We propose a general method to prove the uniqueness of the inversion problems described by the first-kind integral equations. The method depends on the analytical properties of the Fourier transform of the integral kernel and the finiteness of the total states (or probability, if normalized), the integration of the“local”density of states, which is a rather moderate condition and satisfied by many inversion problems arising from physics and engineering.

We present computations using orientation-free discrete velocity models for the dispersion relationship of ultrasound propagation in monatomic hard-sphere gases (or a type of gas composed of system of vortices). Comparisons with previous verified fixed-orientation results for the propagation of the sound mode in rarefied gases show that, if collective excitations are considered, an orientation-free eight-velocity model can capture more physical insights. We also demonstrate the symmetry property of the Spectra using the orientation-free eight-velocity model.

We critically examine the concepts of quantum geometrical phases which have been widely applied to calculate mesoscopic persistent currents in the current literature. We point out that the method used in these calculations is essentially in conflict with the basic concepts of quantum geometrical phases. We give an example calculation of mesoscopic ring Aharonov-Anandan, Aharonov-Casher phases and persistent current to show some of the misconceptions involved in the current literature.

Noticing that the angular momentum operator L_z commutes with the square of radius operator, R², of the orbit track of an electron in a uniform magnetic field, we reveal that a new entanglement is inherent to the common eigenvector of the operators L_z and R².

By virtue of the Einstein-Podolsky-Rosen(EPR)-pair eigenstates |η> we derive the result of quantum teleportation of a two-mode squeezed state. The calculation can be greatly simplified by using the natural representation of the two-mode squeezing operator in the complete and orthonormal |η> representation.

We discuss the transformation from pure states to mixed states in a bipartite system H_AH_B and provide the sufficient condition for this transformation. We also provide a necessary and sufficient condition for one class of this transformation. Meanwhile, the method of realization for the transformation from pure states to mixed states is also present. Furthermore, we brief discuss the application.

We have obtained the exact solution of the Einstein-Maxwell equations outside the central mass with magnetic moment, and at the same time, we have investigated their asymptotic properties.

We discuss the Gaussian beam effect on test of the equivalence principle using a free-fall interferometer. A two-lens assembly is used to improve the propagating character of the laser beam, and the beam radius is collimated to about 3.0 mm. The analysis shows that the gravity acceleration difference induced by the Gaussian beam effect could be less than 10^-15g for our double free-fall experimental design, but it would be 10^-9g for the absolute measurement of the gravity acceleration with usual single free-fall method.

A new ultra-low frequency passive vertical vibration isolation system is constructed by connecting the torsion spring isolator with a reverse pendulum. The theoretical analysis shows that the new system can achieve a much longer resonant period and have a smaller size than the current torsion spring isolators with the same geometric parameters.

The transition from the phase-unlocking state to phase-locking state is found at the desynchronization of synchronous chaos of coupled oscillators. In the phase-locking case, the motions of all oscillators are chaotic and desynchronous, however spatial ordering is identified in their phase distribution.

Color superconductivity is investigated in the frame of a two flavor instanton-induced model. The ratio of diquark to quark-antiquark coupling constants is restricted to be c/(N_c -1) with 1 ≤ c ≤ 2.87 and controls the formation region and amplitude of color superconductivity. While the finite current quark mass changes the chiral transition significantly, it does not considerably change the color superconductivity.

The rotational bands up to spin of 16ħ in the neutron-rich ¹⁰⁶Mo nucleus have been investigated by measuring high-fold prompt γ-ray coincidence events following spontaneous fission of ²⁵²Cf with Gammasphere detector array. The ground-state band, the one-phonon and two-phonon γ-vibrational bands, as well as a quasiparticle band have been confirmed and expanded. The other four collective rotational bands, three of them proposed as two-quasiparticle bands and one of them proposed as β-vibrational band, have been newly observed. The characteristics of these collective bands and the possible configurations for the quasi-particle bands are discussed.

