A new spectral problem is introduced and the associated hierarchy of nonlinear evolution equations is derived with the help of the zero curvature equation as well as recursive operators. It is found that the Gerdjikov--Ivanov (GI) equation, which is one of three important derivative nonlinear Schrödinger equations, exactly belongs to the hierarchy as a special reduction. A powerful tool of the trace identity is used to establish the bi-Hamiltonian structure for the whole GI hierarchy. Moreover, it is shown that GI hierarchy admits an infinite common set of conserved quantities which are in involution in pairs under Poisson's bracket. This indicates that the whole GI hierarchy is completely integrable in Liouville's sense.

Scalar particles might be in the universe as diffuse gaseous clouds or compact objects and might be even present in D-stars. The astrophysical consequences are discussed in detail. Especially, D-stars may be considered as an elegant candidate. The Einstein ring should be observable with microarcsecond x-ray imaging mission if D-stars exist.

The thermoelastic effect of the suspension fibre in the torsion pendulum experiment with magnetic damping was studied. The disagreement in the oscillation periods was reduced by one order of magnitude through monitoring the ambient temperature and thermoelastic correction. We also found that the period on uncertainty due to noise increases with the amplitude attenuation after thermoelastic correction.

A simple interferometer was used to monitor the seismic noise effect on the equivalence principle test using the free-fall interferometric method. The experimental result showed that this effect was below λ/100, where λ is the wavelength of the laser beam, and the uncertainty of the differential gravity acceleration of the individual free-fall result due to this effect was about 0.6μGal.

In a two-dimensional area-preserving map we found a kind of noninvertibility that is induced by a piece-wise smooth property of the map. This can lead to the appearance of such kinds of elliptic islands that attract the iterations from a set of initial values outside themselves, while behaving regularly inside. We suggest calling such islands quasi-attractors.

A new pumping--probing scheme for the optically pumped cesium beam frequency standard has been experimentally tested in our laboratory. The stability of the optically pumped cesium beam frequency standard was measured by comparing its 10MHz output with an HP5071A commercial cesium atomic clock. The result shows that the frequency stability for the 1s and 30000s sample times are 1.2×10^-11 and 3.7×10^-13, respectively. It was proved that the new pumping scheme works well.

A self-affine analysis of multiparticle production in pp collisions at 400GeV/c was performed by using the method of continuously varying scale and the method of the factorial moments of continuous order. The self-affine generalized fractal dimensions and multifractal spectrum have been obtained. The self-affine multifractal spectrum is concave downward with a maximum at q=0, f(α(0)) = D(0) = 1.D(q) decreases with increasing q showing that there is self-affine multifractal behaviour in multiparticle production at the 400GeV/c pp collisions. The Levy index μ > 1 indicates that a non-thermal phase transition may exist in the pp collisions at 400GeV/c.

The level states of the nucleus ¹²⁴Cs have been populated through the ¹¹⁶Sn(¹¹B,3n) reaction at a beam energy of 45 MeV, provided by the HI-13 tandem accelerator of the China Institute of Atomic Energy. A number of low-lying states are constructed. The level states in the πh_11/2 vg_7/2 side band are extended down to lower spin by one h. The level energies and spins in the rotational bands are determined through the establishment of various connections, which confirm the spin assignment of the yrast band in¹²⁴Cs based on excitation energy systematics. It is revealed that with the present spin assignment, the πh_11/2 vg_7/2 side band shows signature inversion at low-spin region and the inversion occurs at a spin of about 16ħ.

Levels in the neutron-rich ¹⁰⁴Mo nucleus have been investigated by observing prompt γ-rays from the spontaneous fission of ²⁵²Cf with the Gammasphere detector array. The ground-state band, the one-phonon and the two-phonon γ-vibrational bands as well as a quasiparticle band have been confirmed and expanded with spin up to 14ħ. Other two side bands probably built on new quasiparticle states are identified. The possible configurations for the quasiparticle bands are discussed. Two of the quasiparticle bands show larger moments of inertia and may have pair-free characteristics. The levels of the ground-state band, the one-phonon γ-band and the two-phonon γ-band calculated from a general collective model are in close agreement with the experimental data.

