Direct-method phase extension has been applied to two-dimensional electrondiffraction data of the protein streptavidin. Structure-factor amplitudesfrom electron diffraction were combined with phases from the correspondingelectron micrographs. Maximum-entropy discrimination and cluster analysiswere used to derive a solution from a large number of random trials. The phase extension from 0.3 to 0.25nm led to substantial improvement of thereconstructed projection image quality.

This paper focuses on the study of localized Lie symmetries under the infinitesimal transformation of an infinite continuous group for the finite-degree-of-freedom systems. Based on an invariance of differential equation under an infinitesimal transformation, we present the localized Lie symmetries including direct and inverse problems for the finite degree-of-freedom mechanical systems. We also give the definitions,determining equations, structural equation and conserved laws of localized Lie symmetries, and further, the Lie symmetries under the infinitesimal transformation of a finite continuous group derived from localized Lie symmetry. Finally, an example is discussed to illustrate these results.

A form invariance of Raitzin's canonical equations of a nonholonomic mechanical system is studied. The Raitzin canonical equations of the system are established. The definition and criterion of the form invariance in the system under infinitesimal transformations of groups are given. The relation between the form invariance and the conserved quantity of the system is obtained and an example is also given to illustrate the application of the result.

In this paper, the discrete mKdV lattice is solved by using the modified Jacobian elliptic function expansion method. As a consequence, abundant families of Jacobian elliptic function solutions are obtained. When the modulus $m\rightarrow 1$, these periodic solutions degenerate to the corresponding solitary wave solutions, includingbell-type and kink-type excitations.

A quasi-wavelet numerical method (QWNM) is introduced for solving the convection--diffusion equation (CDE). The results manifest that the calculated bandwidth has an extremum. When the bandwidth takes the value of the extremum, the accuracy of the solution for the CDE by using the QWNM is relatively high, and better than that by using the up-wind scheme. Under the condition of stochastic boundary disturbances of different amplitudes, the results of the QWNM are a little worse than those of the up-wind scheme when the integral time is longer. However, when stochastic boundary disturbances of equal amplitudes occur, the solutions of the equation by using the QWNM and the up-wind scheme can be identical if the bandwidth takes an integer greater than or equal to 20. When the parameter is stochastically disturbed, the root-mean-square error of the quasi-wavelet solution of the equation is smaller than that of the up-wind scheme solution if the bandwidth is 10. When the initial values are stochastically disturbed and the bandwidth equals 10, the accuracy of the quasi-wavelet solution is relatively high, and better than that of the up-wind scheme solution.

A direct approach to perturbation theory for the nonlinear Schr\"{o}dinger equation is developed based on the separation of variables. The first-order effects of perturbation on a bright soliton, i.e. the slow time dependence of soliton parameters and the first-order correction are derived.

By using the equivalent particle theory, the adiabatic approximation solutions of the Korteweg--deVries type equation (including KdV equation, cylindrical KdV equation and spherical KdV equation) in dust ion-acoustic solitary waves were obtained. The method can be extended to other nonlinear evolution equations.

In this paper, the analytical formulae of bound-continuous transition matrix elements for Coulomb wavefunctions are obtained, and the recurrence relations of different power order transition matrix elements are also derived. The results may be useful in a great diversity of scattering problems for atoms or molecules.

Solving the Klein--Gordon equation and Dirac equation with ring-shaped non-spherical oscillator gives the exact bound state wavefunction and energy equation,and the relations between non-relativistic Schr\"{o}dinger equation,Klein--Gordon equation and Dirac equation with equal scalar and vector potentials.

Using the Hellings--Nordtvedt theory, some expressions are obtained of the mass defect effect for a type of charged celestial body in a gravitational field with a nonzero cosmological constant $\lambda$. And the mass defects are obtained in several other types of fields and under different conditions by discussing the parameters in the expressions. These are meaningful calculations of the radiated energies in the processes of forming those kinds of celestial bodies in astrophysics.

In this paper a local discrete cosine transformation (DCT) domain Volterra prediction method is proposed to predict chaotic time series, where the DCT is used to lessen the complexity of solving the coefficient matrix. Numerical simulation results show that the proposed prediction method can effectively predict chaotic time series and improve the prediction accuracy compared with the traditional local linear prediction methods.

