Non-Noether symmetries and conservative quantities of nonholonomic nonconservative dynamical systems are investigated in this paper. Based on the relationships among motion, nonconservative forces, nonholonomic constrained forces and Lagrangian, non-Noether symmetries and Lutzky conservative quantities are presented for nonholonomic nonconservative dynamical systems. The relation between non-Noether symmetry and Noether symmetry is discussed and it is further shown that non-Noether conservative quantities can be obtained by a complete set of Noether invariants. Finally,an example is given to illustrate these results.

By analogue with the methods and processes in continuous mechanics, a Lagrangian formulation and a Hamiltonian formulation of discrete mechanics are obtained. The dynamical equations
including Euler--Lagrange equations and Hamilton's canonical equations of the discrete nonconservative holonomic systems are derived on a discrete variational principle. Some illustrative
examples are also given.

By virtue of the method of multiple-scale and the quasi-discreteness
approach, we have discussed the nonlinear vibration equation of a 3D
discrete monatomic lattice with its nearest-neighbours interaction. The 3D
simple cubic lattices have the same localized modes as a 1D discrete
monatomic chain with cubic and quartic nonlinearity. The nonlinear vibration
in the 3D simple cubic lattice has 3D distorted solitons and 3D envelop
solitons in the direction of $k_{x}=k_{y}=k_{z}=k$ and $k=\pm
\pi$/6$a_{0}$ in the
Brillouin zone, as well as has 3D vortices in the direction of
$k_{x}=k_{y}=k_{z}=k$ and $k=\pm \pi$/$a_{0}$ in the Brillouin zone.

The complete flexural vibration band gaps are studied in the thin plates
with two-dimensional binary locally resonant structures, i.e. the composite
plate consisting of soft rubber cylindrical inclusions periodically placed
in a host material. Numerical simulations show that the low-frequency gaps
of flexural wave exist in the thin plates. The width of the first gap
decreases monotonically as the matrix density increases. The frequency
response of the finite periodic thin plates is simulated by the finite
element method, which provides attenuations of over 20dB in the frequency
range of the band gaps. The findings will be significant in the application
of phononic crystals.

The influence of the disturbance caused by the imperfection of the
engineering coupling constants
in the perfect state transfer is calculated. The results show that
the fidelity for the perfect state transfer is seriously affected
by the errors occurring near the input and output spins. Such
results are helpful for the realization of the perfect state
transfer in the case where there exist errors in experiments.

It has recently been shown that linear optics alone would suffice to
implement efficient quantum
computation. Quantum computation circuits using coherent states as
the logical qubits can be constructed from very simple linear
networks, conditional
measurements and coherent superposition resource states. We present the
quantum game under quantum noise and a proposal for implementing the
noisy quantum game using only linear optics.

The relation between corresponding trigonometric functions in two rotating
coordinate systems is presented. The transformation formula for a vector in
the two rotating spherical coordinate systems is obtained. The scattering
fields for a spherical target irradiated by a plane electromagnetic wave in
an arbitrary direction are derived. These fields in a particular case
retrogress to those available in the literature. The obtained results have
great potential in practical applications.

We present a scheme to realize the basic two-qubit logic gates such as the
quantum phase gate and SWAP gate using a detuned microwave cavity
interacting with three-level superconducting-quantum-interference-device
(SQUID) qubit(s), by placing SQUID(s) in a two-mode microwave cavity and
using adiabatic passage methods. In this scheme, the two logical states of
the qubit are represented by the two lowest levels of the SQUID, and the
cavity fields are treated as quantized. Compared with the previous method,
the complex procedures of adjusting the level spacing of the SQUID and
applying the resonant microwave pulse to the SQUID to create transformation
are not required. Based on superconducting device with relatively long
decoherence time and simplified operation procedure, the gates operate
at a high speed, which is important in view of decoherence.

In this paper, we extend Parikh' recent work to the Vaidya--de Sitter black
hole which is non-stationary. We view Hawking radiation as a tunnelling
process across the event horizon and calculate the tunnelling probability
when the particle crosses the event horizon. From the tunnelling probability
we also find a leading correction to the semiclassical emission rate.