High-spin states in ^178,180Ir have been studied via the ^152,154Sm(³¹P, 5nγ) reactions through excitation functions, x-γ and γ -γ-t coincidence measurements. A doubly decoupled band has been identified in each of the isotopes. The level spacings for such structures in odd--odd
^178-186Ir have been inspected and thus a regular level staggering as a function of the neutron number is revealed. This particular phenomenon may be associated with bandmixing at lower excitation energies.

High-spin states in the odd-proton nucleus ¹³⁵Pm have been investigated using the ¹⁰⁷Ag(³²S, 2p2n)¹³⁵Pm reaction. Seven rotational bands have been observed in ¹³⁵Pm. The yrast band based on a decoupled h_11/2 proton is found to have a band crossing ω_c ～ 0.43MeV/ħ. Two positive-parity bands based on the two signature components of the πg_7/25/2⁺[413] Nilsson orbital have been observed in the main sidebands. The favoured band with (π,α)=(+,-1/2) has been shown to populate below the first pair of proton alignment. Both bands have shown upbend at ω₁ ～ 0.26 MeV/ħ and ω₂ ～ 0.43 MeV/ħ. These crossing frequencies can be attributed to the decoupling of the first pair of H_11/2 quasi-proton and H_11/2 quasi-neutron, respectively. Four weaker bands have been observed in sidebands too. Among them, two states are possibly built on a πd_5/23/2⁺[411]configuration.

A theory is developed for magnetically confined Fermi gas at a low temperature based on the density functional theory. The theory is illustrated by the numerical calculation of the density distributions of Fermi atoms ⁴⁰K with parameters according to DeMarco and Jin's experiment [Science, 285(1999)1703]. Our results are in close agreement with the experiment. To check the theory, we also performed calculations using our theory at a high temperature, which compared very well to the results of the classical limit.

Differential cross sections for the elastic scattering of electrons by H₂ at 100 eV and 150 eV have been calculated and compared with experiments. We use the momentum space method in which the electron-molecule system has a single centre and the interaction of electron-nuclei is expanded by a multipole expansion. The static exchange calculation is supplemented by a phenomenological polarization potential. Electron-molecule scattering is reduced to an electronic problem by the Born--Oppenheimer approximation, using closure over the vibrational and rotational states.

L-shell partial production cross sections ofL_α-, L_β-, L_γ- rays by electron impact were measured by observing the counts of x-rays from an impacted thin tungsten target. The total production cross sections and mean ionization cross sections were deduced from the measured results. The electron beam energy range was found to be 11-36keV. The influence of electrons reflected by the backing on ionization cross sections has been corrected. The experimental results agree well with the theoretical predictions.

A normalized two-dimensional band-limited Weierstrass fractal function is used for modelling the rough surface. An analytic solution of the scattered field and variance of scattered intensity from this Weierstrass fractal surface is given based on the Kirchhoff theory. The result shows that the scattering pattern in the near forward direction can be approximated to the slope of a linear equation.

The two-photon polarized entangled state is generated from the type II spontaneous parametric down-conversion pumped by a femtosecond pulse. The two-photon interference is observed in the Hong-Ou-Mandel interferometer. The high visibility of the interference is restored with narrow band interference filters placed in front of the detectors.

A cavity-modified master equation is derived for a coherently driven V-type three-level atom coupled to a single-mode cavity in the bad cavity limit. The influences of the cavity-induced quantum interference on the steady-state populations are analysed. We show that the population inversion can occur due to the effect of cavity-induced quantum interference.

The modified Jaynes-Cummings model of a single two-level atom placed in the common domain of two cavities or interacting with two quantized modes is studied by a dynamical algebraic method. With the help of an SU(2) algebraic structure, we then obtain the eigenvalues, eigenstates, time evolution operator and atomic inversion operator for the system. We proceed to investigate the modified Jaynes-Cummings model governed by the Milburn equation and present the exact solution of the Milburn equation.