Phase synchronization of chaotic systems induced by periodic signals is studied experimentally and numerically. Three kinds of periodic signals are chosen to drive Chua circuits, including the periodic signal in the Chua circuit, sinusoidal and pulsed signals. Under conditions of small mismatch between the natural frequencies of the periodic and the chaotic signals,appropriate amplitudes of the driving signals, and appropriate duty cycles of the pulse, phase synchronization can be achieved. Even when the duty circle reduces to 3{\%}, it can still drive the chaotic signals into phase synchronization, which is interesting for applications.

This paper presents an improved resonant parametric perturbation method based on the modulation of a nonlinear map for controlling chaos. The control target can be any periodic orbit, which is not necessarily what is embedded in the chaotic attractor.Application of the method is illustrated for a common current-programmed DC/DC converter which has been known to easily become chaotic for a wide parameter range. The control effects of chaos are demonstrated with computer simulations.

The problem of making a stable Takagi--Sugeno (TS) fuzzy system chaotic by using the state feedback control of arbitrarily small magnitude is studied. The feedback controller used is a simple sawtooth function of the system state.The improved Marotto theorem has been obtained and applied to mathematically prove that the controlled system is chaotic in the sense of Li and Yorke. In particular, an explicit formula for the computation of chaotification parameters is obtained. A numerical example is used to visualize and illustrate the theoretical results.

Incorporating distributed recurrent networks with high-order connections between neurons, the identification and synchronization problem of an unknown chaotic system in the presence of unmodelled dynamics is investigated. Based on the Lyapunov stability theory, the weights learning algorithm for the recurrent high-order neural network model is presented.Also, analytical results concerning the stability properties of the scheme are obtained. Then adaptive control law for eliminating synchronization error of uncertain chaotic plant is developed via Lyapunov methodology. The proposed scheme is applied to model and synchronize an unknown Rossler system.

The firing activities of Hindmarsh--Rose (HR) neurons are studied by means of numerical simulation and bifurcation analysis.A single HR neuron exhibits various firing patterns, such as quiescent state, periodic spiking, periodic bursting and chaos,when the external current input is changed. The fast/slow dynamical analysis is applied to explore the dynamical behaviour of the HR model. The complete synchronization of two coupled identical HR neurons with electrical coupling mimicking gap junctions can be realized in certain ranges of the coupling strength, whenever each individual neuron shows quiescency,periodic firing and chaos. The criteria for complete synchronization are analysed theoretically, and the corresponding numerical simulation is presented as well. The persistence of the interspike intervals bifurcation structure of the coupled HR neuronal system under electrical coupling is also discussed.

A novel active backstepping control method is presented for synchronizing two identical R\"{o}ssler hyperchaotic systems with each other, and extended to achieve the generalized synchronization of the Chua chaotic system with the R\"{o}ssler hyperchaotic system. It is a systematic design approach and consists of a recursive procedure interlacing the choice of a Lyapunov function with the design of active control. In particular, this technique gives flexibility in constructing a control law.Numerical experiments verify the feasibility and effectiveness of the proposed control technique.

The decay of $^{72}$Ga has been investigated by means of $\gamma
$-ray spectroscopy. The $^{72}$Ga nuclei were produced through the
$^{71}$Ga(n, $\gamma)^{72}$Ga reaction. The Compton-suppressed
spectrometer and high-purity Ge detectors have been used singly and in
coincidence, separately, to study $\gamma$-rays in the $\beta ^{-}$
decay of $^{72}$Ga to $^{72}$Ge. Ninety-three events of $\gamma$-rays
were reported, of which 7
were observed for the first time. A decay scheme of $^{72}$Ga including 4
new levels is proposed which accommodates 87 of these transitions. Spins and
parities for new levels are proposed from calculated log$ft$ values, modes on
the observed decay, and some nuclear reaction experimental results.

By use of a tensor method, the transform formulae for the beam coherence-polarization matrix of the partially polarized Gaussian Schell-model (GSM) beams through aligned and misaligned optical systems are derived. As an example, the propagation properties of the partially polarized GSM beam passing through a misaligned thin lens are illustrated numerically and discussed in detail. The derived formulae provide a convenient way to study the propagation properties of the partially polarized GSM beams through aligned and misaligned optical systems.

In this paper, the light-emitting spot sizes and throughputs of the four types of probes are studied using the finite-difference time-domain method, and these probes are also compared in performance.
Among these probes, a pyramidal AlGaAs tip coated entirely with a thin Ag film can provide the highest throughput and a single near-field spot size. Probe coated with a 3nm Ag film and incident
light with a wavelength of 800nm seems to offer the optimum condition for high throughput and ultra-small spot size, which enables the realization of ultra-high density storage.