The difference of spectral statistics properties between single-j and two-j shell models has been studied in the frame of the cranking model. The results show that the system becomes more regular when single-j space (i_13/2) is replaced by a two-j shell (g_7/2+d_5/2), although the basis size of the configuration space is unchanged. However, the degree of chaos of the system changes slightly when configuration space is enlarged by extending the single-j shell (i_13/2) to two-j (i_13/2 +g_9/2) shell.

The lifetime measurements of the high-spin states in the yrast band of ¹³⁰Ce have been performed by using the Doppler shift attenuation method in conjunction with the reaction ¹¹⁶Sn(¹⁶O,2n)¹³⁰Ce at a projectile energy of 73MeV. The reduced transition probabilities B(E2) deduced from these measurements show a great reduction in the vicinity of the backbending region. The previously reported anomalously high B(E2) value was not observed in the present experiment. This result is in agreement with theoretical prediction based on a realistic nucleon-nucleon interaction.

Asymmetric nuclear matter is investigated by the Dirac Brueckner Hartree-Fock (DBHF) approach with a new decomposition of the Dirac structure of nucleon self-energy from the G matrix. It is found that the isospin dependence of the scalar and vector potentials is relatively weak, although both potentials for neutron(proton) become deep(shallow) in the neutron rich nuclear matter. The results in asymmetric nuclear matter are rather different from those obtained by a simple method, where the nucleon self-energy is deduced from the single particle energy. The nuclear binding energy as a function of the asymmetry parameter fulfills the empirical parabolic law up to very extreme isospin asymmetric nuclear matter in the DBHF approach. Behaviour of the density dependence of the asymmetry energy is different from those obtained by non-relativistic approaches, although both give similar asymmetry energy at the nuclear saturation density.

We calculate the correction to the two-gluon decay width due to the finite extension of the vertex function. We obtain the corrected factor to the zero-range vertex γ = 1.32, γ = 1.45, γ = 1.26 for η_c,x_c0, and x_c2, respectively. With the decay width Γ(η_c → 2g) we extract the value α_s(m_c) = 0.28±0.05 which agrees with that calculated from the same correction to the process Γ(J/ψ → 3g). This correction to the process Γ(η_c → 2g) is not as large as that to the process Γ(J/ψ → 3g).

We study the reconstruction of the source function in space-time directly from the measured Hanbury-Brown/Twiss (HBT) correlation function using the maximum entropy principle. We find that the problem is ill-defined without at least one additional theoretical constraint as input. Using the requirement of a finite source lifetime for the problem we find a new Gaussian parametrization of the source function directly in terms of the measured HBT radius parameters and its lifetime, where the latter is a free parameter which is not directly measurable by HBT. We discuss the implications of our results for the remaining freedom in building source models consistent with a given set of measured HBT radius parameters.

We have theoretically investigated the time delay of a chirped light pulse, defined as the temporal difference of peaks of the output and input light pulses after transmitting a Fabry-Pérot interferometer. The results show that for an interferometer of known parameters, the chirp of the light pulse makes the time delay intensively become smaller. The mismatch between the central frequency of the light pulse and the resonance frequency of the interferometer also has an influence on the time delay. Under some circumstances, this mismatch will induce a time delay smaller than t₀ that is defined as the one-way traverse time of the light inside the interferometer.

We investigate an all-solid-state continuous wave (cw) green (532 nm), femtosecond near-infrared (823.1 nm) and blue (402 nm) laser system which is pumped by a diode-laser-pumped intracavity frequency-doubled and all-self-structuring cw Nd:YVO₄/KTP 532 nm green laser. The cavity parameters of the Nd:YVO₄/KTP laser have been optimized and the maximum 5.6 W TEM₀₀ green laser is obtained at a 22 W pump power with an optical-optical conversion efficiency of 25.5%. A Ti:Sapphire laser and the nonlinear second harmonic generation by a crystal BBO is used to obtain different wavelengths. A femtosecond laser with average output power of 300 mW at 823.1 nm and 73 mW at 402 nm is obtained when the green pump power is 2.5 W. The spectral full width at half maximum are 32.3 nm and 5.1 nm, which can sustain the pulses of 22fs and 33.3 fs, respectively.

