We extend the formal series symmetry theory proposed in Refs. [1-4] to the (2 + 1) dimensional discrete Toda equation. Two sets of infinitely many symmetries of this equation are found. Every one set of symmetries constitute a generalized W∞ algebra which contains the usual W∞ algebra as its subalgebra.
When and where a charged particle with given energy will enter or leave the magnetic field in a mass spectrometer, and how we use quantum mechanics to calculate them are interesting problems. The double-wave description of the system leads to the results that are similar to that of classical mechanics but the energies of particles take quantized discrete values.
We study the time evolution of a quantum system with Hamiltonian consisting of time-dependent linear combination of SU(1,1) and SU(2) generators. A proper hermitian invariant operator has been found to obtain not only closed formulas for the time evolution of quantum states but also the time evolution operators for both the SU(1, 1) and SU(2) systems. The time evolution operators have been used to investigate the time-dependent two photons and SU(2) squeezing states and squeezing properties of the time-dependent SU(1,1) coherent states.
The intrinsic absorption spectra of Hg1-xCdxTe semiconductor with energies above the band gap are presented by analyzing experimental results, Kane theory and some empirical laws. It is found that Anderson's theorical expression derived from the Kane model and Chu et al' s empirical rule obtained from the measured data agree well with the intrinsic optical absorption behaviour of Hg1-xCdxTe bulk thin films. Moreover, the intrinsic absorption of Hg1-xCdxTe epitaxial layer is discussed.
Partial cross sections of two-and three-neutrons evaporation channels following the fusion reaction 12C+93Nb have been measured for center-of-mass energies from 25.0 to 40.5 MeV by off-line γ technique. The total fusion cross sections and average angular momenta as a function of energy have been deduced from these cross sections on the basis of statistical evaporation model calculation( CAS CADE). The fusion cross sections are well reproduced by the simplified coupled channel model (CC FUS). The average angular momenta deduced from the partial cross section ratios are consistent with that extracted from the CCFUS calculation.
Based on multiple-scattering self-consistent-field method, we have investigated the electronic structrue of molecular bonding orbital and molecular Rydberg orbital in a unified manner for a C60 molecule. The results have been compared with other theoretical and experimental data and our calculated transition energies are in a fairly good agreement with experimental observations. Our results can be used to indentify the experimental spectra. Furthermore, our calculated quantum defects for Rydberg series can be used to study the corresponding collision process of "e+ C60+".
The adsorption kinetics of PABA molecules on silver surface and the influnce of chloride ions to it are discussed in detail. It is found that the adsorption of PABA on the silver surfaces is heterogeneous. The adsorption rate constant is affected by the difference of surface states greatly, but the heterogeneity parameter is in less degree. The adsorption heterogneity of PABA is changed by the competitive adsorption of chloride ions. PABA molecules with the of concentration of chloride ions. have turned homogeneous adsorption gradually from heterogeneous adsorption. The adsorption energy of PABA on silver surface is reckoned by the isotherms . It is further proved that the heteroge -neity of chemical adsorption means the adsorption state on the surface is not only one.
Two different atomic species-sodium and cesium-have been resonantly excited in a cell by a cw dye laser and a cesium lamp, respectively. The density of the excited Na(3P) atoms in the cell is measured directly using the absorption-equivalent-width technique on the lines of the diffuse series. To isolate the heteronuclear contribution in the fluorescence spectrum, a modulation detection technique has been adopted. The energy-pooling collisions between Na(3P) and Cs(6P) have been observed and cross sections have been measured.
The dynamical behavior of nonlinear absorption in photoisomeric molecular with two ismoers was discribed theoretically. And the various factors influencing the dynamic nonlinear absorption properties were analyzed and discussed.
Genetic algorithm is used to design a binary optical system with 8 grey levels to implement the wavefront transformation from gaussian beam to circularly flat - top beam. The comparison with the staionary phase method and the input - output method shows that genetic algorithm is more appropriate to design binary optics for profile reshaping than the other two methods.
