This paper deals with the Verma module of quantum group U_q(B₂) when q is a root of 1. It estimates how many classes of Verma submodules which are not isomorphic to each other are contained in Verma module. The character of irreducible highest weight module of U_q(B₂) has also been given.

In this letter, the strong symmetry and its inverse are first given, and then six sets of symmetry of the variable coefficient modified Korteweg-de Vries (mKdV) equation are obtained, finally the variable coefficient mKdV hierarchy is discussed.

Making use of the generalized tortoise transformation, the radial part of the Klein-Gordon equation can be reduced to the standard wave equation around the event horizon in the higher dimensional Vaidya space-time. Both the location of event horizon and the radiation temperature of black hole are shown automatically.

A modified method of absolute efficiency calibration for germanium detector has been developed based on the fact that the intensities of capture γ-rays can be determined by the 1368KeV γ-rays from sodium activation when a NaCI sample is irradiated by thermal neutrons. As a verification of this method, the intensity of the 4.44MeV γ-ray from an Am-Be neutron source was determined.

We compare modern variational and nonvariational calculations of molecular scattering and present for H₂Br system the selected numerically exact state-to-state reaction probabilities obtained from quantum variational scattering calculations, on the most accurate available potential energy surface.

In this report, a modified ‘position dispersion’ method, in which the detecting aperture in the far-field is replaced by a circular board, is given to enhance the measurement sensitivity of nonlinear index, while keeps the simplicity. An increase of 5 times in sensitivity is obtained in our experiment, in which we employed a solution to produce the thermally induced nonlinearity.

Auto-oscillations and chaotic behavior were investigated experimentally in a plasma system produced by discharge through mixing He-Ne gases. The glow power spectra and the differential phase-space portraits show period-doubling and Ruelle-Takens routes to chaos. Periodic windows embedded in chaos and multiple subharmonic bifurcations occurring in the windows were observed.

Ultra low q equilibrium with q_a < 0.1 isstudied on Southwestern Institute of Physics-Reversed Field Pinch (SWIP-RFP) device. The plasma current duration over 360μs is obtained. The edge safety factor q_a is about 0.056. The distribution of safety factor is decreased with the minor radius increasing.

Concentration-dependent Raman spectra of Y_1-xGd_xBa₂Cu₃O_7-δ(x=0.4, 0.6, 0.8 and 1.0) show that the Raman mode from O(4) bridging shifts upward due to the increased symmetry of crystal potential. The linewidth and intensity of 508cm^-1 mode are decreased and increased with increasing x, respectively which is attributed to the charge transfer from the CuO basal planes to the CuO₂ planes. Two second-order Raman modes at 798 and 896cm^-1 have been observed and confirmed.

The form of the bigger clusters composed of aggregate ultrafine Fe particles possesses obvious fractal character and regularity. With the increase of aggregate density, the extended, compensated and collapsed states emerge successively, and the fractal features are decreased. The ideal fractal dimension D₀ of magnetic aggregate clusters is suggested between 2 and 4.

By using local theory and taking into account retardation, we investigate the plasmonpolariton modes of a finite Cantor-type heterostructures which are composed of two alternating materials with their thicknesses following Cantor sequence. The effects of an external magnetic field applied parallel to the interfaces are considered. We find that the modes have fractal structure due to the special geometry of the system, and the dispersion relations of the modes are strikingly modified by the external magnetic field. Some new modes appear because of the application of the field. By plotting the profiles of the amplitudes of the electric field, we also investigate the localization properties of the modes.

A new type of inhomogeneous system was constructed by depositing Ag thin films on fractal surfaces. The I-V characteristics of such samples exhibit a non-linear effect in air and a voltage breakdown effect in vacuum. Based on the special structure geometry of the samples, these unusual phenomena can be explained by the random tunnelling junction model under different environment.

Samples of Bi_2.2Sr_1.8Ca_1.05Cu_2.15-xNa_xO_8+y (x=0, 0.7) were prepared by melt-processing technique. The maximum transition temperature increased up to 100 K, and T_c0 achieved 92.5K. In order to study the mechanism of T_c increasing, samples were annealed in a flowing oxygen, atmosphere. The reversibility of T_c was observed in undoped sample, while the T_c of Na-doped sample had no significant changes. We believe that the T_c is correlated with a redistribution of holes between the BiO layers and the CuO planes. Doping sodium changes the hole density of CuO planes into an “optimium” value so as to increase T_c.

The quantum X-Y model of interacting spins on square lattices is simulated by a loop-cluster algorithm. It is shown that the method can be used to simulate the systems efficiently at low temperatures for lattices as large as 32x32x200.

Fe/Cu compositionally modulated films made by rf sputtering were investigated with ferromagnetic resonance. Spin wave resonances related to interlayer exchange coupling were observed and the phase change of the spin wave was shared by both the Fe and Cu sublayers. The effective spin wave dispersion coefficient was found to increase with increasing thickness of Cu sublayers.

The electrical conductivity of the one-band Hubbard model on a two-dimensional square lattice at half-filling is studied through the grand canonical quantum Monte Calro method. Our results support that there exists an insulator-to-metal transition for the half-filled Hubbard model at high temperature.

The effects of the annealing temperature and time on the structure and magnetic properties of the sputtered BiDy-iron garnet films were investigated. X-ray diffraction analysis shows that the as-sputtered films are amorphous. After annealing at about 550°C, amorphous films crystallize into the garnet phase and an unknown phase. The intensity of the unknown phase decreases with increasing annealing temperature and time and vanishes at 650°C for 30min. It is found that the unknown phase has a large influence on the half-width of the (420) x-ray diffraction peak. The as-sputtered films have a very small magnetization of about 1 emu/g at room temperature. When films are annealed above 570°C, the magnetization increases rapidly with increasing annealing temperature and time.