Based on the principle of self-adaptive Simpson integration method, and by incorporating the‘fifth-order’Filon’s integration algorithm [Bull. Seism. Soc. Am. 73(1983) 913], we have proposed a simple and efficient numerical integration method, i.e., the self-adaptive Filon’s integration method (SAFIM), for computing the synthetic seismograms at large epicentral distances. With numerical examples, we have demonstrated that the SAFIM is not only accurate but also very efficient. This new integration method is expected to be very useful in seismology, as well as in computing similar oscillatory integrals in other branches of physics.

The Perk-Schultz model with SU_{q}(m\n) spin boundary impurities is constructed by dressing the c-number reflecting K matrix with local L-matrix which acts non-trivially on an impurity Hilbert space. The eigenvalue of the transfer matrix and the corresponding Bethe ansatz equations with different c-number reflecting K-matrices are obtained by using the nested Bethe ansatz method (m ≠ n). When m=1,n=2, our results come back to that of super-symmetric t-J model with SU_{q}(1\2) spin boundary impurities.

Based on the newly constructed state |l,r>> [FAN et al., Chin. Phys. Lett. 16(1999)706], where l is the angular mometum quantum number and r denotes the electron's orbit radius in a uniform magnetic field, we propose a new angular momentum-phase coherent state by introducing a new operator A. A and A^{†} are annihilation and creation operator in the |l,r>> space, respectively. The coherent state is A's eigenket and possesses non-orthonormal and overcomplete properties, it is constructed on the certain superposition of zero-angular momentum states along the radius direction.

Based on the neat <η| representation of two-mode squeezing operator which entangles signal-mode and idle-mode, where <η| is the common eigenvector of two particles' relative position and the total momentum exhibiting a maximal entanglement between the two modes, we study some kind of squeezing mixing 1-3 modes and 2-4 modes for a pair of two-mode (1-2 modes and 3-4 modes) squeezed states. The explicit form of such mixed squeezed states is derived and the new entanglement is analysed.

The relative entropy of entanglement of a mixed state σ for a bipartite quantum system can be defined as the minimum of the quantum relative entropy over the set of completely disentangled states. Vedral et al. [Phys. Rev. A 57(1998)1619] have recently proposed a numerical method to get the relative entropy of entanglement E_{re} for two-qubit systems. This paper shows that the convex programming method can be applied to calculate E_{re} of two-qubit systems analytically, and discusses the conditions under which the method can be adopted.

The generalized two-parametric Hilbert-Palatini action is
constructed, which not only includes the well-known Hilbert-Palatini and Ashtekar gravitational theory as special cases, but also gives new results. In Hamiltonian formulation, the phase space variables and the corresponding Hamiltonian constraints can be obtained, including the Ashtekar and Barbero type constraints. Moreover, the results of this action are the same as those given by the parametric canonical transformations, although these two methods are completely different.

The statistical entropy of the Kaluza-Klein black hole is studied by counting the black hole states which form an algebra of diffeomorphism at Killing horizon with a central charge. It is shown that the entropy yielded by the standard Cardy formula agrees with the Bekenstein-Hawking entropy only if we take period T of function u as the periodicity of the Euclidean black hole. On the other hand, the first-order quantum correction to the entropy is proportional to logarithm of the Bekenstein-Hawking entropy with a factor -1/2.

We obtain a general unstable periodic solution near the homoclinic orbit of the Duffing oscillator with weak periodic perturbation by using the direct perturbation technique. Theoretical analysis reveals that the stable periodic orbits are embedded in the Melnikov chaotic attractor. The corresponding numerical results show that fitting control parameters into the stability conditions can control chaos in the system, and the phase difference between the two sinusoidal forces added to the Duffing equation plays an important role in controlling chaos.

A newly proposed method, i.e. the adaptive higher-order nonlinear finite impulse response (HONFIR) filter based on higher-order sparse Volterra series expansions, is introduced to predict hyper-chaotic time series. The effectiveness of using adaptive HONFIR filter for making one-step and multi-step predictions is tested based on very few data points by computer-generated hyper-chaotic time series including Mackey-Glass equation and 4-dimensional nonlinear dynamical system. A comparison is made with some neural networks for predicting the Mackey-Glass hyper-chaotic time series. Numerical simulation results show that the adaptive HONFIR filter proposed here is a very powerful tool for making prediction of hyper-chaotic time series.