We have measured the Raman spectra of β- and α-barium metaborate in crystal and liquid states from room temperature to 1873 K, with a semiconductor laser as the laser source, coupled with a time-resolved detection system to eliminate the dense thermal emission background when temperature was considerably high. Temperature-dependent Raman spectra can clearly indicate that the phase transformation from β- and α-barium metaborate has been completed during 1273-1300 K. Variations of different kinds of microstructure units with temperature are identified and discussed.

The 0.01M two-photon absorption dye trans-4-[p-(N-hydroxyethyl-N-methylamino)styryl]-N-methyl- pyridinium p-toluene sulfonate (abbreviated as HMASPS) doped polymer has been prepared. When pumped by the picosecond pulse from the pulsed mode-locked Nd:YAG laser, the polymer emits more intense upconverted fluorescence and superradiance compared to the solution sample of the dye. The two-photon pumped lasing with oscillating pulses has also obtained. Compared to the dye in its solution state, the emission spectra of the polymer are all blue-shifted. The polymer has a long upconverted fluorescent lifetime of about 4.041±0.04 ns.

Using a technique applied previously to the vibrationally excited molecular nitrogen (N^*₂) in the region of daytime and nighttime aurora, the emission intensity of the N₂ second positive band system in an inductively coupled plasma (ICP) was analysed and the vibrational temperature of nitrogen molecules in the ICP is thus determined. The result shows that the vibrational temperature increases with the increase of the neutral gas pressure from 0.04Pa to 10Pa, then decreases with the further increase of the pressure from 10Pa to 100Pa. Also, this is explained by using the Boltzmann relation between the vibrational temperature and the concentration of the vibrationally excited N^*₂(X¹Σ⁺_g) molecules.

The expressions of electron density fluctuation produced by dust particles in a dusty plasma are derived. It is shown that the fluctuation comes from three different sources. The first source is the thermal motion of the dust particles, which is of a fluctuation power spectrum proportional to n_dZ². The second source is the charge change of the dust particles, which is of a power spectrum proportional to n²_dZ³. The third source is the eigen-mode oscillation of the dust particles, which is of fluctuation power spectrum proportional to √n_d. The powerful electron density fluctuation exists in a dusty plasma due to the fact that the dust particles are high charged. The results may explain the strong electromagnetic scattering by a space dust layer in the Earth's mesosphere.

Based on the framework of magnetohydrodynamic theory, a simple model is proposed to study the mitigation effect of finite Larmor radius on the Rayleigh-Taylor instability in Z-pinch implosions. In this model, taking account of T_i ≥t T_e in Z-pinch implosions we believe that the magnetohydrodynamic plasma responds to a perturbation (～ exp[i( k .x - ωt)]) at frequency (ω + ik²_⊥ρ²_iΩ_i) instead of frequency ω, where k²_⊥ρ²_i is due to the finite Larmor radius effects expressed from the general kinetic theory of magnetized plasma. Therefore the linearized continuity and momentum equations for the perturbed mass-density and velocity include the finite Larmor radius effects. The calculations indicate that in the wavenumber region of interest the finite Larmor radius effects can mitigate the Rayleigh-Taylor instability in Z-pinch implosions.

The technique of toroidal current modulation has been successfully used in suppressing magnetohydrodynamic (MHD) perturbations effectively on HT-7 superconducting tokamak. When the ratio of amplitude of plasma modulated current ΔI_p versus the equilibrium plasma current I_p0 is about 12-30%, the resonance surface is moved outside the island width, the suppression of MHD perturbations is observed. The disruption induced by tearing mode instability is delayed or avoided. Different formats of frequency modulated are compared.

