A system of first-order differential equations is expressed in the form of first-order Lagrange equations. Based on the theory of symmetries and conserved quantities of first-order Lagrange systems, the perturbation to the symmetries and adiabatic invariants of first-order Lagrange systems are discussed. Firstly, the concept of higher-order adiabatic invariants of the first-order Lagrange system is proposed. Then, conditions for the existence of the exact and adiabatic invariants are proved, and their forms are given. Finally, an example is presented to illustrate these results.

A scheme for teleporting a two-particle entangled state via a three-particle entangled state is proposed. It is shown that the probability of successful teleportation is twice the modulus square of the smaller Schmidt coefficient of the entangled three-particle state.

In view of making the best use of information coming from past observational data, a new difference scheme with multi-time levels (p>3) is suggested. Some mathematical characteristics of the scheme, which is called the retrospective scheme, are discussed. The numerical results of some examples show that the calculation accuracy of linear and nonlinear advection equations computed with the retrospective scheme is higher than that obtained via the leapfrog scheme. The scheme can be applied to many fields, such as meteorology, engineering physics, astronautics, environment and economy etc, where systematic observations are made normally.

A homogeneously broadened two-mode laser system with multiplicative coloured noise is investigated when the mode coupling constant ξ=2. An analytical result is obtained when two-dimensional decoupling theory is applied to the system. The intensity auto-correlation function and effective eigenvalue of the laser system are calculated when the difference of pump parameters, multiplicative noise strength and noise correlation time are varied. It is shown that the multiplicative noise can enhance the fluctuations while the noise colour can reduce the fluctuations in the laser system.

The electron-photon delayed coincidence technique has been used to measure precisely the lifetime for the 4p^{1}P^{0} state in calcium. The lifetime of this state was obtained by measuring the time correlation spectrum between the inelastically scattered electrons and the corresponding de-excitation photons. By using the least-squares fitting program to fit Gale's equation to the data points, a value of (4.15±0.17) ns was obtained. The result was compared to some of the earlier experimental measurements.

The Fourier transform spectrum of the ν_{2}+2ν_{3} band of the HDO molecule was recorded with a resolution of 0.02 cm^{-1}. The spectrum was rotational analysed and the spectroscopic parameters of the (0,1,2) state were estimated in terms of Watson's effective rotational Hamiltonian model and also the model in the Padé-Borel approximation form. They reproduce the upper energy levels with an accuracy close to the experimental uncertainty of 0.001 cm^{-1}.

Two optical set-ups to implement wavelet transform with a single lens have been proposed, in which the wavelet filter was placed in front of the imaging lens or on the frequency plane. The general formula of the complex field distribution of the output plane has been deduced. The analysing wavelet functions of the band-pass wavelet filters with double and circular slits have been discussed.

The filamentation instability of laser beams propagating in nonlocal nonlinear media is investigated. It is shown that the filamentation instability can occur in weakly nonlocal self-focusing media for any degree of nonlocality, and in defocusing media for the input light intensity exceeding a threshold related to the degree of nonlocality. A linear stability analysis is used to predict the initial growth rate of the instability. It is found that the nonlocality tends to suppress filamentation instability in self-focusing media and to stimulate filamentation instability in self-defocusing media. Numerical simulations confirm the results of the linear stability analysis and disclose a recurrence phenomenon in nonlocal self-focusing media analogous to the Fermi-Pasta-Ulam problem.

A universal theory of steady-state one-dimensional photorefractive spatial solitons is developed which applies to the steady-state one-dimensional photorefractive solitons under various realizations, including the screening solitons in a biased photorefractive medium, the photovoltaic solitons in open- and closed-circuit photovoltaic-photorefractive media and the screening-photovoltaic solitons in biased photovoltaic-photorefractive media. Previous theories advanced individually elsewhere for these solitons can be obtained by simplifying the universal theory under the appropriate conditions.

CONDENSED MATTER: STRUCTURAL, MECHANICAL, AND THERMAL PROPERTIES

The nucleation and growth of two-dimensional islands in a surfactant-mediated epitaxy system have been studied by computer simulation. To improve the recent results published in the literature, we use a configuration-dependent energy barrier for the exchange process at the island edge in our model. The simulations produce fractal islands at high temperatures or low deposition fluxes, and a transition to regular compact islands occurs at lower temperatures or higher fluxes, in good agreement with the recent experimental results. The barrier for the island-edge exchange has quite a strong effect on the island density as a function of temperature and flux. A small change of the island-edge exchange barrier induces a large variation of the island density in the low-temperature or high-flux region. The flux-dependent island density shows a clear scaling-law behaviour in the intermediate-flux region. The scaling exponent increases evidently as the island-edge exchange barrier increases.

CONDENSED MATTER: ELECTRONIC STRUCTURE, ELECTRICAL, MAGNETIC, AND OPTICAL PROPERTIES

The oxygen and silicon ions have been obtained respectively from pulsed energetic dense oxygen plasma and silane plasma generated by electrodeless discharge. The oxygen ions have been injected into superconducting Nb films, and the Si ions into superconducting YBCO films in order to investigate the variation of their superconductivity with the ions injected into them. Auger profile data show that the injection depths range from 20 to 40nm in the films, depending on the injection condition and film material. The resistance－temperature relations (R-T curves) indicate that the superconductivity remains unchanged in the photoresist-masked part of the film, but is significantly changed in the exposed part. The evenness of the film surface remains unchanged after injection. This technique may serve as an alternative to the planar inhibiting fabrication technique in the fabrication of the multi-layer structure of superconducting films, and also possibly to the conventional plasma source ion implantation technique in material surface processing.

The demagnetization curves of nanocomposite magnets have been calculated using a one-dimensional model. The results are in agreement with experimental results. The shoulders of the demagnetization curve have also been explained based on the model.

The effect of long-range interactions on the spontaneous polarization and the Curie temperature of the ferroelectric film is investigated by use of the Landau theory. On the assumption that the nearest-neighbour interaction remains constant, we find that the spontaneous polarization and the phase transition temperature increase with the enhancement of the long-range interactions. In the case of positive extrapolation length, the critical thickness of the ferroelectric film, in which a size-driven phase transition occurs, decreases with the enhancement of the long-range interactions.

The dependence of long wavelength photoemission upon the size of Ag nanoparticles embedded in a BaO semiconductor is predicted and discussed theoretically. The calculated results show that the increase in the diameter of the Ag nanoparticle, in the range from 1.5 to 37.0nm, leads to the emergence of a roughly Gaussian form of the photoemission spectra and the peaks become markedly narrower. The results also show that the increase in the diameter of the Ag nanoparticle leads to the decrease of the long wavelength threshold. The incident light wavelength corresponding to the peak value of the photoemission gets bigger with the increase of the size of Ag nanoparticles, thus showing a redshift.

In the space-time of a non-Kerr-Newman black hole, the Dirac energy levels and their crossing regions are investigated. Near the event horizon of the black hole there are crossing Dirac energy levels, which lead to the occurrence of non-thermal radiation.

In this paper, we investigate the thermodynamics of the global monopole anti-de-Sitter black hole in the grand canonical ensemble following the York's formalism. The black hole is enclosed in a cavity with a finite radius where the temperature and potential are fixed. We have studied some thermodynamical properties, i.e. the reduced action, thermal energy and entropy. By investigating the stability of the solutions, we find stable solutions and instantons.

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