The definition and criterion of the form invariance of Nielsen equations are given. The relation between the form invariance and the Noether symmetry is studied. Some examples are given to illustrate the application of the result.

In this paper, we present Noether's theorem and its inverse theorem for nonholonomic systems of non-Chetaev's type with unilateral constraints. We present first the principle of Jourdain for the system and, on the basis of the invariance of the differential variational principle under the infinitesimal transformations of groups, we have established Noether's theory for the above systems. An example is given to illustrate the application of the result.

Starting from a time-dependent rotation U(t) in SU_{2} group element space, we derive its corresponding quantum mechanical dynamic Coriolis term and the relationship between U(t) and rotational angular velocity. Throughout our discussion, the technique of integration within an ordered product of operators is fully used, which has the advantage that the correspondence between the classical rotation and the quantum rotation is in a transparent fashion. A new angular-velocity formula is also derived.

The variational approach is applied to the study on the effect of Coulomb interaction between electrons on the dimerization in a one-dimensional commensurability-two Peierls system, such as trans-polyacetylene. For the case of omitting direct repulsion between electrons in the bonds between sites W, it is confirmed that the weak interactions tend to enhance the dimerization; but when W is included, this enhancement will be attenuated. If |W| is sufficiently large, the net effect of electron-electron interactions will reduce the magnitude of the electron-phonon-induced dimerization.

A multistage adaptive higher-order nonlinear finite impulse response (MAHONFIR) filter is proposed to predict chaotic time series. Using this approach, we may readily derive the decoupled parallel algorithm for the adaptation of the coefficients of the MAHONFIR filter, to guarantee a more rapid convergence of the adaptive weights to their optimal values. Numerical simulation results show that the MAHONFIR filters proposed here illustrate a very good performance for making an adaptive prediction of chaotic time series.

Two measures of earthquakes, the seismic moment and the broadband radiated energy, show completely different scaling relations. For shallow earthquakes worldwide from January 1987 to December 1998, the frequency distribution of the seismic moment shows a clear kink between moderate and large earthquakes, as revealed by previous works. But the frequency distribution of the broadband radiated energy shows a single power law, a classical Gutenberg-Richter relation. This inconsistency raises a paradox in the self-organized criticality model of earthquakes.

Using Parisi and Sourlas dimensional reduction, four-dimensional quantum chromodynamics is reduced to a two-dimensional principal chiral model by suitable superspace embedding. The frame T^{a} cannot be regarded as a fixed one and the frame connection field \varω_{μ}(x) becomes a dynamical gauge field in two dimensions, giving rise to a confining potential. As a result of the original SU(3) Yang-Mills field obtains another SU(3) local symmetry and turns into SU(3)×SU(3) local symmetry－one group element as exp (iδ\varphi^{a}T^{a}) with fixed frame T^{a}, the other gauging the frame T^{a}.

The uncoupled basis set is used to describe the interaction between the ultrashort pulses and the Na atom. Several polarization configurations of laser pulses have been investigated, which produce different effects on the two-step photoexcitation process. The study shows that the final states of the transitions driven by ultrashort laser pulses have a strong dependence on the laser polarization configuration. A comparison of the two different basis sets shows that the uncoupled basis set may provide more information than the coupled basis set, such as angular distribution of the atom in the final states of the transitions.

Nanocrystalline (nc) materials are characterized by a typical grain size of 1-100nm. The uniaxial tensile deformation of computer-generated nc samples, with several average grain sizes ranging from 5.38 to 1.79nm, is simulated by using molecular dynamics with the Finnis-Sinclair potential. The influence of grain size and temperature on the mechanical deformation is studied in this paper. The simulated nc samples show a reverse Hall-Petch effect. Grain boundary sliding and motion, as well as grain rotation are mainly responsible for the plastic deformation. At low temperatures, partial dislocation activities play a minor role during the deformation. This role begins to occur at the strain of 5%, and is progressively remarkable with increasing average grain size. However, at elevated temperatures no dislocation activity is detected, and the diffusion of grain boundaries may come into play.

