A new periodic travelling wave solution of Kdv equation is obtained in manifold Diffs¹/ s¹ ( t ) which is relevant to the coadjoint orbit Diffs¹ / s¹ of Virasoro group.

Systematics of energy spectra and B(E2) with substantial improvements in the N_πN_v scheme are presented. The correlation of energy spectra over an extended region is pointed out and a simple explanation is given. A method for verifying the simple B(E2) systematics is also suggested.

Finite nucleus properties are studied in a relativistic effective interaction approach. Density dependent coupling constants of the meson-nucleon interactions are adopted to incorporate the relativistic Brueckner- Har tree-Fock results in the relativistic mean field (RMF) or relativistic Hartree-Fock (RHF) approach. It is desired to remedy the deficiencies of RMF and RHF without losing the features of the relativistic G matrix and at the same time retain the simplicity. The calculated ground state properties with the density dependent coupling constants are in a good agreement with experiment. The contribution of isovector mesons in RHF is discussed.

In the present work we used Hartree-Fock-Slater local-density discrete variational method to calculate the energy level of some rare earth doped BaF₂ crystals and proposed that the Eu, Dy and Yb elements will change their valence from +3 to +2 under irradiation and thus change the optical properties of the crystals. The results show that this radiation effect model is in good agreement with experiments.

Squeezing properties of field in the system of a Kerr medium embedded in a nondegenerate two-photon absorption cavity interacting with a two-mode uncorrelated coherent field are discussed. We find that both the two-mode squeezing and the sum squeezing of field can arise and can be enhanced due to the Kerr effect.

The density and surface tension of the K₂ O-Nb₂ O₅ molten system between 50 and 56mol% K₂ O melts were measured from 1080 to 1180°C. The concentration of K₂ O from 50 to 56mol% in melt not only caused the density of melt to decrease, but also induced the surface tension to decrease. Both composition gradient and the temperature coefficient of density exist extremum within this composition range. These properties are possibly employed to explain why the KNbO₃ crystal should be grown at the composition from 52 to 54mo1% K₂ O at above 1150°C.

Magnetron sputtered diamond-like carbon (DLC) films were irradiated by cw CO₂ laser. It was found that the laser irradiation increased the visible absorption, decreased the optical gap of DLC and decreased lightly the infrared transmittance. The absorption curves of the as-deposited and the irradiated films indicated that the irradiation decreased the hydrogen content and the sp³ hybrid structure and altered the absorption mode of C-CH₃.

A new system of Canter fractal models was created and studied, the density of states (DOS) as well as wavefunctions of the phonon in this kind of structure were calculated and discussed, in which it shows a new kind of branch rules for the DOS and new characteristics for the wavefunctions.

For a monatomic one-dimensional chain of particles interacting via a nearest-neighbor purely anharmonic potential of any even order (such a chain is called purely anharmonic chain), it is proved that there really exist exact localized modes.

The scaling and the scaling-relevant spectral properties of Penrose tiling are investigated. The fractal dimension d_f of this tiling is analytically obtained, which is two, equal to its Euclidean dimension. Similar to usual self-similar structure, the vibrational density of states for Penrose lattice is also found to follow a power law p(ω) ~ω^{d_s -1} with spectral dimension d_s= 2 , which accounts for a special vibrational excitation in quasicrystals: the fracton-like excitation, whose state is critical. The simulation of random walk on this Penrose lattice indicates that the diffusive dimension d_w= 2, thus the relation d_s = 2d_f/d_w holds.

Theoretical calculations of the quantum confined Stark shift for the first heavy hole exciton (hhl--el) in step quantum well are given. A significant change in Stark shift is achieved in specially stepped potential shape, which is more than two times larger than the conventional rectangular quantum well. The structure has the advantage of a large change in absorption, which is one of the best candidates for the optical modulators utilizing the quantum confined Stark effect (QCSE) in GaAs/AlGaAs. Relations between QCSE and stepped structure are discussed in the optimization for large Stark shift.

Introducing the coherent state ansatz and the time-dependent variational principle, we obtain the two partial different equations of motion from Hamiltonian. Employing the method of multiple scales, we reduce these equations into the envelope function equation and find the amplitude function satisfied a nonlinear Schrödinger equation. We get the periodic wave solution and analyse its stability antiferromagnet KCuF₃.

The Curie temperature and polarization in a ferroelectric cylinder with infinite length have been examined using Landau free energy expansion. The Curie temperature and polarization decrease with decreasing cylinder diameter for the positive extrapolation length, and reach zero at the critical size. For negative extrapolation length, both Curie temperature and polarization increase with decreasing cylinder diameter.

A novel idea is proposed to suppress the soliton self-frequency shift of femtosecond soliton pulse in dispersion-decreasing fibers. The expression of the soliton self-frequency shift as a function of the pulse width and the fiber dispersion parameter is derived. The numerical simulation is also given, and is in agreement with analytical results.

Raman spectra of LiNbO₃ crystals with different hydrogen-ion-exchanged time were examined. E(TO) and A₁ (TO) modes appear gradually in the transverse A₁- and E-symmetry spectra respectively with increasing the exchange time and the dependence of their intensities on the exchange time is also observed. We attribute these results to both the internal strains resulting from the ordering-disordering distribution of H ions in the sample and the enhanced photorefractive effect.

Diamond films have been grown on high pressure synthesized cubic boron nitride (c-BN) particles by hot-filament chemical vapor deposition method, and heteroepitaxial diamond films on the c-BN (100) facets with no-evident defects were obtained, but polycrystalline diamond films were formed only on the c-BN (111) facets.

Effect of hydrolysis catalysts (HCl and C₅H₈O₂) on structural evaluation of gelderived nanocrystalline TiO₂ powders was studied. Crystallization temperature of the HCl catalyzed gel is about 200K lower than that of the C₅H₈O₂ catalyzed one. But in the later gel the anatase phase transforms to rutile at a lower temperature, and the transformation is completed in a much more narrow temperature range.

The chromosome oscillation diving metaphase is explained as the result of fluctuation of forces exerted on the chromosome. In this letter a simple model for chromosome oscillation is proposed and the formulas of force fluctuation and the root mean square displacement of the chromosome in the oscillation are derived.