We study the properties of atoms and cavity field in the two-atom Tavis--Cummings model where the two atoms interact with each other and are also driven by an external classical field. We consider the special case that the cavity is initially in a coherent state. The atomic inversion, the average photons number and the Mandel parameter in the driven Tavis--Cummings model are given and analysed numerically. We pay special attention to the dynamical behaviour of the atoms and the cavity field modified by the external field.

The transmission probability of the two-mode mazer injected with V-type three-level atoms is studied, and the effects of the atomic coherence on it are examined. It is shown that the atomic coherence can affect the transmission probability. In the plots of the atomic transmission probability versus the dimensionless centre-of-mass momentum, there are resonance peaks and non-resonance platforms. The heights of these resonance peaks and non-resonance platforms can be adjusted by the atomic coherence
parameter and by the relative coupling strength of the two transition channels.

We present the explicit analytical results of all the eigenstates and eigenvalues by using a parameter $\lambda$ without the assumption of Bethe ansatz for three different kinds of seven bosonic modes mixing models. It is shown that the parameter is determined by the roots of a simple polynomial.Besides, we also accurately obtain the explicit analytical expressions of infinite eigenstates and energies without any unknown parameter.

The two models of three-level (one upper level and two lower
levels, or two upper levels and one lower level) atom embedded
in a double-band photonic crystal are adopted. The atomic transitions
from the upper levels to the lower levels are assumed to be
coupled by the same reservoir which are respectively the isotropic
photonic band gap (PBG) modes, the anisotropic PBG modes and the free
vacuum modes.
The effects of the fine structure of the atomic ground state levels
in the model with one upper level and two lower levels, and
the quantum interferences in the model with two upper levels
and one lower level on the spontaneous emission spectrum of
an atom are investigated in detail. Most interestingly,
it is shown that new spontaneous emission lines are produced from the fine
splitting of atomic ground state levels in the isotropic PBG case. The
quantum interferences induce additional narrow spontaneous lines near
the transition from the empty upper level to the lower level.

We consider the relaxation processes of parametric excitation of magnons in
a microwave resonator. Using the approach of unitary transformation, we
calculate the effective amplitude of three-boson terms of Hamiltonian,
especially for photon--magnon interaction which is expected to contribute to
the resonance linewidth of ferromagnets.

The nonlinear optical properties of two newly synthesized molecules
9-Ethyl-3-{\{}2-[4-(2-Pyridin-4-yl-vinyl)-phenyl]-vinyl{\}}-9H-carbazole
(EPVPC) and
9-Octadecyl-3-{\{}2-[4-(2-Pyridin-4-yl-vinyl)-phenyl]-vinyl{\}}-9H-carbazole
(OPVPC) have been studied with hybrid density functional theory (DFT/B3LYP).
The generalized few-state model is employed to calculate the two-photon
absorption cross sections of the compounds. The theoretical results are in
good agreement with the available experimental measurements. It is found
that the maximal two-photon absorption (TPA) cross sections of the compounds
can be well described by a three-state model. The numerical simulation shows
that both compounds have large two-photon absorption (TPA) cross sections
and, furthermore, OPVPC displays a little stronger TPA activity than EPVPC
in a lower frequency region.

A complex optical model potential modified by incorporating the concept of bonded atom which takes into consideration the overlapping effect of electron clouds between two atoms in a molecule is employed to calculate the total cross sections for electron scattering in such molecules as N$_{2}$,
NO, NO$_{2}$, CH$_{4}$, CF$_{4}$, CF$_{3}$H, C$_{2}$H$_{2}$ and C$_{2}$H$_{4}$ at 30--5000eV using the additivity rule model at Hartree--Fock level. The quantitative total cross sections are compared with those obtained in experiments and other theories, wherever available, and good agreement is obtained at 30--5000eV. It is shown that the modified calculation results are much closer to the available experimental data than the unmodified ones at lower energies, especially below 500eV. Therefore,considering the overlapping effect of electron clouds in the complex optical model potential could be helpful for better calculation results about electron scattering total cross sections from molecules.

PHYSICS OF GASES, PLASMAS, AND ELECTRIC DISCHARGES

A model is built to study chemical processes in plasmas generated in helium with trace amounts of air at atmospheric pressure or low pressures. The plasma lifetimes and the temporal evolutions of the main charged species are presented. The plasma lifetimes are longer than that in air plasma at
atmospheric pressure, but this is not true at low pressures. The electron number density does not strictly obey the exponential damping law in a longer period.