The Gross--Pitaevskii equation which describes the motion of a Bose--Einstein
condensed (BEC) atom in an elongated trap is solved analytically, and a solitary-wave solution
is obtained in the low-density case without neglecting the effect of the interatomic
interaction on the transverse function. It is shown that this effect leads to
the velocity of the solitary wave slowing down and the profile
of the solitary wave widening.

In this paper we numerically investigate the chaotic
behaviours of the fractional-order Ikeda delay system. The results show
that chaos
exists in the fractional-order Ikeda delay system with order less than 1.
The lowest order for chaos to be able to appear in this system is found
to be 0.1. Master--slave
synchronization of chaotic fractional-order Ikeda delay systems with linear
coupling is also studied.

A simple full-state asymptotic trajectory control (FSATC) scheme is proposed
to asymptotically drive full states of a unified chaotic system (UCS) to
arbitrary desired trajectories. The FSATC uses only information, i.e. one
state of the UCS. A sinusoidal wave and two chaotic variables are taken as
illustrative tracking trajectories to verify that using the proposed FSATC
can make full UCS states track desired trajectories with high tracking
accuracy in a finite time.

We present a new least-mean-square algorithm of adaptive filtering to
improve the signal to noise ratio for magnetocardiography data collected
with high-temperature SQUID-based magnetometers. By frequently adjusting the
adaptive parameter $\alpha $ to systematic optimum values in the course of
the programmed procedure, the convergence is accelerated with a highest
speed and the minimum steady-state error is obtained simultaneously. This
algorithm may be applied to eliminate other non-steady relevant noises as
well.

Based on the multi-slit
method,
a new method is introduced to measure the non linear
force caused emittance growth in a RF photoinjector. It is possible to
reconstruct the phase space of a beam under some
conditions by the multi-slit method. Based on the reconstructed
phase space, besides the emittance, the emittance
growth from the distortion of the phase space can also be measured. The
emittance growth results from the effects of nonlinear force acting on
electron, which is
very important for the high quality beam in a RF photoinjector.

The physical design and cooling test of a C-band 2MeV
standing wave (SW) accelerating tube are described in this paper. The
designed accelerating structure consists of 3-cell buncher and 4-cell
accelerating section with a total length of about 163mm，excited with 1MW
magnetron. Dynamic simulation presents that about 150mA beam pulse current
and 30{\%} capture efficiency can be achieved. By means of nonlinear Gauss
fit on electron transverse distribution, the diameter of beam spot FWHM
(full width at half maximum of density distribution) is about 0.55mm.
Cooling test results of the accelerating tube show that frequencies of
cavities are tuned to 5527MHz and the field distribution of bunching section
is about 3:9:10.

The concept of partially coherent nonparaxial modified Bessel--Gauss (MBG)
beams is proposed. Based on the generalized Rayleigh-Sommerfeld diffraction
integral, the analytical propagation equations of nonparaxial MBG beams in
free space are derived and analysed, and some special cases are discussed.
In particular, under the paraxial approximation our results reduce to the
corresponding paraxial ones. Numerical calculation examples are given to
illustrate the dependence of intensity and spectral degree of coherence on
the beam order $m$, \textit{$\xi $} and $f$ parameters, and to compare
the difference between the paraxial and nonparaxial results.

Strong optical feedback in a birefringent dual frequency He--Ne laser with a
high reflectivity feedback mirror has been investigated for the first time.
The output characteristics of two orthogonally polarized modes are
demonstrated in two different optical feedback cases: one is for both modes
being fed back and the other is for only one of the modes being fed back.
Strong mode competition can be observed between the two modes with strong
optical feedback. And when one mode's intensity is near its maximum, the
other mode is nearly extinguished. When both modes are fed back into the
laser cavity, the mode competition is stronger than when only one mode is
fed back. The difference in initial intensity between the two orthogonally
polarized modes plays an important role in the mode competition, which has
been experimentally and theoretically demonstrated.