We have developed a three-dimensional electron-photon Monte Carlo transmission (MCT) code. The conversion-transmissivity coefficient of hot electron x-ray, η_ct, is analysed theoretically and simulated numerically using the MCT code. Experiments of disc and cylindrical targets have been performed at the Shenguang-II laser facility. A multi-channel filter-fluorescence spectrometer was used to obtain the hard x-ray spectrum. The temperature and energy of hot electrons are induced from the hard x-ray spectrum and the η_ct value. The average energy fraction of hot electrons is 14% of incident laser energy for the 1ωN_d laser and the spherical target, and the average temperature of hot electrons is 36keV, while 15% for the 1ωN_d laser and the cavity target with the average temperature of 54keV. Also, we obtained the results of 5.6% and 13.3 keV for the 3ωN_d laser and the disk target, 4.9% and 17.9keV for the 3ωN_d laser and the half cavity target with a thin wall, and 2.1% and 22.45keV for those with a thick wall. The experimental results agree with theory and simulation.

The principle of the minimum energy dissipation rate is applied to toroidal plasmas with a coaxial direct current helicity injection. The relaxed states are analysed based on the analytical solutions of the resulting Euler-Lagrangian equations. Three typical states are found. The relaxed states are close to the Taylor state if the ratio of current density to magnetic field on the boundary is small enough. The states will deviate from the Taylor state when the ratio increases, but when it approaches a critical value the central part of relaxed plasmas may approach a force free state and above the critical value both current and magnetic field may reverse in the central part.

During pellet injection and supersonic molecular beam injection, we have observed the increase of electron density and the enhancement of hard x-ray radiation, but the runaway electrons normally decrease without additional fueling when the density of plasma increases. This phenomenon may come from synergetic effects of Dreicer and avalanche runaway electrons. The experimental results are consistent with the calculation based on the theory of avalanche runaway in the HL-1M Tokamak.

The liquid structure of Cu₇₀Ni₃₀ alloy has been investigated using a θ - θ high-temperature x-ray diffractometer. At all temperatures above its liquidus, a distinct pre-peak has been found around a scattering vector magnitude of 13.5nm^-1. The height of the pre-peak decreases gradually with increasing temperature but it is clearly existent up to temperature of 1400°C. This behaviour indicates that stable medium-range order atomic clusters exist in the melt. It is concluded that the short-range order atomic clusters of liquid Cu₇₀Ni₃₀ alloy mainly consist of Cu atoms with centered Ni atoms. The appearance of the pre-peak in the structure factor of liquid Cu₇₀Ni₃₀ alloy is caused by the interaction between centered Ni atoms locating in the neighbouring atomic clusters.

In the framework of tight binding model, the electronic transmission properties of two-dimensional Penrose-lattices with free boundary condition are studied by using the generalized eigenfunction method [Phys. Rev. B 60(1999)13444]. The electronic transmission coefficients for Penrose lattices with different size and width are calculated, and the result shows strong energy dependence because of the quasi-periodic structure and quantum coherent effect. Around the Fermi level E = 0, there is an energy region with zero transmission amplidutes, which suggests that the studied systems are insulating. The spatial distributions of several typical electronic states with different transmission coefficient are plotted to display the propagation process.

Amorphous silicon nanowires were prepared by heating Si substrate at high temperature using an Ni (or Au) catalyst. The nanowires have a diameter of 10 - 40 nm and a length up to several tens of micrometers. Different from the well-known vapor-liquid-solid mechanism, a solid-liquid-solid mechanism appeared to control the nanowire growth. The heating process had strong influence on the growth of silicon nanowires. It was found that ambient gas was necessary to grow nanowire. This method can be used to prepare other kinds of nanowires.

