The Mei symmetry of Tzénoff equations under the infinitesimal transformations of groups is studied in this paper. The definition and the criterion equations of the symmetry are given. If the symmetry is a Noether symmetry, then the Noether conserved quantity of the Tzénoff equations can be obtained by the Mei symmetry.

In this paper, we have studied the unified symmetry of a nonholonomic
mechanical system in phase space. The definition and the criterion
of a unified symmetry of the nonholonomic mechanical system in
phase space are given under general infinitesimal transformations
of groups in which time is variable. The Noether conserved
quantity, the generalized Hojman conserved quantity and the Mei
conserved quantity are obtained from the unified symmetry. An
example is given to illustrate the application of the results.

This paper is devoted to the study of the underlying linearities of the coupled
Harry--Dym (cHD) soliton hierarchy, including the well-known cHD equation. Resorting
to the nonlinearization of Lax pairs, a family of finite-dimensional Hamiltonian
systems associated with soliton equations are presented, constituting the
decomposition of the cHD soliton hierarchy. After suitably introducing the
Abel--Jacobi coordinates on a Riemann surface, the cHD soliton hierarchy can be
ultimately reduced to linear superpositions,
expressed by the Abel--Jacobi variables.

In this paper, the Fisher equation is analysed. One of its travelling wave solution
is obtained by comparing it with KdV--Burgers (KdVB) equation. Its amplitude, width
and speed are investigated. The instability for the higher order disturbances to the
solution of the Fisher equation is also studied.

In this paper a quantum dialogue scheme is proposed by using N batches of single
photons. The same secret message is encoded on each batch of single photons by the
sender with two different unitary operations, and then the N batches of single
photons are sent to the receiver. After eavesdropping check, the message is encoded
on the one remaining batch by the receiver. It is shown that the
intercept-and-resend attack and coupling auxiliary modes attack can be resisted more
efficiently, because the photons are sent only once in our quantum dialogue scheme.

We investigate schemes for quantum secret sharing and quantum dense
coding via tripartite entangled states. We present a scheme for
sharing classical information via entanglement swapping using two
tripartite entangled GHZ states. In order to throw light upon the
security affairs of the quantum dense coding protocol, we also
suggest a secure quantum dense coding scheme via W state by
analogy with the theory of sharing information among involved users.

Applying Parikh's quantum tunnelling method, this paper has studied the quantum
tunnelling radiation of Schwarzschild de Sitter black hole with a global monopole.
The result shows that the tunnelling rates at the event horizon and the cosmological
horizon are related to Bekenstein--Hawking entropy and the derived radiation
spectrum is not precisely thermal when considering energy conservation and
self-gravitation interaction.

The stability of the Schwarzschild black hole is restudied in the Painlevé
coordinates. Using the Painlevé time coordinate to define the initial time, we
reconsider the odd perturbation and find that the Schwarzschild black hole in the
Painlevé coordinates is unstable. The Painlevé metric in this paper
corresponds to the white-hole-connected region of the Schwarzschild black hole
(r>2m) and the odd perturbation may be regarded as the angular perturbation.
Therefore, the white-hole-connected region of the Schwarzschild black hole is
unstable with respect to the rotating perturbation.

The steady-state properties of a bistable system are investigated when both the
multiplicative noise and the coupling between additive and multiplicative noises are
coloured with different values of noise correlation times \tau_1 and \tau_2.
After introducing a dimensionless parameter R(R=\alpha/D, D is the intensity
of the multiplicative noise and \alpha is the intensity of the additive noise),
and performing the numerical computations, we find the following points: (1) For the
case of R>1, \lambda (the intensity of correlation between additive and
multiplicative noises),\tau_{1} and \tau_{2} can induce the stationary
probability distribution (SPD) transition from bimodal to unimodal in structure, but
for the cases of R\leq1, the bimodal structure is preserved; (2) \alpha can also
induce the SPD transition from bimodal to unimodal in structure; (3) the bimodal
structure of the SPD exhibits a symmetrical structure as D increases.

A new lattice Bhatnagar--Gross--Krook (LBGK) model for a class of the generalized
Burgers equations is proposed. It is a general LBGK model for nonlinear Burgers
equations with source term in arbitrary dimensional space. The linear stability of
the model is also studied. The model is numerically tested for three problems in
different dimensional space, and the numerical results are compared with either
analytic solutions or numerical results obtained by other methods. Satisfactory
results are obtained by the numerical simulations.

A time delay equation for the sea--air oscillator model is studied. The aim is to
create an asymptotic solving method of nonlinear equation for the El Ni\tilde{\rm
n}o--Southern Oscillation model. And based on a class of oscillators of the
model, employing the method of ENSO singular perturbation, the asymptotic solution
of corresponding problem is obtained. It is proven from the results that the method
of singular perturbation can be used for analysing the sea surface temperature
anomaly in the equatorial eastern Pacific of the atmosphere--ocean oscillation for
ENSO model.