The classical Gerchberg--Saxton algorithm is introduced into the image
recovery in fractional Fourier domain after adaptation. When this algorithm
is applied directly, its performance is good for smoothed image, but bad for
unsmoothed image. Based on the diversity of fractional Fourier transform on
its orders, this paper suggests a novel iterative algorithm, which extracts
the information of the original image from amplitudes of its fractional
Fourier transform at two orders. This new algorithm consists of two
independent Gerchberg--Saxton procedures and an averaging operation in each
circle. Numerical simulations are carried out to show its validity for both
smoothed and unsmoothed images with most pairs of orders in the interval [0,
1].

We study three-body entanglement induced by spontaneous
emission in a three two-level atoms system by using the entanglement
tensor approach. The results show that the amount of entanglement
is strongly dependent on the initial state of the system and the species
of atoms. The three-body entanglement is the result of the coherent
superposition of the two-body entanglements. The larger the
two-body entanglement is, the stronger the three-body entanglement
is. On the other hand, if there exists a great difference in three two-body entanglement measures,
the three-body entanglement is very weak.
We also find that the maximum of the two-body entanglement
obtained with nonidentical atoms is greater than that obtained
with identical atoms via adjusting the difference in atomic frequency.

Slowing a light pulse in a degenerate two-level system is observed with a
double-frequency sweeping technique. The effects of coupling beam intensity,
cell temperature and frequency detunings of the coupling and probe beams in
resonance, on the slowing of light propagation in such a system are
investigated. It is found that group velocities depend strongly on
polarization combinations. A group velocity $v_{\rm g}$=6760m/s of light pulses in
caesium vapour is obtained under the optimal parameters.

A quantum identification system based on the
transformation of polarization of a mesoscopic coherent state is proposed.
Physically, an initial polarization state which carries the identity
information is transformed into an arbitrary elliptical polarization state.
To verify the identity of a communicator, a reverse procedure is
performed by the receiver. For simply describing the transformation
procedure, the analytical methods of Poincar\'{e} sphere and quaternion are
adopted. Since quantum noise provides such a measurement uncertainty for the
eavesdropping that the identity information cannot be retrieved from the
elliptical polarization state, the proposed scheme is secure.

We have investigated the steady-state cavity-field properties of a
single-mode two-photon micromaser when the atoms in a cascade
three-level configuration are initially prepared in a mixture of
the upper and intermediate states. The mean photon number,
trapping state and sub-Poissonian effect are discussed with
upper (intermediate)-state population changing from 1(0) to 0(1).
These properties are very different from those in a pure two- or
one-photon transition process, due to the competition among
different transition processes. In particular, the trapping states
of nonzero photons are discovered in this system under some
conditions, which is contrary to the previous findings.

The phase dependence and independence of the response of a trichromatically
driven two-level medium to an arbitrarily intense probe field have been
studied.
The sum of the relative phases of the sideband components of the
trichromatic field compared to the central component plays a crucial role in
the response of the medium. For a weak probe field, as the sum of the
relative phases changes from $0$ to $\pi $, multiple switching can be
achieved, in which switching from normal to anomalous dispersion occurs in
multiple separate frequency regimes. The remarkable dependence on the sum
phase is also shown for a strong probe field. On the other hand, when the
sum of the two relative phases is fixed, the changes in the respective phases
have no influence on the response of the medium.

The investigation on the oxidation behaviour of Si$_{1-x}$Ge$_{x}$ alloys
($x$=0.05, 0.15, and 0.25) is carried out. It is found for the first time that
on the oxide film a germanium nano-cap with a thickness of 1.8--2.8nm
and a few Ge nanoparticles with diameters ranging from 5.5 nm to 10 nm are
formed by the low-temperature laser-assisted dry oxidation of Si$_{1 -
x}$Ge$_{x}$ substrate. A new scanning method on the decline cross-section of
the multiple-layer sample is adopted to measure the layer thickness and the
composition. Some new peaks in photoluminescence (PL) spectra are
discovered, which could be related to the nano-cap and the nano-particles of
germanium. A suitable model and several new calculating formulae with the
unrestricted Hartree--Fock--Roothaan (UHFR) method and quantum confinement
analysis are proposed to interpret the PL spectra and the nano-structure
mechanism in the oxide.