The electrical conductivity of shock-compressed iron was measured up to 208GPa by using an improved design in experiment assembly in which the iron sample was encapsulated in a single-crystal sapphire cell. High-pressure shock compressions were generated by the plate impact technique with the two-stage light-gas gun. The measured conductivity of iron varies from 1.45 x 10⁴Ω^-1cm^-1 at 101GPa and 2010K to 7.65 x 10³Ω^-1cm^-1 at 208GPa and 5220K. After examining these data together with those reported, we found that the Bloch-Grüneisen expression is still valid at high pressures and temperatures, even up to 208GPa and 5220K, at least for ε-iron, which is significant in the filed of condensed matter physics and deep interior earth science.

By virtue of the method of multiple scales, we study a chain of
parametrically driven nonlinear oscillators with a mass impurity. An equation is presented to describe the nonlinear wave of small amplitude in the chain. In our derivation, the equation is applicable to any eigen mode of coupled pendulum. Our result shows that a nonpropagation soliton emerges as the lowest or highest eigen mode of coupled pendulum is excited, and the impurity tends to pin the nonpropagation soliton excitation.

We have determined the Debye temperature of the MgCNi₃ superconductor by using the Rietveld refinement method based on the powder x-ray diffraction data. MgCNi₃ crystallizes in the cubic perovskite structure with space group Pm3m and lattice constant a = 3.8089Å. The temperature factors of the atoms Mg, C and Ni are 0.52, 0.45 and 0.44, respectively. The Debye temperature of MgCNi₃ is calculated to be _D = 440K.

We have measured the equation of state for liquid nitrogen compressed dynamically to pressure of 10-60GPa by employing a two-stage light-gas gun. The data show a continuous phase transition above the shock pressure of 33GPa, as indicated previously by shock wave experiments. A theoretical model has been derived to examine the experimental data by inducing molecular dissociative fraction. According to theoretical and experimental data the phase transition was thought to be a molecular dissociative phase transition.

We investigate a periodic microstructure induced by 355 nm ultraviolet polarized laser on polyimide surface and the dependence of the structures on laser parameters. Laser-induced periodic surface structures (LIPSS) of sub-micrometer size were generated on three kinds of polyimide films by a polarized Nd:YAG laser of 355 nm within a wide range of laser fluence. The chemical structure of polyimide, the film-making process, the number of laser pulses and the laser fluence greatly influenced the formation of LIPSS. The periodicity of LIPSS was decided by the wavelength, the incidence angle of the laser beam and the apparent refractive index of the material.

Using an ab initio total energy and force method, we have investigated the stability of different structures of Ge(111):Sb(1 ML) as a function of the lateral lattice constant. We find that the (2 x 1)-reconstruction of Ge(111):Sb experimentally found to be stable at the equilibrium lattice constant of Ge is also the stable structure for slightly dilated Ge films (< 1%), while for larger dilatations the (1 x 1)-structure becomes stable. For compressed Ge films the (√3 x √3)T₄-structure (found experimentally on Si(111):Sb) becomes competitive and it is stable for the lattice constants compressed larger than 5\%. Furthermore, we find that for each structure, the equilibrium lattice constant is different from the bulk Ge crystal. Our results are helpful for understanding of surfactant mediated island growth on strained films.

Using an exact diagonalization method, we study an extended Hubbard model with an electron-lattice interaction for an organic ferromagnetic chain with radical coupling. The result shows that the ferromagnetic ground state originates from the antiferromagnetic correlation between adjoining sites, which is enhanced by the on-site e-e repulsion. The intersite e-e repulsion induces the imhomogeneous distribution of the charge density. The dimerization is decreased by the e-e interaction and the radical coupling. The electron-lattice interaction and the radical coupling can transfer the spin density and charge density between the main chain and the radicals.