The spatiotemporal chaos in the system described by a one-dimensional nonlinear-drift wave equation is suppressed by non-feedback pinning method. By adding additive external noise to the controlled state, we find that the deviation from the target space-time pattern increases in a power law with noise intensity. The possible controlling mechanism is discussed.

Sigma decay and its relation with chiral phase transition are discussed at finite temperature and density in the framework of the Nambu-Jona-Lasinio model. The decay rate for the process σ → 2π to first order in 1/N_{c} (inverse number of colors) expansion is calculated as a function of temperature T and baryon density n_{b}. In particular, only when the chiral phase transition happens around the tricritical point, the σ decay results in a non-thermal enhancement of pions in the final state distributions in relativistic heavy ion collisions.

The possibility to search for the isoscalar 1^{-}^{+} exotic state through the J/ψ decay process J/ψ → ω + X,X → V+V at upgraded BEPC (Beijing Electron-Positron Collider)/BES (Beijing Spectrameter) is discussed for two cases: single state and multi-state coupling in terms of the generalized moment analysis method. The results show that this possibility exists only for the case of single state case.

Using the topcolor-assisted technicolor models, we give the anomalous Wtb couplings arising from the exchange of the new gauge bosons (ETC gauge boson, colorons and Z') and calculate their contributions to the b → sγ branching ratio. We find that the contributions mainly come from colorons and the recent measured value of the b → sγ branching ratio gives a strong constraint on the masses of colorons.

The Reflection Asymmetric Shell Model has been formulated
to describe the high spin states of octupole deformed nuclei.
The long-range separable forces of quadrupole, octupole and hexadecapole as well as monopole and quadrupole pairing are included in the Hamiltonian. The bases, on which the Hamiltonian is diagonalized, are the eigenstates of angular momentum and parity obtained by projecting the octupole deformed multi-quasiparticle states onto good angular momentum and good parity. The general features of rotational octupole bands in even-even nuclei can be reproduced by the model and the calculated result is in good agreement with experiment.

The out-of-plane squeeze-out effect in relativistic heavy ion collisions is used to estimate the reaction plane by performing a modified transverse momentum analysis. A technique for investigating the azimuthal correlation between the out-of-plane squeeze-out and directed in-plane flow is described. A clear signature of the azimuthal correlation is evidenced in the 600 A MeV Au+Au reaction from the quantum molecular dynamic model calculations.

We discuss the moment analysis method for the 0^{++} and 2^{++} coupling mode of f_{J}(1710) for incomplete phase space in the radiative decay J/ψ → γK^{+}K^{-}, and give a new formulation of analyzing the f_{J}(1710) structure for the Beijing Spectrometer detector at the Beijing Electron-Positron Collider. The incomplete detection phase space results in a significant effect on the moment analysis.

For intermetallic compound TiAl, the interatomic potentials in the Finnis-Sinclair model were constructed by empirically fitting to the properties of L1_{0} TiAl tetragonal phase and the pressure-volume relations. In the calculations of point defect properties of TiAl alloy with this potentials, it was shown that the thermal concentration of antisite defects was higher than that of other point defects. With similar formation energies, five possible interstitial configurations were stable. This model was consistent with the embedded atom method or embedded defect method and adequate for simulation of defects in TiAl alloy.

Time delay properties of a Fabry-Perot interferometer are investigated. We found that the group velocity of light through a Fabry-Pérot interferometer can be reduced to 10^{-4} of the light speed in vacuum and the time delay is 210 ns, when the reflectivity is 0.999 and the distance between two mirrors is 1cm. The system is analogous to the recently proposed one-dimensional photonic band-gap structures with a defect [Zhu et al. Opt. Commun. 174(2000)139]

We consider a two-dimensional (2D) trapped ion model in which two laser beams drive the corresponding vibrational motions and are carrier resonant with the two-level of the ion. Due to the coherent superposition of two sub-Rabi oscillations involved in the bimodal vibrations, the Rabi frequency degeneration and offset may occur in this model. This provides a possibility to generate the pair coherent state in the 2D trapped ion.

A two-dimensional single-mode laser model with cross-correlations between the real and imaginary parts of the quantum noise as well as the pump noise is investigated. The general closed form of the laser intensity Langevin equation (GILE) is obtained under a stable locked phase resulting from the cross-correlation λ_{q} between the real and imaginary parts of the quantum noise. Because of the presence of a new term containing λ_{q}, we can unify the two opposite intensity Langevin equations which correspond to the two special cases for |λ_{q}| → 0 and |λ_{q}| → 1 in the GILE. It is expected that the transient and stationary properties of the laser model can be changed qualitatively when λ_{q} varies.