The dynamical evolution and stability of
bright dissipative holographic solitons in biased photorefractive materials
in which the self-trapping beam obtains a gain from the pump beam via two-wave
mixing has been investigated numerically. Results show that these solitons are stable relative to small
perturbations. Adjusting some system parameters, such as the bias field and
the angle between beams, can easily control the generation of such solitons.
Potential applications in optical switches or repeaters are discussed.

We investigate the properties of waveguides induced by one-dimensional grey
screening solitons in biased photorefractive crystals. The results show that
waveguides induced by grey screening solitons are always of single mode for all
intensity ratios, i.e. the ratios between the peak intensity of the
soliton and the dark irradiance. Our analysis indicates that the
energy confined near the centre of the grey soliton and the propagation constant of
the guided mode of the waveguide induced by the grey screening soliton
increase monotonically with intensity ratio increasing. On the other hand,
when the soliton greyness increases, the energy confined near the centre
of the grey soliton and the propagation constant of the guided mode of the
waveguide induced by the grey screening soliton decrease monotonically.
Relevant examples are provided where photorefractive crystal is of the
strontium barium niobate type.

The low-frequency band gap and the corresponding vibration modes in
two-dimensional ternary locally resonant phononic crystals are restudied
successfully with the lumped-mass method. Compared with the work of C. Goffaux
and J. S\'{a}nchez-Dehesa ({\em Phys. Rev.} B {\bf 67} 14 4301(2003)), it is shown that
there exists an error of about 50{\%} in their calculated results of the band
structure, and one band is missing in their results. Moreover, the in-plane
modes shown in their paper are improper, which results in the wrong conclusion
on the mechanism of the ternary locally resonant phononic crystals. Based on
the lumped-mass method and better description of the vibration modes
according to the band gaps, the locally resonant mechanism in forming the
subfrequency gaps is thoroughly analysed. The rule used to judge whether a
resonant mode in the phononic crystals can result in a corresponding
subfrequency gap is also verified in this ternary case.

Based on the modification of the radial pulsation equation
of an individual bubble, an effective medium method (EMM) is presented for
studying propagation of linear and nonlinear longitudinal acoustic waves
in viscoelastic medium permeated with air bubbles. A classical theory
developed previously by Gaunaurd (Gaunaurd GC and \"{U}berall H, {\em J.
Acoust. Soc. Am}., 1978; 63: 1699--1711) is employed to verify the EMM under linear approximation
by comparing the dynamic (i.e. frequency-dependent) effective parameters,
and an excellent agreement is obtained. The propagation of longitudinal
waves is hereby studied in detail. The results illustrate that the nonlinear
pulsation of bubbles serves as the source of second harmonic wave and the
sound energy has the tendency to be transferred to second harmonic wave.
Therefore the sound attenuation and acoustic nonlinearity of the
viscoelastic matrix are remarkably enhanced due to the system's resonance
induced by the existence of bubbles.

Density functional theory (DFT) (B3p86) has been used to optimize the
structure of the molecule Ta$_2 $. The result shows that the ground
state of molecule Ta$_2 $ is a 7-multiple state and its electronic
configuration is $^{7}\Sigma _{u}^{ + }$, which shows the spin
polarization effect for molecule Ta$_2 $ of transition metal elements for
the first time. Meanwhile, spin pollution has not been found because the
wavefunction of the ground state does not mix with those of higher states.
So, the fact that the ground state of molecule Ta$_2 $ is a 7-multiple state
indicates a spin polarization effect of molecule Ta$_2 $ of the transition metal
elements, i.e. there exist 6 parallel spin electrons and the non-conjugated
electrons are greatest in number. These electrons occupy different space
orbitals so that the energy of molecule Ta$_2 $ is minimized. It can be
concluded that the effect of parallel spin of the molecule Ta$_2$ is larger
than the effect of the conjugated molecule, which is obviously related to
the effect of d-electron delocalization. In addition, the Murrell--Sorbie
potential functions with parameters for the ground state $^{7}\Sigma
_{u}^{ + }$ and other states of the molecule Ta$_2$ are derived. The
dissociation energy $D_\e$, equilibrium bond length $R_\e$ and vibration
frequency
$\omega_\e$ for the ground state of molecule Ta$_2$ are 4.5513eV,
0.2433\,nm
and 173.06\,cm$^{-1}$, respectively. Its force constants $f_2$, $f_3$ and
$f_4$ are 1.5965$\times $10$^{2}$aJ$\cdot$nm$^{-2}$, --6.4722$\times
$10$^{3}$aJ$\cdot$nm$^{-3}$ and 29.4851$\times
$10$^{4}$aJ$\cdot$nm$^{-4}$,
respectively. Other spectroscopic data $\omega_{\e}$ $\chi_{\e}$,
$B_{\e}$ and $\alpha_{\e}$ for
the ground state of Ta$_2 $ are 0.2078\,cm$^{-1}$, 0.0315
cm$^{-1}$ and 0.7858$\times $ 10$^{-4}$\,cm$^{-1}$,
respectively.