X-ray photoelectron spectroscopy has been used to characterize the oxidation states in Ta/NiO_x/Ni₈₁Fe₁₉/Ta magnetic multilayers prepared by rf reaction and dc magnetron sputtering. The exchange coupling field and the coercivity of NiO_x/Ni₈₁Fe₁₉ are studied as a function of the ratio of Ar to O₂ during the deposition process. The chemical states of Ni atoms in the interface region of NiO_x/NiFe were also investigated by XPS and the peak decomposition technique. The results show that the ratio of Ar to O₂ has a great effect on the chemical states of nickel in NiO_x films. Thus the exchange coupling field and the coercivity of Ta/NiO_x/Ni₈₁Fe₁₉/Ta are affected seriously. Also, the experiment shows that XPS is a powerful tool in characterizing magnetic multilayers.

We have investigated a new ferrite-ceramic composite material with inductive and capacitive properties fabricated by a solid-state reaction method. We analyse the effects of composite mechanism and microstructure on the magnetic and electric properties. The results show that the new materials can be used as not only the inductor materials, but also the capacitor materials in a wide frequency range of 1 kHz-1.8 GHz. The real part of permeability of the composite material is between 10 and 5.6, the imaginary part of permeability is between 1.2 and 0.5, and the dielectric constant is about ten times larger than the ordinary ferrite materials. It is suggested that the new composite materials will be widely used in anti-electromagnetic interference fields and radio frequency communication fields.

Under the influence of an applied electric field, the variation of apparent viscosity of electrorheological (ER) fluid flow causes ER effects. According to the Bingham model, which is widely used for describing the rheological properties of ER fluids, this variation should be very weak at high shear rate. To clarify the ER effects in ER journal bearings at high shear rate, a numerical study is presented. It is found that under influence of the applied electric field, ER effects in ER journal bearings can be affected by not only the apparent viscosity of ER fluids but also the movement of yield surface in the clearance of ER journal bearing. In the case of low shear rate, both are effective on the lubricant film pressure of ER journal bearings. In the case of high shear rates, the main factor is the extension of non-yield region in the bearing clearance.

We propose a model of the magnetic coupling (MC) of a rotating black hole (BH) with the surrounding accretion disc in order to study the radial temperature profile in the inner region of the disc, in which a linear map from the angular coordinate on the BH horizon to the radial coordinate on the thin disc is given by closed magnetic field lines. The MC power and torque are derived by using a modified equivalent circuit. It is shown that the MC effects on the temperature profile are related intimately to the BH spin, resulting in the variation of the value and the position of the peak temperature. It turns out that the value range of the color temperature of the disc is extended by the MC effects.

The density of N-clusters (the cluster which contains N galaxies) in the universe is shown from observations to scale with N as n_N ∝ N^-τ with τ = 3/γ +1 and the correlation exponent γ ≈ 1.8. Correspondingly, a scaling relation τ = 29-9γ/12-4γ between the two exponents, which agrees with the observations, is found analytically in our naive clustering model.

We analytically study the turbulent acceleration of solar protons by strong Langmuir plasmons in Cerenkov processes . It is shown that among the wave spectra with self-retained source only the Pelletier spectrum (W_k ∝ k^-7/2) can result in energy spectrum of non-relativistic protons, which gives a good fit to that observed from solar flare event. It is quite possible that strong Langmuir turbulence presents in coronal active region, with three-dimensional, isotropic and stationary spectrum proportional to k^-7/2, and is responsible for the acceleration of flare protons.

We re-analyse the relationship between the x-ray luminosity
(L_X) and the temperature (T) of groups and clusters of galaxies, based on the largest sample of 40 groups and 188 clusters. We employ the moving median statistics for the data set, along with the proper linear regression. Our newly established L_X-T relations for groups and clusters show no significant difference within statistical uncertainties,
yielding L_X ∝ T^2.79±0.01 (groups) and L_X ∝ T^2.54±0.004 (clusters). This also supports the hierarchical scenario of structure formation in which groups are simply the scale-down version of clusters. It is argued that the break in the L_X-T relation on group scales detected in previous studies may suffer from sparse data sample and poor statistical methods.