In the history, perturbation method was unsuccessful in the solution of nonlinear standing waves. This problem is reviewed. It is apparent that the first order solution of the wave equation for standing wave by the perturbation method gives the basic solution, determining the basic wave form of the standing wave. The second and higher order solutions modify the time - dependent motion of the particle at different points on the wave form due to the nonlinearity, and hence only the time derivatives of the higher order quantities should be preserved. The results thus obtained are stable and essentially agree to the exact solution of the wave equation.
PHYSICS OF GASES, PLASMAS, AND ELECTRIC DISCHARGES
In this paper, we use the dispersion relation of Tokamak internal kink mode in ion kinetic regime to analyse the frequency and the growth rate of s0, the magnetic shear. We find that there is a critical shear s0c , and the resistive internal kink mode can only be excited when s0>s0c, i. e. , when q00c0 case, the growth rate of the resistive internal kink mode is several times of that obtained from the MHD regime, which is consistent with the fast crash phenomena of sawtooth. Comparison has been made of the results with experiments in the HL - 1 device for sawtooth stabilization or its period prolongation in case of hydrogen pellet refueling.
CONDENSED MATTER: STRUCTURAL, MECHANICAL, AND THERMAL PROPERTIES
With the conventional X-ray diffraction and grazing-incidence X-ray diffraction. We have investigated the MgO-rich layer characteristics in the magnesium diffused lithium niobate single crystal, when the magnesium-ion indiffusion process in the layer is carried out in atmosphere. It is found that the MgO-rich layer exhibits the crystal structure of Li3Mg2NbO6 and Mg4Nb2O9, when indiffusion time for magnesium-ion is short. these aspects indicate that Li3Mg2NbO6 is in the subsurface layer of MgO-rich layer and Mg4Nb2O9 forms an uniform layer in the MgO-rich layer.When further increasing diffusion time the lithium-ion outdiffusion from the bulk of lithium niobate become prominent and Li3Mg2NbO6 and Mg4Nb2O9 compounds disappear in succession, and LiNb3O8 compound structure appears consequentially. It is observed by scanning electron microscopy that the surface of magnesium diffused lithium niobate indicates a multicrystal structure, the decomposing and disappearing processes of these surface layer compounds are also revealed
Study on the crystallization process of amorphous (Fe0.99,Mo0.01)78Si9B13(FMSB) alloy with and without solid state reaction at their surfaces were carried out under pressures from 3 to 5 GPa at a temperature range of 510 to 660℃ . When the amorphous FMSB alloy with the reaction was annealed at the temperature range, it is transformed into nanocrystalline α - Fe( Al) at 4 GPa and α - Fe (Mo, Si), (Fe, Mo)3B or Fe2B at other pressures, which were as same as the crystallization products of the amorphous alloy without the reaction at the same pressures. The crystallization mechanism of the amorphous alloy with the reaction was suggested on the basis of therrnodynamic theory and a simple solid model.
Molecular-beam epitaxy and dynamic growth with long-range space and temporal correlations are analysed using scaling analysis approach. Rough and dynamic exponents are gained in strong-coupling and weak-coupling region respectively. Discussions are given and the reason why the weak-coupling region results are agree with that of dynamical renormalization group is also explained.
A 500 nm titanium film was deposited on a polished (1102) oriented sapphire (α-A12O3) substrate using electron beam evaporation under ultra high vacuum conditions. Isothermal furnace annealing has been used to cause the solid-state reaction between Ti film and sapphire substrate. Inter-facial reaction of Ti/α-Al2O3 was studied in detail from room temperature (RT) to 850 ℃ using XRD (including general and low incident angle X-ray diffractions), AES (Auger electron spec-troscopy, including the depth profile and the shape analysis of Auger spectra across the interface) and SIMS (Secondary ion mass spectrometry) etc. surface analysis techniques. It was found that at RT and after 300℃ 30 min. annealing, Al2O3 was reduced by titanium to produce metallic A1 accumulated at the interface. After 600 ℃ 30 min. annealing, Ti3Al and TiO2 were formed. After 850 ℃ 30 min annealing , the amount of Ti3A1 is increased with the temperature, at meantime the new phases of a number of titanium oxides(TixOy)and Al2TiO5(Al2O3·TiO2) were detected. After 850℃ 4 h annealing, it indicates that apart from the phases described above, Ti2Al and TiAl3 were formed. We suggest the chemical equations of reaction corresponding to the different temperature zones and discuss the limitation of the prediction from thermodynamic consideration by using bulk material data.
