In this paper, the symmetries and the conserved quantities for systems of generalized classical mechanics are studied. First, the generalized Noether's theorem and the generalized Noether's inverse theorem of the systems are given, which are based upon the invariant properties of the canonical action with respect to the action of the infinitesimal transformation of r-parameter finite group of transformation; second, the Lie symmetries and conserved quantities of the systems are studied in accordance with the Lie's theory of the invariance of differential equations under the transformation of infinitesimal groups; and finally, the inner connection between the two kinds of symmetries of systems is discussed.

A fast evolutionary programming (FEP) is proposed to train multi-layer perceptrons (MLP) for noisy chaotic time series modeling and predictions. This FEP, which uses a Cauchy mutation operator that results in a significantly faster convergence to the optimal solution, can help MLP to escape from local minima. A comparison against back-propagation-trained networks was performed. Numerical experimental results show that the FEP can help MLP better capturing dynamics from noisy chaotic time series than the back-propagation algorithm and produce a more consistently modeling and prediction.

The growth mechanism of fractal islands on a two-dimensional nonlattice substrate with periodic boundary conditions has been investigated by using Monte Carlo technique. Results show that the fractal dimension d_{f} of the final ramified islands is almost independent of the diffusion step length, mobility and rigid rotation of the islands. The characteristics of the size distribution of the discs in an island do not change the dimension d_{f} of the island. However, we find that d_{f} increases linearly with the surface coverage ρ of the system and its slope decreases with the increase of the mean diameter of the discs.

Electron scattering from argon in a laser field is investigated empolying the second-order perturbation theory. The absolute differential cross sections of e-Ar scattering with multiphoton exchange in special scattering geometries G1 (for small-angle scattering) and G2 are calculated. Our results are found to be better than other theoretical results as compared with the experimental data.

The transient properties of laser-cooled two charged particles in a Paul trap are studied numerically. We find the existence of characteristic lifetime of an attractor, which is thought to be an important feature of the transient dynamics of the weakly dissipative system. The theoretical analysis shows that it is caused by pseudo-periodic orbit which is the residual sign of periodic orbit of the focus-saddle bifurcation. Study of dissipative coupled standard maps shows that this is a general conclusion for weakly dissipative system.

The high backing pressure argon gases adiabatically expand into vacuum through a pulsed gas jet to nucleate into large clusters. The clusters were heated by a 45fs, 2.3×10^{16} Wcm^{-2} Ti: sapphire laser. The high energy of the ions produced in the cluster explosion was measured using time-of-flight spectrometry. The maximum and average kinetic energy of the ions were 0.2MeV and ～12.5keV, respectively, indicating that the femtosecond laser interactions with argon clusters are more energetic than interactions with atoms and molecules.

We have studied the steady spontaneous emission spectrum of a four-level Doppler-broadened system driven by three coherent fields. It is found that the fluorescence spectrum is composed of nine contributions. The spectral components have quite different widths and peak heights compared with the case of the standard driven two-level or three-level resonance fluorescence. We provide numerical results in support of our arguments for arbitrary values of the atomic and field parameters.

CONDENSED MATTER: STRUCTURAL, MECHANICAL, AND THERMAL PROPERTIES

Hydrogenated amorphous silicon carbide (a-SiC:H) films were grown by using an organic source, xylene (C_{8}H_{10}), instead of methane (CH_{4}) in a conventional plasma enhanced chemical vapor deposition system. The optical band gap of these samples was increased gradually by changing the gas ratio of C_{8}H_{10} to SiH_{4}. The film with high optical band gap was soft and polymer-like and intense photoluminescence were obtained. Room temperature electro-luminescence was also achieved with peak energy at 2.05 eV (600 nm) for the a-SiC:H film with optical band gap of 3.2 eV.

A complete spectrum criterion and a next nearest neighbor model are proposed. Research indicates: 1) Using this criterion can remove the long existing puzzle that different parameters produce different bond lengths. The criterion greatly improve the reliability of optical method for determining the Mn^{2+}-F^{-} distance R. 2) The exponent n and coefficient K in the inverse power law 10Dq=KR^{-n} are obviously affected by next nearest neighbor. 3) Considering the effect can lead to a better result, the next nearest neighbor model is thus more strict and reliable.

Generalized phase transition (GPT) refers to the transition process of material systems from one steady-state to another. It includes equilibrium phase transition (EPT) and nonequilibrium phase transition (NPT), and phase transitions intermediate between them. In this paper some results on the study of critical scaling relations of the NPT and EPT are obtained. We developed the critical scaling theory of EPT and advanced a universal critical scaling theory of GPT. The critical scaling relations(scaling laws) has more niversality. The critical exponents calculated from our theory are identical with the results of experiments and other theories about EPT and NPT systems. Because the basic model of the theory does not depend on the concrete material system, it has a certain unversality. Its results thus can be applied to generlized phase transition systems, such as the electrorheological fluid and magnetorheological fluid systems.

The elastic strain energy and Gibbs free energy of cubic BN (cBN) thin film in biaxial stress field are calculated. The results show that the stress in cBN thin films has an impact on the formation of cubic phase. It is concluded that the high compressive stress in the cBN thin films is not the cause of cBN formation. This conclusion is different from that predicted by compressive stress model; however, it could well account for the experimental results. At a given substrate temperature, there is a compressive stress threshold, below which cBN phase is thermodynamically stable and above which hexagonal BN(hBN) phase is thermodynamically stable. At room temperature the compressive stress threshold is calculated to be 9.5 GPa.

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

The homotopy continuation method is used to solve the electrostatic boundary-value problems of strongly nonlinear composite media, which obey a current-field relation of J=σ E+χ|E|^{2}E. With the mode expansion, the approximate analytical solutions of electric potential in host and inclusion regions are obtained by solving a set of nonlinear ordinary different equations, which are derived from the original equations with homotopy method. As an example in dimension two, we apply the method to deal with a nonlinear cylindrical inclusion embedded in a host. Comparing the approximate analytical solution of the potential obtained by homotopy method with that of numerical method, we can obverse that the homotopy method is valid for solving boundary-value problems of weakly and strongly nonlinear media.

The phase transitions in the Blume-Emery-Griffiths (BEG) model and antiferromagnetic Potts model on the diamond lattice are investigated using the cluster-variation method in the pair approximation. The ferrimagnetic phases are found to be different from those on the simple-cubic lattice. The phase diagrams of the BEG model are also calculated. In the vicinity of the parameter line where the BEG model reduces to the three-state antiferromagnetic Potts model, new types of phase diagram are obtained. The results are different from those of the mean-field theory, which is a good approximation only for large coordination number of the lattice.

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