We demonstrated a phase-sensitive method for studying the Raman-enhanced nondegenerate four-wave mixing (RENFWM). The reference beam is another four-wave mixing signal, which propagates along the same optical path as the RENFWM signal. This method is used for studying the phase dispersion of the third-order susceptibility x⁽³⁾ and for the optical heterodyne detection of the RENFW signal.

Generation of third-order harmonics at 800 nm of femtosecond laser pulses is studied in neutral atmospheric air and in plasma of optical breakdown in air. Its efficiency is measured at different fundamental laser intensities. A maximum efficiency is observed at the intensity when optical breakdown in atmospheric air starts. The factors that exhibit the main effects on the harmonic generation, including self-focusing in a neutral air and self-focusing in plasma, are discussed.

With the help of a weak linearly polarized low-frequency field, we study high-order harmonic generation in a circularl polarized high-frequency field. Although the low-frequency field is not intense enough to ionize the atom, it can accelerate the electron more efficiently. As a result, the application of this field can generate harmonics with a much higher energy compared to the monochromatic case.

Large sized and optical quality GdCa₄O(BO₃)₃(GdCOB) crystal with calcium partially substituted by strontium (Sr) ions was grown for the first time. The x-ray powder diffraction shows that the Sr ion has an effect on the cell parameters of the GdCOB crystal. Second-harmonic generation (SHG) experiments were performed on the Sr:GdCOB and GdCOB crystals along the spatial phase-matching direction. The results show that the cw green laser output power is 1.04W when the laser diode pump power is 10W in the Nd:YVO₄/Sr:GdCOB intracavity laser. Considering the slope efficiency of Nd:YVO₄ and the fundamental laser in cavity, the intracavity SHG conversion efficiency of the GdCOB crystal is 21% while it is 24% for the Sr:GdCOB crystal, the SHG conversion efficiency is improved by 14%. The effect of the Sr ions on the nonlinearity of the GdCOB crystal is also discussed by using the anion group theory.

When a powerful femtosecond laser pulse was tightly focused into a bulk quartz, plasma generation occurred only in a very small focal volume. This extremely confined interaction led to an explosive expansion and generated a sub-micrometre void with a diameter as small as 200-300nm. The dependence of the size of the void on the laser energy or pulse duration was investigated and the mechanism of this process was associated dominantly with the multiphoton ionization.

Single-axis acoustic levitation of four polymer samples has been realized in air under the ground-based laboratory conditions for the purpose of space environment simulation of containerless processing. The levitation capabilities are investigated by numerical calculations based on a model of the boundary element method corresponding to our levitator and following Gor'kov and Barmatz's method. The calculated results, such as the resonant distance between the reflector and the vibrating source and the positions of levitated samples, agree well with experimental observation, and the effect of gravity on the time-averaged potential for levitation force is also revealed. As an application, the containerless melting and solidification of a liquid crystal, 4-Pentylphenyl-4' methybenzoate, is successfully accomplished, in which undercooling up to 16K is obtained and the rotation and oscillation of the sample during solidification may result in fragmentation of the usual radiating surface growth morphology.

The propagation behaviour of an initial thermal perturbation in liquid argon is simulated by the molecular dynamics method. The 12-6 Lennard--Jones potential and mirror boundary conditions are employed in the 32768-particle three-dimensional simulation. Macroscopic characteristics such as the kinetic temperature, pressure and momentum profiles are monitored during the simulation in order to examine the heat propagation behaviour under a timescale comparable with the relaxation time. The results show that the behaviour is still diffusion-like; no features predicted by the Cattaneo--Vernotte model have been found. The wave-like front of the local temperature may be caused by the adiabatic compression and expansion by the pressure wave generated by the thermal expansion.

The distribution of the reflection power ratio for a neutron or x-ray diffracted from a cylindrical crystal immersed in an homogenous incident beam is obtained by the numerical solution of the transfer equations for the first time. The profile well reflects all the physical properties of the absorption and extinction behaviour in the crystals. A systematic investigation of the secondary extinction for cylindrical and spherical crystals was carried out based on these results.

