilibrium solvation energy. In the deriva...The Stokes shift response function, which is related to the time dependent solvation energy, is calculated with the dielectric response function and a novel expression of nonequilibrium solvation energy. In the derivation, relationship between the polarization and the dielectric response function is used. With the dipole-in-a-sphere model applied to the system coumarin 343 and water as the solvent, encouraging agreement with the experimental data from Jimenez et al. is obtained [Nature 369, 471 （1994）].展开更多
This paper proposes a method to ascertain the stability of two dimensional linear time invariant discrete system within the shifted unit circle which is represented by the form of characteristic equation. Further an e...This paper proposes a method to ascertain the stability of two dimensional linear time invariant discrete system within the shifted unit circle which is represented by the form of characteristic equation. Further an equivalent single dimensional characteristic equation is formed from the two dimensional characteristic equation then the stability formulation in the left half of Z-plane, where the roots of characteristic equation f(Z) = 0 should lie within the shifted unit circle. The coefficient of the unit shifted characteristic equation is suitably arranged in the form of matrix and the inner determinants are evaluated using proposed Jury’s concept. The proposed stability technique is simple and direct. It reduces the computational cost. An illustrative example shows the applicability of the proposed scheme.展开更多
文摘The Stokes shift response function, which is related to the time dependent solvation energy, is calculated with the dielectric response function and a novel expression of nonequilibrium solvation energy. In the derivation, relationship between the polarization and the dielectric response function is used. With the dipole-in-a-sphere model applied to the system coumarin 343 and water as the solvent, encouraging agreement with the experimental data from Jimenez et al. is obtained [Nature 369, 471 （1994）].
文摘This paper proposes a method to ascertain the stability of two dimensional linear time invariant discrete system within the shifted unit circle which is represented by the form of characteristic equation. Further an equivalent single dimensional characteristic equation is formed from the two dimensional characteristic equation then the stability formulation in the left half of Z-plane, where the roots of characteristic equation f(Z) = 0 should lie within the shifted unit circle. The coefficient of the unit shifted characteristic equation is suitably arranged in the form of matrix and the inner determinants are evaluated using proposed Jury’s concept. The proposed stability technique is simple and direct. It reduces the computational cost. An illustrative example shows the applicability of the proposed scheme.
