Seeking invariants for blow-analytic equivalence

We introduce some blow-analytic invariants of real analytic function-germsand discuss their properties. As a consequence, we obtain, for instance, the multiplicity of function-germs is a blow-analytic invariant.     

Calculation of nuclear magnetic shieldings XIV. Relativistic mass—velocity corrected perturbation Hamiltonians

A two-component relativistic SCF perturbation theory, based on the Douglas—Kroll—Hess (DKH) transformation, has been applied to the calculation of nuclear magnetic shielding tensors of hydrogen halides, HX (X = F, Cl, Br, I). Calculations were performed via the unrestricted coupled Hartree—Fock (CHF) scheme using gauge-including atomic orbitals (GIAOs) at four different levels. In the level I calculation, both the scalar relativistic (SR) and spin—orbit (SO) interactions were included in the zero-order Hamiltonian. However, the magnetic pertubation Hamiltonians were treated non-relativistically. The results of these calculations indicated a large interplay between the SR and SO interactions. The level I calculation was found to be insufficient to explain the full relativistic effect on the halogen atom shieldings. In order to reproduce the full relativistic effect, the mass-velocity effect on the magnetic perturbation Hamiltonians was introduced in the levels II—IV calculations. Inclusion of the mass-velocity effects into all of the perturbation Hamiltonians made in levels III and IV improved the results greatly. The cross term between the nuclear attraction potential and the magnetic vector potential was introduced approximately in level IV. The level III calculation agreed most closely with the four-component relativistic random phase approximation (RPA) calculation.     

一族可积Hamilton方程

本文利用屠规彰格式,导出了一族新的可积系,包含４个未知函数,具有双Ｈａｍｉｌｔｏｎ结构,且以ＴＣ族为特例。