Mo ions are implanted into aluminium with a high ion flux and high dose at elevated temperatures of 300°C, 400°C and 500°C. X-ray diffraction spectra show that the Al₁₂Mo phases are formed. Rutherford backscattering spectroscopy indicates that a profile of Mo appears in Al around the depth of 550nm and with an atomic concentration of ～7%, when Mo is implanted to the dose of 3×10¹⁷/cm² with an ion flux of 45μA/cm²(400°C). If the dose increases to 1×10¹⁸cm² at the same ion flux, the penetration of Mo ions in Al can reach a depth of 2μm, which is greater than the ion project range Rp(52.5nm). The results show that anomalous diffusion takes place. Owing to the intense atom collision cascades, the diffusion coefficient increases greatly with the increase of the ion flux and dose. The Mo diffusion coefficients in Al are calculated. The Mo retained dose in Al increases obviously with the increase of the ion flux.

By using the antitrace map method, we investigate the light transmission for generalized Fibonacci multilayers. Analytical results are obtained for transmission coefficients in some special cases. We find that the transmission coefficients possess a two-cycle or six-cycle property. The cycle properties of the trace and antitrace are also obtained.

A molecular dynamics simulation method is used to study the growth of narrow single-wall carbon nanotubes. It is found that the growth temperature and the species of small carbon clusters in the feedstock are important for the quality of the nanotubes grown. There is a temperature range of 1000-1500K in which the narrow armchair single-wall carbon nanotubes can grow rapidly via adduction of C₂ dimers, even without the existence of catalysts. The narrow zigzag tubes cannot keep open-ended growth. If the feedstock consists of various species of carbon clusters, the tubes cannot keep open-ended growth. At higher temperatures, the narrow nanotubes close rapidly in the noncatalytic environment, and the products grown are fullerene-like capsules.

The Hugoniot equation-of-state (EOS) of porous iron with an average initial density of 6.904g/cm³ has been measured in the pressure range from 90 to 160GPa, and a good straight fitting D = 2.997+1.603μ has accordingly been obtained, where D is the shock wave velocity and μ the particle velocity, both in units of km/s. Combining this with the Hugoniot EOS of non-porous iron, the Grüneisen EOS and the Rankine-Hugoniot energy conservation relation, and taking the possible solid--liquid transition correction, we have calculated the Grüneisen parameter γ of iron and obtained the γ₀ρ₀ = γρ =const, with γ₀ = 1.945 and ρ₀ = 7.856cm³, ρ being the density.

Loop-shaped contrasts were observed in the as-grown Al_70.3Pd_20.6Mn_9.1 icosahedral quasicrystal (IQC) by means of x-ray diffraction topography (Lang's method). One possible direction of the apparent Burger vectors of loop-shaped defects (LSDs) was determined to be B = [1ī0ī01] by the invisibility criterion, whose physical component is parallel to the two-fold axis 1/τ[ī/0, 1/1, 0/ī] of the IQC. Apart from the relaxation of strain fields around the faceted dodecahedral holes and lamellar precipitates, LSDs may well originate from the growth of the quasicrystal, which shows that these defects could be a kind of intrinsic defect in the quasicrystals.

The reoccurrence of pits has been found on the surfaces of c-axis YBa₂Cu₃O_7-δ (YBCO) films grown epitaxially on 10°vicinal SrTiO₃ substrates by pulsed laser deposition. They are always associated with films with a step-terrace structure, while polycrystalline films have no pits. Pit formation is attributed to the large interfacial stress induced by vicinal substrate and oxygen deficiency of the YBCO film during the tetragonal-to-orthorhombic (T-O) phase transition, which cannot be released by forming twins, and leads to rupturing of the film surface. By reducing the oxidation partial pressure for the T-O phase transition to 80Pa, no pits were formed, and the YBCO film is superconducting at 60K.