By using the density functional theory (B3LYP) and four highly accurate
complete basis set (CBS-Q, CBS-QB3, CBS-Lq, and CBS-4M) ab initio methods,
the $X$(C, N, O)--NO$_{2}$ bond dissociation energies (BDEs) for
CH$_{3}$NO$_{2}$, C$_{2}$H$_{3}$NO$_{2}$, C$_{2}$H$_{5}$NO$_{2}$,
HONO$_{2}$, CH$_{3}$ONO$_{2}$, C$_{2}$H$_{5}$ONO$_{2}$, NH$_{2}$NO$_{2}$
(CH$_{3})_{2}$NNO$_{2}$ are computed. By comparing the computed BDEs and
experimental results, it is found that the B3LYP method is unable to predict
satisfactorily the results of bond dissociation energy (BDE); however, all
four CBS models are generally able to give reliable predication of the
$X$(C, N, O)--NO$_{2}$ BDEs for these nitro compounds. Moreover, the CBS-4M
calculation is the least computationally demanding among the four
CBS methods considered. Therefore, we recommend CBS-4M method as a
reliable method of computing the BDEs for this nitro compound system.

CONDENSED MATTER: STRUCTURAL, MECHANICAL, AND THERMAL PROPERTIES

Song Li, Liu Shuang, Zhang Geng-Min, Liu Li-Feng, Ma Wen-Jun, Liu Dong-Fang, Zhao Xiao-Wei, Luo Shu-Dong, Zhang Zeng-Xing, Xiang Yan-Juan, Shen Jun, Zhou Jian-Jun, Wang Gang, Zhou Wei-Ya

Field emission from single-walled carbon nanotube (SWNT) nonwoven has been
investigated under high vacuum with different vacuum gaps. A low turn-on
electric field of 1.05\,V/$\mu $m is required to reach an emission current
density of 10 $\mu $A/cm$^{2}$. An emission current density of 10
mA/cm$^{2}$ is obtained at an operating electric field of 1.88\,V/$\mu $m. No
current saturation is found even at an emission current of 5\,mA. With the
vacuum gap increasing from 1 to 10 mm, the turn-on field decreases
monotonically from 1.21 to 0.68\,V/$\mu $m, while the field amplification is
augmented. The good field-emission behaviour is ascribed to the combined
effects of the intrinsic field emission of SWNT and the waved topography of
the nonwoven.

A new compound with the same chemical composition as
Li$_{3}$AlB$_{2}$O$_{6}$ but with a different x-ray powder diffraction
pattern as reported before was synthesized and studied experimentally by M.
He, Chen X L {\em et al} (\textit{J. Solid State Chem.} {\bf 163}, 369
(2002)), but there lacks first principles study on
the structure of it. Using conjugant gradient (CG) molecule dynamics (MD)
simulation with a full relaxation of the atomic positions and of the shape
and size of the cell, the structure of Li$_{3}$AlB$_{2}$O$_{6}$ is studied
from first principles. For the density functional, the local density
approximation (LDA) and the generalized gradient approximation (GGA)
forms
are used respectively. Both the LDA and GGA results support the experimental
structure of M. He {\em et al}. The result of MD simulation using GGA agrees with
the experimental result much better. The energy bands are also studied, the
band gap given by LDA and GGA are 5.65 eV, 5.34eV, respectively.