The boundary turbulence and transport in density scanning experiment were investigated using a fast reciprocating Langmuir probe in the HT-7 tokamak.With the increase of the central line averaged plasma density, an enhanced shear of the radial electric field was observed at plasma edge, which could account for the reduction of edge transport and the improvement of global particle confinement. The reduced particle transport was demonstrated by the increase of the particle confinement time and the decrease of the perpendicular diffusion coefficient. The features of the ionization-and-radiation-driven turbulence, ${\tilde {T}_\e } \mathord{\left/{\vphantom {{\tilde {T}_\e } {T_\e }}} \right. \kern-\nulldelimiterspace} {T_\e}\sim {\tilde {n}_\e } \mathord{\left/ {\vphantom {{\tilde {n}_\e } {n_\e }}}\right. \kern-\nulldelimiterspace} {n_\e }$ and $\theta \_\tilde {T}_\e \tilde
{n}_\e \sim \pi $, were found in the plasma edge region, which suggests the importance of the ionization and radiation in the turbulence driving.

One important parameter for the plasma source ion implantation (PSII) process is the target temperature obtained during the surface modification. Because the power input to the target being implanted can be large, its temperature is quite high. The target temperature prediction is useful, whether the high temperature is required in the experiment. In addition, there is likely
to be temperature variation across the target surface, which can lead to locally different surface properties. In this paper, we have presented a model to predict and explain the temperature distribution on a hemispherical bowl-shaped vessel during plasma source ion implantation. A two-dimensional fluid model to derive both the ion flux to the target and the energy imparted to the substrate by the ions in the plasma sheath simulation is employed. The calculated energy input and radiative heat loss are used to predict the temperature rise and variation inside the sample in the thermal model. The shape factor of the target for radiation is taken into account in the radiative energy loss. The influence of the pulse duration and the pulsing frequency on the temperature distribution is investigated in detail. Our work shows that at high pulsing frequencies the temperature of the bowl will no longer rise with the increase of the pulsing frequency.

In a partially ionized plasma the presence of bound electrons can significantly alter the laser plasma parametric instabilities. In this paper the nonlinear dispersion relation in intense laser partially ionized plasma is analysed. The growth rate of the forward stimulated Raman scattering
is significantly enhanced by the presence of bound electrons; on the other hand the backward stimulated Raman scattering is unaffected.

The deuterium--tritium (D--T) burning plasma characteristic in an aspect ratio A=2 tokamak reactor is studied based on a simple equilibrium configuration,the Soloviev-type configuration. Operation limits for the Troyon beta value and for the Greenwald density value as well as for the ITER H-mode
confinement scaling are used as the benchmark. It is found that in addition to suitable elongation, large triangularity has advantage for arriving at high beta value and obtaining high fusion power output. Compared to the present ITER design, the A=2 system can have very good merit for the
avoidance of disruptions by setting rather high edge q value while keeping relatively large total toroidal current. The main disadvantage of decreasing the aspect ratio is due to the loss of more useful space in the inward region that leads to the decrease of toroidal magnetic field in the plasma
region, then worsening the fusion merit. Our analysis and calculation also present a trade-off in this respect. Due to simple equilibrium configuration assumed, some other important issues such as the bootstrap current alignment cannot be optimized. However, the present analysis can offer an insight into the advantages of the medium aspect ratio reactor system that is a blank in present-day tokamak study.

CONDENSED MATTER: STRUCTURAL, MECHANICAL, AND THERMAL PROPERTIES

An array of random-oriented zinc oxide nanowires (ZnO NWs) was fabricated on silicon substrate by thermal evaporation. After a thermal evaporation process, the silicon substrate was covered with a large number of uniformly distributed ZnO islands, from which non-aligned NWs with a diameter of several ten nanometres were grown. During this process, the temperature around the substrate was intentionally kept below 500$^\circ$C for practical consideration. From these ZnO NWs field emission was achieved. The turn-on field, under which a 10$\mu $A/cm$^{2}$ current density was extracted, was
measured to be 3.0V/$\mu$m. Also, the emission site distribution was investigated using the transparent anode technique. The field emission was observed to have occurred from the whole sample surface. These results suggest that ZnO NWs have great potential application in flat panel displays.

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

Reverse polarization in polythiophene under an applied electric field has been studied in the framework of the tight-binding model. It is found that the applied electronic field has a great influence on the excited states of polythiophene. The effect of the heteroatoms on the polarization has been calculated and analysed carefully. It is indicated that a reverse polarization of biexcitons in polythiophene will be observed more easily.The heteroatoms increase this reversed polarization strength apparently.