A model of random porous media degradation via several fluid displacing, freezing and thawing cycles is investigated. The fluid transport is based on the deterministic method with dispersion effect. The research shows that the topology and the geometry of the porous media have a strong effect on displacement processes. The distribution of throat size N(r) after displacement but before freezing damage shows that the major change, after successive cycles, happens at throat radius r > 0.9. The distribution of velocities normal to the interface of viscous fingering in percolation cluster is also studied. When iterations n≥10, the scaling function distribution is very sharp.

A novel four-wavelength all-fiber laser based on fiber Bragg gratings is presented. The four wavelengths are 1555.8, 1556.6, 1557.4 and 1558.2 nm, respectively. Each output laser is < 0.3 nm in line-width and > 1 mW in power. The suppression ratio between adjacent wavelengths is > 30 dB. The laser was applied in a wavelength division multiplexing (WDM) system and the 100 km transmission of 1.2 Gb/s nonreturn-to-zero code, 1.2 Gb/s return-to-zero code, 2.5 GHz analogue signal and 5 GHz analogue signal was realized with it.

The mechanisms of photoinduced microstructures in an azobenzene polymer film are presented. They are based on the spatial periodic modulation of optical intensity and the photoisomerization of azobenzene molecules with the movement of main chains. Experiment and theory jointly point out the possibility of photoinducing desired spatial microstructures in azobenzene organic polymer via adequate optical lattices and adequately polarized ‘writing’beams.

The formula for the intensity of surface second-harmonic generation circular dichroism (SHG-CD) in helical molecular films is presented. The influence of the pitch and radius of helical molecules on the surface SHG-CD intensity is numerically analysed. The existence of a peak in curves of the surface SHG-CD intensity versus the pitch and radius is predicted. The relation between the pitch and radius for different azimuthal angles is also discussed.

WANG Zheng-Ping, LIU Jun-Hai, SONG Ren-Bo, JIANG Huai-Dong, ZHANG Shu-Jun, FU Kun, WANG Chang-Qing, WANG Ji-Yang, LIU Yao-Gang, WEI Jing-Qian, CHEN Huan-Chu, SHAO Zong-Shu

The nonlinear-optical coefficients of RCOB (R = Gd,Y) crystals are measured. The spatial distribution of d_{eff} effective nonlinear-optical coefficient) is determined subsequently. Our experiments show that the maximum d_{eff} occurs at the second quadrant. The second-harmonic-generation efficiency reaches 48% for a 6 mm-long, (113.2°, 47.4°)-cut GdCOB, and 41.5% for a 5mm-long, (113°, 36.5°)-cut YCOB, respectively. The intracavity frequency doubling of GdCOB is reported for the first time.

The rare-earth ions (Yb^{3+}, Tm^{3+}) and Li^{+}, Bi^{3+} ions doped GdCa_{4}O(BO_{3})_{3} crystals were grown using the Czochralski pulling method. The second-harmonic-generation conversion efficiencies of the GdCOB:Yb and GdCOB:Tm crystals are 31.3% and 33.3%, respectively, while the undoped GdCOB crystal is 27.9%. The conversion efficiencies of Yb^{3+}, Tm^{3+} doped GdCOB are improved by 12% and 19%, respectively, compared to that of the undoped one. The conversion efficiencies of Li^{+}, Bi^{3+} doped GdCOB crystals are 33% and 38.3%, which are improved by 15% and 37% as compared to that of the undoped crystal. The results are discussed using the anion group theory.

The temporal behaviour and spectral distribution of white-light continuum generation in H_{2}O using a focused intense 800 nm 130 fs Ti: Sapphire laser were studied. The results indicated that the white-light continuum spectrally ranged from 1000 to 400 nm, which was mainly attributed to self-phase modulation related to Kerr effect and ionization. The pulse duration of different spectral components of the generated white-light continuum, which was measured with frequency up-conversion technique, was obtained around 137 fs. It revealed a comparable time resolution as the original laser pulse.

Magnetohydrodynamic phenomena in the CT-6B Tokamak based on Mirnov oscillations have been investigated by applying the limiter biasing potentials and changing the vacuum chamber gas pressure and plasma displacement. The results show that setting up a radial electric field at the plasma edge could drive electromagnetic instabilities in the tokamak plasma. Magnetic oscillation frequency upon application of a positive bias decreases about 10-15% and then after a delay time, τ_{d} = 2.5 - 3 ms increases about 20-25% with respect to their value without biasing. In the negative bias regime the oscillation frequency increases about 10% in 1 ms after the application of the bias pulse. The poloidal rotation velocity changes during two steps are related to its link with the radial electric field and the time scale of the density gradient. The frequency of oscillations increases with the increasing chamber gas pressure and decreases with the increasing the outward plasma displacement.