CONDENSED MATTER: ELECTRONIC STRUCTURE, ELECTRICAL, MAGNETIC, AND OPTICAL PROPERTIES
The effect of zero-point lattice vibration on the CDW of MX Complex is investigated in a wide range of electron-phonon coupling by using a self-consistent renormalization method. In contrast to the polyacetylene, where the bond order wave exists well in arbitrary coupling, the effect of the quantum fluctuation on CDW of MX solid distinctly depends on the coupling. When the coupling is strong, the reduction of CDW is small;But, if the coupling is weak, the CDW is seriously suppressed and even nearly destroyed. This contrast is related to the fact that for weak coupling, the frequencies of both the acoustic and optical branches are small in polyacetylene, but these frequencies are not well different from the bare value ω0 in MX solid.
The relationship between dielectric loss factor D (tanδ) and frequency for ZnO-Sb2O3-BaO and ZnO-Bi2O3-Sb2O3-BaO varistor ceramics has been investigated. A new dielectric loss peak was found near by 2MHz at room temperature for the sample in the absence of Bi2O3, the corresponding electron trapping level was about 0.18 eV, it was considered that the loss peak resulted from intrinsicdefect Zni . It was assumed that the formation of intrinsic defect Zni was restricted by ion Bi, it was consistent with experimental fact that the degradation properties of varistor ceramics under the long duration load voltage are improved with the increasing amount of Bi2O3.
The few-body theory has been extended to study the electronic properties of the quantum dots subjected to a magnetic field, which contains three electrons. We have analytically proved that the "magic angular momenta" are orginated from the symmetries of the quantum mechanics. Based on the few-body theory, calculations confirm the conclusion stated above. The influences of magnetic field and confined potential on the ground states of three electron systems has been numerically calculated.
On the basis of experiments, the ZrO2 grain boundaries are classified into three types: the " clean" grain boundaries, the grain boundaries with amorphous phases and the grain boundaries with crystal phases. The structure and property of the three types of grain boundaries are analyzed on .the grounds of microstructure and lattice defects. The conductivity of the crystal grain boundary phases is calculated with the effective-medium theory and found to be three times higher than that of the matrix, and an idea of further enhancing the ionic conductivity of ZrO2 by modifying grain boundaries is thus proposed. The effect of the ZrO2 grain boundaries on the emf of the oxygen sensor is discussed with simplified models.
Based on the free electron model, a self-consistent approach is adopted to calculate the Fermi energy and its variation with the layer thickness and the magnetlization alignment in magnetic multilayers . Then we study the effect of the thickness of magnetic and non-magnetic layers, especially of electron density on the oscillation period of interlayer exchange coupling in such multilayer. A comparison of our theoretical results with those obtained by using the grand potential method is made, we find that the oscillation period is strongly dependent on the electron density. When the electron density in magnetic layer is different from that in spacer, the period will change as changing the thickness ratio of spacer to magnetic layer. This new result agree with the latest experimental data. In addition, our calculation also shows that the coupling strength is mainly determined by the polarization force experienced by electrons, while the band mismatch does influence the phase and even the period of the coupling oscillation.
Polarized Raman spectra of all four symmetry species in single crystal LiB3O5 have been measured at room and high temperature. The vibrational modes are classified by the method factor group analysis and the internal vibration bands are tentatinely assigned to vibrations of BO3 triangle and BO4 tetrahedron. Based upon the experimental results of LO-TO splitting , the effective charges of polar modes and the static dielectric constants are calculated.
The phase formation of the samples with the norminal composition (Y1-xCex)Ba2Cu3O7-δ(x = 0,0.05,0.1, 0.3, 0.55,1.0)has been studied by Raman spectroscopy. It is found that the impurity phases of BaCeO3 and BaCuO2 have been formed with Ce doping, besides the orthorhombic Y-123 phase. The results suggest that Ce element may not substitute for Y element to form a Ce-123 phase. Moreover, Ce element formed an impurity phase BaCeO3 with Ba.