With the increasing of x, the ZFC (zero-field cooling) M-T curves for the
polycrystals La0.6-xGdxSr1.4MnO4(x=0, 0.1, 0.2, 0.4,0.6) change from spin-glass-like to paramagnetic, and each ZFC M-T curve has an inflection point at 20K. These behaviours can be understood by considering the respective contributions of Mn and Gd to the total magnetism. In addition, for all the samples, thermal activation conducting behaviours are observed from 100 K to room temperature. Due to the strong antiferromagnetic coupling between neighbouring Mn ions, there is no obvious magnetoresistance effect until the magnetic field strength rises to 3.98$\tm10^6$A/m.

The Aharonov--Bohm (AB) interference oscillations manifested through transmission of an electron in a mesoscopic device with a double-ring in the presence of a magnetic impurity serving as the spin-flipper are studied.The spin-flipper is demonstrated to indeed cause the partial decoherence of
the AB interference. Moreover, it is found that the spin-up/down transmission coefficients are
asymmetric in the flux reversal while the reflection coefficients as well as that the total transmission coefficient are symmetric.

The resonant tunnelling through parabolic quantum well structures under a uniform transverse magnetic field is investigated by a simple numerical method. Numerical results of the transmission coefficient are obtained for several GaAs--AlxGa1-xAs parabolic well structures. It is found that the resonant peaks shift towards the higher energy region as the magnetic field increases, and some new resonant peaks emerge when the magnetic field becomes stronger. The J-V characteristics of a parabolic quantum well are discussed for the cyclotron centre located at different positions. It is also found that the cyclotron centre located at the parabolic well centre is helpful to explain the experiment, and the peak current densities decrease and shift to higher bias with the increase of
magnetic field. The influence of mixed crystal effect on the J-V characteristic under a uniform transverse magnetic field is also investigated.

The electron tunnelling phase time $\tau ^{\rm p}$ and
dwell time $\tau _{\rm D}$ through an associated delta potential barrier $U (x)=\xi \delta (x)$ are calculated and both are in the order of 10$^{-17} -10^{-16 }$s. The results show that the dependence of the phase time on the delta barrier parameter $\xi $can be described by the characteristic length $l_{\rm c} =\hbar^{2}/m_{\e}\xi $ and the characteristic energy $E_{\rm c}=m_{\e}\xi^{2}/\hbar^{2}$ of the delta barrier, where $m_{\e}$ is the electron mass, $l_{\rm c}$ and $E_{\rm c}$ are assumed to be the effective width and height of the delta barrier with $l_{\rm c}E_{\rm c}=\xi$, respectively. It is found that $\tau_{\rm D}$ reaches its maximum and $\tau _{\rm D}=\tau ^{\rm p}$ as the energy
of the tunnelling electron is equal to $E_{\rm c}$/2, i.e.~as $l_{\rm c} =\mathchar'26\mkern-10mu\lambda _{\rm DB}$, $\mathchar'26\mkern-10mu\lambda_{\rm DB} $ is de Broglie wave length of the electron.

A highly sensitive photodeflection spectroscopy technique with femtosecond time resolution has been developed. Using this technique, we have measured accurately the shape of acoustic pulses, which were generated from the ultrafast phonon emission in a germanium plate. Supersonic expansion of
photoexcited electron-hole plasma was observed. The characteristic velocity of plasma diffusion was evaluated. It exceeded the longitudinal sound velocity in germanium by a factor of 4.0.

A new composition content quaternary-alloy-based phase change thin film,Sb-rich AgInSbTe, has been prepared by DC-magnetron sputtering on a K9 glass substrate. After the film has been subsequently annealed at 200$^\circ$C for 30min, it becomes a crystalline thin film. The diffraction peak of antimony (Sb) are observed by shallow (0.5 degree) x-ray diffraction in the quaternary alloy thin
film. The analyses of the measurement from differential scanning calorimetry (DSC) show that the crystallization temperature of the phase change thin film is about 190$^\circ$C and increases with the heating rate.By Kissinger plot, the activation energy for crystallization is determined to be 3.05eV. The reflectivity, refractive index and extinction coefficient of the crystalline and amorphous phase change thin films are presented. The optical absorption coefficient of the phase change thin films as a function of photon energy is obtained from the extinction coefficient. The optical band gaps of the amorphous and crystallization phase change thin films are 0.265eV and 1.127eV, respectively.