Power spectra of electron density and floating potential fluctuations in the velocity shear layer of the HT-6M edge region have been measured and analysed. All the spectra have three distinct frequency regions with the spectral decay indices typical of self-organized criticality systems (0, -1 and -4) when Doppler shift effects induced by the plasma E x B flow velocity have been taken into account. These results are consistent with the predictions of the self-organized criticality models, which may be an indication of edge plasma turbulence in the HT-6M tokamak evolving into a critical state independent of local plasma parameters.

Efficient direct heating of electrons by ion Bernstein waves has been obtained on the HT-7 tokamak. Off-axis heating, which is considered to be the result of electron Landau damping, was observed and studied by means of soft x-ray imaging. The measured power deposition was found to be independent of magnetic field through scanning the toroidal field from 1.5 to 1.7 T, in contrast to the ion heating results. It is suggested that the electron Landau damping is dominant in this heating regime.

The low frequency electromagnetic wave instability in an unmagetized inhomogeneous dusty plasma has been pointed out. It has been noticed that there exists a stable mode if the propagation of the wave vector along the density gradient is ignored. However, the mode becomes unstable by including the propagation of the wave in the opposite direction of the density gradient.

We showed that, in contrast to the results in literature, the Bragg peak intensity of Ni_{80}Fe_{20}/Cu superlattices is enhanced at the incident x-ray energy slightly higher than the absorption edge of the heavier element (Cu). The atomic density at Ni_{80}Fe_{20}/Cu interface was analysed by the diffraction anomalous fine structure technology with the incident angle of x-ray fixed at the first Bragg peak. Our results demonstrate the epitaxy growth of Ni_{80}Fe_{20}/Cu superlattices. Upon annealing, the epitaxity of Ni_{80}Fe_{20}/Cu multilayers becomes poor but the local crystallinity in each layer is improved.

The microstructures of Na_{2}Si_{2}O_{5} from room temperature up to 1773 K are studied by high temperature Raman spectroscopy. Deconvolutions of complex Raman spectra of crystal and amorphous states (glass and melt) are described. The results show that the temperature-dependent Raman spectra clearly indicate phase transition. Relative abundance of various kinds of SiO_{4} tetrahedrons (each Si binding to different number of bridging oxygens) can be qualitatively and quantitatively resolved as to be varied obviously with different temperatures. It manifests that high temperature Raman spectroscopy provides a useful tool for the microstructure research under high temperature and helps to explain the properties of silicate glasses and melts.

The microstructure of computer generated nanocrystalline coppers is simulated by using molecular dynamics with Finnis-Sinclair potential, analysed by means of radial distribution functions, coordination number, atomic energy and local crystalline order. The influence of the grain size on the nanocrystalline structure is studied. The results reveal that as the grain size is reduced, the grain boundary shows no significant structural difference, but the grain interior becomes more disordered, and their structural difference diminishes gradually; however, the density and the atomic average energy of the grain boundary present different tendencies from those of the grain interior.

The longitudinal velocity V_{l} and shear velocity V_{s} of ultrasonic wave propagated along arbitrary three perpendicular directions of the Zr_{41.2}Ti_{13.8}Cu_{12.5}Ni_{10.0}Be_{22.5} bulk metallic glass (Zr/Ti BMG) have been measured at ambient pressure, under hydrostatic pressure (up to 0.5 GPa) and uniaxial compression (up to 70 MPa) using the pulse echo overlap method. The third order elastic constants and the Grüneisen parameter related to the anharmonic properties were derived and discussed. It was found that the BMG with marked different microstructural characteristics comparing with the amorphous carbon exhibited different behaviours related to shear vibratory under high pressure.

Thermal conductivity in the normal direction of ultra-thin dielectric films is predicted by molecular dynamics calculations for argon crystal. For film thickness of about 2-10 nm within which real measurements can not yet be implemented, the size dependence of lattice thermal conductivity is captured and a remarkable thermal conductivity drop is found as compared with bulk experimental data. This size effect demonstrates that phonon-boundary scattering in thin films may also be very significant at high temperature even above the Debye temperature. The influence of different potential models is examined according to the comparison between results from the Lennard-Jones potential and a soft-sphere potential.