A state-observer based full-state asymptotic trajectory control (OFSTC) method
requiring a scalar state is presented to asymptotically drive all the states of
chaotic systems to arbitrary desired trajectories. It is no surprise that OFSTC can
obtain good tracking performance as desired due to using a state-observer.
Significantly OFSTC requires only a scalar state of chaotic systems. A sinusoidal
wave and two chaotic variables were taken as illustrative tracking trajectories to
validate that using OFSTC can make all the states of a unified chaotic system track
the desired trajectories with high tracking accuracy and in a finite time. It is
noted that this is the first time that the state-observer of chaotic systems is
designed on the basis of Kharitonov's Theorem.

An information-theoretic measure is introduced for evaluating the dynamical coupling of spatiotemporally chaotic signals produced by extended systems. The measure of the one-way coupled map lattices and the one-dimensional, homogeneous, diffusively coupled map lattices is computed with the symbolic analysis method. The numerical results show that the information measure is applicable to determining the dynamical coupling between two directly coupled or indirectly coupled chaotic signals.

Dynamical behaviours of the motion of particles in a periodic potential under a
constant driving velocity by a spring at one end are explored. In the stationary
case, the stable equilibrium position of the particle experiences an elasticity
instability transition. When the driving velocity is nonzero, depending on the
elasticity coefficient and the pulling velocity, the system exhibits complicated and
interesting dynamics, such as periodic and chaotic motions. The results obtained
here may shed light on studies of dynamical processes in sliding friction.

The cellular automaton model is suggested to describe the traffic-flow at the grade
roundabout crossing. After the simulation with computer, the fundamental properties
of this model have been revealed. Analysing this kind of road structure, this paper
transforms the grade roundabout crossing with inner-roundabout-lane and
outer-roundabout-lane into a configuration with many bottlenecks. Because of the
self-organization, the traffic flow remains unblocked under a certain vehicle
density. Some results of the simulation are close to the actual design parameter.

βdecay in the strong magnetic field of the crusts of neutron stars is analysed by an improved method. The reactions ^{67} Ni(β^{-})^{67} Cu and ^{62} Mn\beta ^{-}^{62} Fe are investigated as examples. The results show that a weak magnetic field has little effect on βdecay but a strong magnetic field (B>10^{12}G) increases β decay rates obviously. The conclusion derived may be crucial to the research of late evolution of neutron stars and nucleosynthesis in r-process.

Zhong Chen, Ma Yu-Gang, Fang De-Qing, Cai Xiang-Zhou, Chen Jin-Gen, Shen Wen-Qing, Tian Wen-Dong, Wang Kun, Wei Yi-Bin, Chen Jin-Hui, Guo Wei, Ma Chun-Wang, Ma Guo-Liang, Su Qian-Min, Yan Ting-Zhi, Zu

In this paper, the isotopic and isotonic distributions of projectile fragmentation products have been simulated by a modified statistical abrasion--ablation model and the isoscaling behaviour of projectile-like fragments has been discussed. The isoscaling parameters α and β have been extracted respectively, for hot fragments before evaporation and cold fragments after evaporation. It looks that the evaporation has stronger effect on α than β. For cold fragments, a monotonic increase of α and β with the increase of Z and N is observed. The relation between isoscaling parameter and the change of isospin content is discussed.

To provide some reference data for estimation of the erosion rates and lifetimes of
some candidate plasma facing component (PFC) materials in the plasma stored energy
explosive events (PSEEE), this paper calculates the sputtering yields of Mo, W and
deuterium saturated Li surface bombarded by energetic charged particles by a new
sputtering physics description method based on bipartition model of charge particle
transport theory. The comparisons with Monte Carlo data of TRIM code and
experimental results are made. The dependences of maximum energy deposition,
particle and energy reflection coefficients on the incident energy of energetic
runaway electrons impinging on the different material surfaces are also calculated.
Results may be useful for estimating the lifetime of PFC and analysing the impurity
contamination extent, especially in the PSEEE for high power density and with high
plasma current fusion reactor.

We first experimentally demonstrate a laser-diode end-pumped self-Q-switched and mode-locked Nd,Cr:YAG green laser with a KTP crystal as the intra-cavity frequency doubler. The device produces
an average output power of 680 mW at 532 nm. The corresponding pulse width of the Q-switched envelope of the green laser is 170±20 ns. The mode-locked pulses have a repetition rate of approximately 183
MHz and the average pulse duration is estimated to be around sub-nanosecond. It is found that the intra-cavity frequency doubling greatly improves the modulation depth and stability of the
mode-locked pulses within the Q-switched envelope.

The viscoelasticity and subharmonic generation of a kind of lipid ultrasound contrast agent are investigated. Based on the measurement of the sound attenuation spectrum, the viscoelasticity of the lipid shell is estimated by use of an optimization method. Shear modulus G_{S}=10MPa and shear viscosity \mu _{S}=1.49N\cdotS/m^{2} are obtained. The nonlinear oscillation of the encapsulated microbubble is studied with Church's model theoretically and experimentally.
Especially, the dependence of subharmonic on the incident acoustic pressure is studied. The results reveal that the development of the subharmonic undergoes three stages, i.e. occurrence, growth and saturation, and that hysteresis appears in descending ramp insonation.