Interfacial reactions between aluminium and polycrystalline cermet TiC_0.6 were investigated using x-ray photoelectron spectroscopy, Auger electron spectroscopy and x-ray diffraction. It was found that titanium exists in two chemical states. The carbide and oxide of titanium can be detected simultaneously, and the atomic ratio of Ti:C:O is 5:3:2. This suggests that TiC_0.6 is a Ti-oxycarbide or oxygenated TiC composite: Ti₅C₃O₂(TiO₂+4TiC_0.75). When Al is deposited in vacuum on the Ti-oxycarbide surface, the active Al atoms react chemically only with TiO₂at room temperature, but not with Tic_0.75 in Ti-oxycarbide. The reaction products are Al₂O₃ and the intermetallic compound Al₃Ti. Annealing the Al/TiC_0.6 interface at 750°C Al reacts also with TiC_0.75 to form a brittle Al₄C₃ phase.

Ultra-violet photoemission spectroscopy measurements for CO
adsorption on the (2×2)-Cs precovered Ru (0001) surface were performed. The Cs 5p(5p_3/2) level (Cs state) locates at 11.3 eV in binding energy for the (2×2)-Cs overlayer on Ru (0001). Upon the CO adsorption, a new peak, which is associated with the Cs 5p state for the Cs adatoms influenced by the neighbouring CO adsorbed (the Cs+CO state), appears at the lower binding energy side of the Cs state. This new peak is at 10.8,eV for the CO saturation where the (2×2)-Cs+2CO compound layer is formed. This result gives clear evidence for local interaction of Cs and CO on the Ru (0001) surface.

Bandgap tuning of the InGaAsP/InP multiple quantum well (MQW) laser structure by the impurity-free vacancy diffusion (IFVD) is investigated using photoluminescence. It has been demonstrated that the effects of the plasma bombardment to the sample surface involved in the IFVD technique can enhance the intermixing of the InGaAsP/InP MQW laser structure. The reliability of the IFVD technique, particularly the effects of the surface decomposition and the intrinsic defects formed in the growth or preparation of the wafer, has been discussed.

An electron pairing theory based on effective electron spin coupling mediated by antiferromagnetically correlated local moments is presented to account for high-T_c phenomena. We show that Kondo scattering and the suppression of the antiferromagnetic superexchange between Cu²⁺ moments lead to local triplet pairing, the mechanism underlying high-T_c superconductivity.

A way to determine some important etching parameters in the step fabrication for highT_c step-edge Josephson junctions is described based on an analysis of the dynamics of the etching process. The optimum thickness of the etch mask is defined with negligible recession of the mask edge during the etch. Under this condition, the equilibrium angle of the steps etched on the SrTiO₃ (STO) substrate with an Nb mask has been calculated to be about 76°. With optimized mask thickness, its sharp sidewall and straight edge, high-quality steps on STO substrates with step height from 200-300 nm and step angle above 70°are made. Josephson junctions and dc-SQUIDs with high reproducibility and less parameter scatter are obtained on the step substrates.

We study analytically the stability of the saturated ferromagnetic ground state (the Nagaoka state) of the Hubbard model in the low electron density limit with the mean-field approach. We find that the critical U_c is just 4πt, where t is the hopping integral between the nearest neighbours, i.e., when U is larger than 4πt,the paramagnetic state is unstable with respect to the ferromagnetic state, and vice versa.

The transport properties of La_0.67Sr_0.33MnO₃ (LSMO) epitaxial films on differently orientated LaAlO₃ substrates have been studied. The as-deposited films with different orientation exhibit different transport behaviours. The resistivity of the films on the (100) and (110) substrates undergoes a metal--insulator transition while the resistivity of the film on the (111) substrate is insulator-like. This is attributed to the discrepancy of oxygen deficiency in the samples which is influenced by the lattice mismatch between the film and the substrate. After being annealed at 700°C in 1-atm flowing pure oxygen for half an hour, all films have the same resistivity behaviour as the bulk LSMO, which may be important for future applications.

The travelling wave method has been used to measure the drift mobility in the paramagnetic-insulator state of La_0.75Sr_0.11Ca_0.14MnO₃ films. The thermal activation of the drift mobility in manganites has been measured for the first time. The mobility varies from 2.5×10^-2cm²/Vs at 310K to about 9.2×10^-2cm²/Vs at 400K. The Arrhenius behaviours of the conductivity and drift mobility indicate that the transport process in manganites above the Curie temperature is dominated by the thermally assisted hopping of small polarons.