We take into account the two-photon process and generalize the Jaynes－Cummings (JC) model to the case of atomic level degenerate in the projections of the angular momenta, and we establish two-photon degenerate JC models with and without the rotating-wave approximation (RWA) quantum theory. Comparing the atom population inversion of the generalized JC model with that of the original JC model, we found that the revival period of the degenerate JC model becomes longer and the maximum amplitude of atomic inversion decreases with RWA. Without RWA, the quantum chaos of the generalized JC model is much weaker than that of the original JC model.

We consider a multistep χ^{(2)} cascading for light pulses with the dispersion of the system taken into account. Using the method of multiple scales we derive a set of coupled envelope equations governing the nonlinear evolution of the fundamental, second and third harmonic waves involved simultaneously in two nonlinear optical processes, i.e. second harmonic generation and sum frequency mixing. We show that three-wave temporal optical solitons are possible in three-and four-step cascading in the presence of a group-velocity mismatch between different pulses.

PHYSICS OF GASES, PLASMAS, AND ELECTRIC DISCHARGES

The relationship between the transported ion current and the cathodic arc current is determined in a vacuum arc plasma source equipped with a curved magnetic filter. Our results suggest that the outer and inner walls of the duct interact with the plasma independently. The duct magnetic field is a critical factor of the plasma output. The duct transport efficiency is to maximize at a value of bias plate voltage in the range +10 V to +20 V, and independent (within our limit of measurement) of the magnetic field strength in the duct. The plasma flux is composed of two components: a diffusion flux in the transverse direction due to particle collisions, and a drift flux due to the ion inertia. The inner wall of the magnetic duct sees only the diffusion flux while the outer wall receives both fluxes. Thus, applying a positive potential to the outer duct wall can reflect the ions and increase the output current. Our experimental data also show that biasing both sides of the duct is more effective than biasing the outer wall alone.

CONDENSED MATTER: STRUCTURAL, MECHANICAL, AND THERMAL PROPERTIES

Small angle X-ray scattering experiments have been performed to study the microstructure of mesoporous silica materials prepared by condensation of tetraethylorthosilicate using non-ionic alkylpolyethyleneoxide (AEO_{9}) and ionic cetyltrimethylammonium bromide (CTAB) surfactant as templates. It is the pores within the nanometre range that produce the main scattering. The scattering of the pure silica systems obey Porod's law. The scattering of the systems with templates remaining in the pores show positive deviations from Porod's law. This may be because the templates produce some additional scattering background and then make the scattering of pores distorted. The results show that the full removal of templates from the pores of the materials by Soxhlet extraction is very easy for AEO_{9}, but it is difficult for CTAB. The positive deviation correction is also performed.

A type of system, in which the specific volume can be divided into several parts according to its Hamiltonian, has been obtained in a grand ensemble. The main character of such a system is that its Hamiltonian is absolutely separable. We also discuss the partial specific volume contributed by thermoelectrons in metals under a free-interaction approximation, and the corresponding Wu－Jing parameter is obtained as a simple example.

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

Within the framework of Feynman path-integral variational theory, we calculate the ground-state energy of a polaron in parabolic quantum wires in the presence of a Coulomb potential. It is shown that the polaronic correction to the ground-state energy is more sensitive to the electron－phonon coupling constant than the Coulomb binding parameter, and it increases monotonically with decreasing effective wire radius. Moreover, compared to the results obtained by Feynman Haken variational path-integral theory, we obtain better results within the Feynman path-integral variational approach (FV approach). Applying our calculation to several polar semiconductor quantum wires, we find that the polaronic correction can be considerably large.

The effects of the substitution of Li for Mg in Mg_{1-x}Li_{x}B_{2}(x=0,0.1,0.2) on their structure and superconductivity have been investigated. It has been found by X-ray diffraction that the substitution of Li for Mg with x=0.1 and 0.2 does not cause phase transformation in these samples. However,the measurements of temperature-dependent normalized magnetization indicate the loss of superconductivity with the increase of Li content in these samples.

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