We provide a Landau theory of the coupled charge density wave and spin density wave order parameters to investigate the possibility of coexistence or competition between the two ordering processes occurring in the two-dimensional doped antiferromagnet. We find that the two ordering processes can coexist only in a certain region of coupling parameters, andthe one with lower transition temperature can only coexist together with the other one with higher transition temperature and can not be stabilized separately. Phase diagrams in different situations are given.

We study the transmission dynamics of a driven two-level system
dissipated by the two leads. Using nonequilibrium Green function, we derive an analytical transmission formula for an electron incident from the left lead, through the double quantum dots, to the right lead. Landauer-type conductance and current are also given. A discussion of the internal tunneling dynamics reveals crucial effects of the localization and delocalization on the transport of the system.

We investigate the dynamical processes taking place in nanodevices by high-frequency dc-ac fields. We found that Rabi oscillations between minibands are clearly identified under theoretical resonant conditions derived by an ideal two bands superlattice model, the resonant conditions have broadened, and the amount of broadening is about four times of the Rabi oscillation frequency. We also want to elucidate the role of different mechanisms that could lead to loss of quantum coherence. Our results show how the dephasing effects of disorder of interface roughness and doping fluctuation that destroy after some periods coherent oscillations, such as Rabi oscillations, can be reduced dramatically if we apply a bias static electric field to the superlattice system. Doping fluctuation's dephasing effect is much stronger than that of interface roughness in coherent process of realistic superlattices.

Using non-rigid bipolaron model modified with the correction of pseudogap effect, we have studied the temperature (T) dependence of the Hall coefficient (R_{H}) in the normal state of several typical high-T_{c} superconductors (e.g. YBa_{2}Cu_{3}O_{7-δ}). The results are in agreement with experiments. It is suggested that the positive maximum in the R_{H}-T diagram corresponds to a point near the bottom of the pseudogap. We have also found that for these high-T_{c} superconductors, W-T can be scaled into a single universal function form, where W is the bandwidth of the non-rigid bipolaron system.

The Trapping force on Rayleigh particles in an optical tweezers system with an oil immersion objective is calculated by an electromagnetic model. The results indicate that the stability of particles trapped will be affected by spherical aberration, which is caused by refractive difference between objective oil and water solution, when the specimen manipulated is suspended in a water solution. The trapping force and depth of potential well will decrease and the minimum of laser power for ensuring the stability of particles trapped will increase with the enhancing trapping depth.

We have investigated experimentally and theoretically the thermocapillary convective flow phenomena in a loop-shaped Pt wire heater of KNbO_{3}(20wt.%) and Li_{2}B_{4}O_{7} solution. Optical evaluations in connection with thermocouple measurements made it possible to get a new type of thermocapillary convective flow in the considered system. To study the kinematical behavior of thermocapillary convection, we have measured the stream velocities of flow. In a theoretical analysis, the flow velocity due to thermocapillary effect alone was estimated by balancing the surface tension forces by viscous forces. The velocity distribution in the solution near the margin of the heater was obtained, which is in agreement with the experimental result.

Arrays of III-nitride semiconductor micro-cone cavities with a base diameter of 3.3μm were fabricated by ion beam etching. The micro-cones consist of a 58nm thick multiple quantum wells of In_{0.22}Ga_{0.78}N/In_{0.06}Ga_{0.94}N as well as a 1.5μm thick epilayer of GaN. Optical resonant modes from a single micro-cone could be clearly observed in the photoluminescence spectra at temperature up to 200 K under a pumping power density two orders of magnitude lower than that for the III-nitride semiconductor micro-disk or micro-ring cavity. Using a novel optical ray tracing method, we have figured out four main types of optical resonant cavities inside the three-dimensional micro-cone, including two Fabry-Perot (F-P) mode types as well as two Whispering Gallery mode types. The three corresponding mode spacings among the four agree perfectly with the experimental results. The advantages of this new class of micro-cavity over the other micro-cavities are discussed. These findings are expected to have impact on the design of the ultraviolet/blue micro-cavity laser diodes.

The photoluminescence of ZnO films deposited on Si substrates by reactive dc sputtering has been studied by using a synchrotron radiation(SR) light source. The excitation spectra show a strong excitation band around 195 nm related to 390 nm emission band. Under SR vacuum ultraviolet excitation, a new emission band peaked at 290 nm was found for the first time, besides the ultraviolet emission band (390 nm) and green band (520 nm).