The effects of thermal annealing on photoluminescence (PL) and structural properties of a-Si_1-xC_x:H films deposited by plasma enhanced chemical vapour deposition from CH₄+SiH₄ mixtures are studied by using infrared, PL and transmittance-reflectance spectra. In a-SiC:H network, high-temperature annealing gives rise to the effusion of hydrogen from strongly bonded hydrogen in SiH, SiH₂, (SiH₂)n, SiCHn and CHn configurations and the break of weak C-C, Si-Si and C-Si bonds. A structural rearrangement will occur, which causes a significant correlation of the position and intensity of the PL signal with the annealing temperature.The redshift of the PL peak is related to the destruction of the confining power of barriers.However, the PL intensity does not have a significant correlation with the annealing temperature for a C-rich a-SiC:H network, which refers to the formation of π-bond cluster as increasing carbon content. It is indicated that the thermal stability of C-rich a-Si_1-xC_x:H films is better than that of Si-like a-Si_1-xC_x:H films.

Organic light-emitting devices (OLEDs) with enhanced brightness and efficiency were developed using an LiF-doped organic layer as an electron-injecting layer besides the aluminium cathode. The typical device structure is glass substrate/indium-tin-oxide/N, N'-bis (3-methyphenyl)-N, N'-diphenylbenzidize/8-tris-hydroxyquinoline aluminium (Alq₃)/LiF-doped Alq₃/Al. An optimized device with an LiF-doped Alq₃ layer showed brightness over 15300 cd/m², while the device without the LiF-doped Alq₃ layer exhibited only 3200 cd/m², also, the luminance efficiency of the former was 4-5 times as that of the latter. This is another way to improve the OLEDs performance, especially in applications of OLEDs with a large active area.

Positron annihilation lifetime spectroscopy has been used to study the free volume properties of the cross-linked polyurethane network as a function of temperature in the range from 15K to 300K. The glass transition of polyurethane was observed and the thermal expansion coefficient of the free volume was calculated. Analysis of the ortho-positronium (o-Ps) lifetime distribution shows that the distribution of the free volume in polyurethane is slightly broadened with the increasing temperature in the glassy state, and then significantly broadened with the increasing temperature above the glass transition.

The average heat capacities of the undercooled Cu-25%Ni, Cu-50%Ni,Cu-50%Ni and Cu-75%Ni melts were derived by using the glass fluxing technique. The undercoolings of the above alloys were 381, 380, 349 and 431K, respectively, which exceed the critical undercooling of the classical nucleation theory. A detailed analysis of the heat transfer condition during the solidification process was carried out, which suggested a linear relationship between the time duration of thermal arrest t_a and the undercooling ΔT. The hypercooling points of the alloys, derived from the relationship between t_a and ΔT, were determined to be 457.7, 461.1, 448.4 and 528.K, respectively.

The modulation-doped Al_0.22Ga_0.78N/GaN heterostructures with different Al_0.22Ga_0.78N barrier thicknesses were grown by means of metal--organic chemical vapour deposition. The Al_0.22Ga_0.78N layer still has pseudomorphic growth when its thickness is 53nm. The mobility of the two-dimensional electron gas (2DEG) at the heterointerfaces is much higher than that of the electrons in GaN films at both 300 and 77K. The dramatic decrease of the 2DEG mobility in an Al_0.22Ga_0.78N/GaN heterostructure corresponds to the partial relaxation of the Al_0.22Ga_0.78N barrier.

A new silicon-based PbTiO₃/Pb(Zr_0.53Ti_0.47)O₃/PbTiO₃ sandwich structure is fabricated by a sol--gel method. Compared with other fabrication processes without PbTiO₃ buffer layers, the annealing temperature is greatly reduced by as much as 100°C. Capacitance--voltage, polarization--electric field and dielectric--frequency properties of this sandwich structure are studied. The Pb(Zr_xTi_1-x)O₃ films are proved to have good dielectric and ferroelectric properties.