Pure W and W--Cu--W trilayer coatings were deposited on an Fe substrate by
d.c. magnetron sputtering. The $\alpha -\beta$ phase evolution,
intragranular stress evolution in sputter-deposited W layer were
investigated by x-ray diffraction. They are directly related to the film
microstructure, density and adhesion. Therefore, control of the film stress
and phase component transition is essential for its applications. The phase
component transition from $\beta$-W to $\alpha $-W and intragranular stress
evolution from tensile to compressive strongly depend on the deposition
parameters and can be induced by lowering Ar pressure and rising target
power. The compressively stressed films with $\alpha $-W phase have a dense
microstructure and high adhesion to Fe substrate.

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

In this paper, the generalized nonlinear Schr\"{o}dinger equation (GNLSE) is
solved by an adaptive split-step Fourier method (ASSFM). It is found that
ASSFM must be used to solve GNLSE to ensure precision when the soliton
self-frequency shift is remarkable and the photonic crystal fibre (PCF)
parameters vary with the frequency considerably. The precision of numerical
simulation by using ASSFM is higher than that by using split-step Fourier
method in the process of laser pulse propagation in PCFs due to the fact
that the variation of fibre parameters with the peak frequency in the pulse
spectrum can be taken into account fully.

CeO$_{2}$/YSZ/CeO$_{2}$ buffer layers were deposited on biaxially textured
Ni substrates by pulsed laser deposition. The influence of the processing
parameters on the texture development of the seed layer CeO$_{2}$ was
investigated. Epitaxial films of YBCO were then grown \textit{in situ} on the
CeO$_{2}$/YSZ (yttria-stabilized ZrO$_{2}$)/CeO$_{2}$-buffered Ni
substrates. The resulting YBCO conductors exhibited self-field critical
current density $J_{\rm c}$ of more than 1 MA/cm$^{2}$ at 77K and
superconducting transition temperature $T_{\rm c}$ of about 91K.

The influence of the magnetic field sweep rate on the hysteresis loops of
exchange bias Ni$_{0.8}$Fe$_{0.2}$/Fe$_{0.5}$Mn$_{0.5}$ bilayers has been
investigated with a vibrating sample magnetometer. It was found that the
sweep rate of 13.6\,kA/4$\pi $ms is high enough to bring about obvious
changes in the hysteresis loops of the exchange bias bilayer. High sweep
rate in the magnetization reversal stage enlarges the coercivity of the
sample, while high sweep rate in the saturation state reduces the
coercivity. The above phenomena were attributed to magnetic viscosity in the
ferromagnetic layer enhanced by the interface exchange interaction and
domain magnetization reversals assisted by thermal fluctuation in the
antiferromagnetic layer respectively.

We have proposed a novel noncontact ultrasonic motor based on
non-symmetrical electrode driving. The configuration of this
electrode and the fabrication process of rotors are presented. Its vibration
characteristics are computed and analysed by using the finite element
method and studied
experimentally. Good agreement between them is obtained. Moreover,
it is also shown that this noncontact ultrasonic motor is operated in
antisymmetric radial vibration mode of $B_{21}$ mode. The maximum revolution
speed for three-blade and six-blade rotors are 5100 and 3700\,r/min at an
input voltage of 20V, respectively. Also, the noncontact high-speed
revolution of the rotors can be realized by the parts of I, III of the
electrode or
II, IV of the electrode. The levitation distance between the stator and
rotor is
about 140$\mu $m according to the theoretical calculation and the experimental
measurement.

ZnO micro-prisms are prepared on the p-type and n-type Si substrates,
separately. The $I$--$V$ curves analysed by AFM show that the interface junctions
between the ZnO micro-prisms and the p-type substrate and between the ZnO
micro-prisms and the n-type Si substrate exhibit p--n junction behaviour and
ohmic contact behaviour, respectively. The formation of the p--n
heterojunction and ohmic contact is ascribed to the intrinsic n-type
conduction of ZnO material. Better field emission performance (lower onset
voltage and larger emission current) is observed from an individual ZnO
micro-prism grown on the n-type Si substrate. It is suggested that the
n-Si/n-ZnO interfacial ohmic contact benefits the electron emission; while
the p-Si/n-ZnO interface heterojunction deteriorates the electron emission.