CeO_{2} film with a thickness of about 80 nm was deposited by a mass-analyzed low-energy dual ion beams deposition technique on Si (111) substrate. Reflection high-energy electron diffraction and x-ray diffraction measurements showed that the film is a single crystal. The tetravalent state of Ce in the film was confirmed by x-ray photoelectron spectroscopy measurement, indicating that stoichiometric CeO_{2} was formed. Violet/blue light emission (379.5 nm) was observed at room temperature, which may be tentatively explained by charge transitions from the 4f band to the valence band of CeO_{2}.

Adsorption of phenylalanine on Cu(001) surface was studied by means of scanning tunneling microscopy in ultra high vacuum and has been found to result in only one superstructure, i.e., c(2 x 4). Moreover, it induces steps faceting to <310> directions and faceted steps bunching to form {3 1 17} facets. In view of the small size of the c(2 x 4) unit cell, phenyl ring of the molecule is suggested to be oriented nearly perpendicular rather than parallel to the surface. A model thus has been proposed for the c(2 x 4) superstructure, where the π-stacking interactions between neighboring phenyl rings, in addition to hydrogen bond formation, are expected to play an important role in stabilization of the superstructure.

The folding behaviour of some sequences of 36 monomers with different proportion of hydrophobic residues in a three-dimensional lattice based on the Miyazawa-Jernigen interaction matrix. It is found that the sequences with good folding properties are those with an optimal number of hydrophobic residues, neither too many nor too few. The reason for the deterioration of folding properties of sequences out of this range has also been analysed.

We have studied the distribution of distances in small-world network by computer simulations. We found that in a small world network, the longest distance between two vertices is just slightly longer than the average distance, indicating that the efficiency of the network is absolute rather than in average. We also investigated the robustness of a small-world network by randomly cutting some long paths in the network. The results show that the network is reliable against random cutting.

We discuss Whether the numbers of x-ray and radio-produced electrons in solar flares are the same. The number of the radio-produced electrons that is estimated with an inhomogeneous source increases by a factor of 10^{3}-10^{4} because of the inhomogeneity and the decreased magnetic field (B=120 G) of the radio source. The number of the x-ray-produced electrons decreases by a factor of 10 - 30 due to the increase of the number density of ions (3 x 10^{10}cm^{-3}). These are the reasons why the number of radio-produced electrons is approximately equal to that of x-ray produced in the 1981 April 27 burst.

The water maser emission from the unusual supergiant, VY CMa, has been observed with the Urumqi 25 m radio telescope. A simple red-shifted maser spectrum was detected in the 1.6 Jy noise level during our monitoring observations. All of the H_{2}O maser features are red-shifted with respect to the VY CMa stellar velocity of 17.6 km.s^{-1}. The spectrum appears to be consisted of two striking like groups and each group has three features. The appearances and the ratio of these three features in the two maser groups are very similar. The H_{2}O maser emission arises from a region close to the supergiant, about 10 stellar radii of the star. The simple red-shifted spectrum could be due to infall masing gas on the near side of the disk. Pulsation of the central star causes oscillations in this portion of the envelope, with shock wave propagating outward and with material falling inward. The masing gas motions are very complex, by which the dramatic changes or the quasi-sinusoidal fluctuation in flux may be explained.

Based on high resolution and high signal-to-noise ratio spectra, we determine the chemical abundances of nearby star HD131023 by using the differential analysis. Abundances of total 24 elements are presented. Some heavy elements, such as Sr, Y, Ba, La, Nd, are found to be overabundant relative to the sun.

As a statistical model of black hole entropy, the brick-wall method based on the thermal equilibrium in a large scale cannot be applied to the cases out of equilibrium, such as the non-static hole or the case with two horizons. However, the leading term of hole entropy called the Bekenstein-Hawking entropy comes from the contribution of the field near the horizon. According to this idea, the entropy of Vaidya-deSitter spacetime is calculated, A difference from the static case is that the result proportional to the area of horizon relies on a time-dependent cutoff. The condition of local equilibrium near the horizon is used as a working postulate.

A reverse condition of accretion flow and its constraints on black hole spin in the quasi-cycle are proposed. It is shown that the necessary condition for the quasi-cycle is that the closed magnetic field lines must dominate over the open ones at the horizon. The efficiency of converting accreted rest mass into radiation energy in the quasi-cycle is proved to increase as the strength of the magnetic transfer process. In addition, a general expression for the efficiency is derived.