A thin oriented bacteriorhodopsin (bR) film is deposited on a stainless steel slide by use of the electrophoretic sedimentation method. A junction is made with electrolyte gels having a counterelectrode to construct a bR-based photoelectric detector. The photoelectric response signal to a 10ns laser pulse is measured. A theory on the photoelectric kinetics of bR is developed based on the concept of the charge displacement current and the bR photocycle rate equations. Comparison between the theoretical and experimental results proves that the bR photoelectric response to a short laser pulse is a multi-exponential process. The decay time constants and amplitudes of each exponential component are obtained by data fitting.

The Langmuir-Blodgett monolayers of 10,12-tricosadiynoic acid
molecules were deposited onto the basal plane of highly oriented
pyrolytic graphite (HOPG) by Schaefer’s method and then observed with the scanning tunnelling microscope (STM). With a view to achieving a parallel molecular arrangement on the graphite surface, the deposition was deliberately conducted at a relatively low surface pressure. As exhibited by the STM images, by this approach the 10,12-tricosadiynoic acid molecules could constitute an ordered structure with their molecular chains lying parallel to the substrate. The model of molecular dimer is put forward for the interpretation of the observed phenomena.

Based on the magnetohydrodynamic energy principle, it is proved that Gold-Hoyle’s nonlinear force-free magnetic field is unstable. This disproves the sufficient criterion for stability of nonlinear force-free magnetic fields given by Krüger that a nonlinear force-free field is stable if the maximum absolute value of the force-free factor is smaller than the lowest eigenvalue associated with the domain of interest.

The proton fraction in β-stable neutron stars is investigated
within the framework of the Skyrme-Hartree-Fock theory using the extended Skyrme effective interaction for the first time. The calculated results show that the proton fraction disappears at high density, which implies that the pure neutron matter may exist in the interior of neutron stars. The incompressibility of the nuclear equation-of-state is shown to be more important to determine the proton fraction. Meanwhile, it is indicated that the addition of muons in neutron stars will change the proton fraction. It is also found that the higher-order terms of the nuclear symmetry energy have obvious effects on the proton fraction and the parabolic law of the nuclear symmetry energy is not enough to determine the proton fraction.

The effect of the strong gravitational field of the strange core of a strange star on its surface electrostatic potential energy distribution is discussed. We present the general-relativistic hydrodynamics equations of fluids in the presence of the electric fields and investigate the surface electrostatic potential distribution of the strange core of a strange star in hydrostatic equilibrium to correct Alcock and coworker's result [Astrophys. J.310(1986) 261]. Also, we discuss the temperature distribution of the bare strange star surface and give the related formulae, which may be useful if we are concerned further about the physical processes near the quark matter surfaces of strange stars.

We have solved the set of equations for advection-dominated accretion flows (ADAFs) around black holes, and found a new class of global solutions with standing radial shocks.Such α-X-type shocks may exist in flows when 0 ≤ α < 0.05. An example solution is given explicitly, for which α=0.01 and γ=1.5. The shock position is R_sh=8.68R_g, which is between the inner sonic point R_s1=3.88R_g and the outer sonic point R_s2=85.92R_g.

We present a new exact solution to Einstein's equations that describes the evolution of inflationary universe models. The inflation is driven by the evolution of a scalar field with an approximate two-loop four-dimensional string potential. In this scenario, the inflation began immediately after the epoch governed by quantum gravity and therefore there is no initial singularity. The successful inflation scenario is expected to appear only at two-loop order. For a₁/|a₂|≥90, the spectral index n_s of the scalar density fluctuations lies well inside the limits set by the cosmic background explorer satellite and the gravitational wave spectral index is n_g ≈1.

A Bayesian approach is used to derive the probability distribution (PD) of the Hubble constant H₀ from recent measurements including supernovae Ia, the Tully-Fisher relation, population II and physical methods. The discrepancies among these PDs are briefly discussed. The combined value of all the measurements is obtained, with a 95% confidence interval of 58.7 < H₀ < 67.3 (km.s^-1.Mpc^-1).