By using the time-dependent multilevel approach, we have calculated the coherent
population transfer among the quantum states of potassium atom by a single
frequency-chirped laser pulse. The results show that the population can be
efficiently transferred to a target state and be trapped there by using an
`intuitive' or a `counter-intuitive' frequency sweep laser pulse in the case of
`narrowband' frequency-chirped laser pulse. It is also found that a pair of
sequential `broadband' frequency-chirped laser pulses can efficiently transfer
population from one ground state of the \La atom to the other one.

The energy levels, oscillator strengths, spontaneous radiative decay rates, and
electron impact collision strengths are calculated for Fe VIII and Fe IX using the
recently developed flexible atomic code (FAC). These atomic data are used to analyse
the emission spectra of both laboratory and astrophysical plasmas. The {\it n}f--3d
emission lines have been simulated for Fe VIII and Fe IX in a wavelength range of
6--14 nm. For Fe VIII, the predicted relative intensities of lines are insensitive
to temperature. For Fe IX, however, the intensity ratios are very sensitive to
temperature, implying that the information of temperature in the experiment can be
inferred. Detailed line analyses have also been carried out in a wavelength range of
60--80 nm for Fe VIII, where the solar ultraviolet measurements of emitted radiation
spectrometer records a large number of spectra. More lines can be identified with
the aid of present atomic data. A complete dataset is available electronically from
http://www.astrnomy.csdb.cn/EIE/.

The multi-charged sulfur ions of S^{q=} (q\le 6) have been generated when hydrogen sulfide cluster beams are irradiated by a nanosecond laser of 1064 and 532,nm with an intensity of 10^{10}\sim 10^{12}W1\cdotcm^{-2}. S^{6+} is the dominant multi-charged species at 1064nm, while S^{4+}, S^{3+} and S^{2+} ions are the main multi-charged species at 532nm. A three-step model (i.e., multiphoton ionization triggering, inverse bremsstrahlung heating, electron collision ionizing) is proposed to explain the generation of these multi-charged ions at the laser intensity stated above. The high ionization level of the clusters and the increasing charge state of the ion products with increasing laser wavelength are supposed mainly due to the rate-limiting step, i.e., electron heating by absorption energy from the laser field via inverse bremsstrahlung, which is proportional to \lambda ^{2}, \lambda being the laser wavelength.

This paper uses the density functional theory (DFT)(B3p86) of Gaussian03 to
optimize the structure of Fe_{2} molecule. The result shows that the ground state
for Fe_{2} molecule is a 9-multiple state, which shows spin polarization effect of
Fe_{2} molecule of transition metal elements for the first time. Meanwhile, we have
not found any spin pollution because the wavefunction of the ground state does not
mingle with wavefunctions with higher energy states. So, that the ground state for
Fe_{2} molecule is a 9-multiple state is indicative of the spin polarization effect
of Fe_{2} molecule of transition metal elements. That is, there exist 8 parallel
spin electrons. The non-conjugated electron is greatest in number. These electrons
occupy different spacious tracks, so that the energy of the Fe_{2} molecule is
minimized. It can be concluded that the effect of parallel spin of the Fe_{2}
molecule is larger than the effect of the conjugated molecule, which is obviously
related to the effect of electron d delocalization. In addition, the Murrell--Sorbie
potential functions with the parameters for the ground state and other states of
Fe_{2} molecule are derived. Dissociation energy D_{e} for the ground state of
Fe_{2} molecule is 2.8586ev, equilibrium bond length R_{e} is 0.2124nm, vibration
frequency \omega _{e} is 336.38,cm^{-1}. Its force constants f_{2}, f_{3},and f_{4} are 1.8615aJ\cdotnm^{-2}, --8.6704aJ\cdotnm^{-3},
29.1676aJ\cdotnm^{-4} respectively. The other spectroscopic data for the ground
state of Fe_{2} molecule \omega_{e} \chi_{e}, B_{e}, \alpha_{e} are 1.5461,cm^{-1}, 0.1339,cm^{-1},7.3428×10^{-4},cm^{-1} respectively.

PHYSICS OF GASES, PLASMAS, AND ELECTRIC DISCHARGES

A ballooning mode equation for tokamak plasma, with the toroidicity and the Shafranov shift effects included, is derived for a shift circular flux tokamak configuration. Using this equation, the stability of the plasma configuration with an internal transport barrier (ITB) against the high n (the toroidal mode number) ideal magnetohydrodynamic (MHD) ballooning mode is analysed. It is shown that both the toroidicity and the Shafranov shift effects are stabilizing. In the ITB region,
these effects give rise to a low shear stable channel between the first and the second stability regions. Out of the ITB region towards the plasma edge, the stabilizing effect of the Shafranov shift causes the unstable zone to be
significantly narrowed.

An analytical scheme on the initial transient process in a simple helical flux
compression generator, which includes the distributions of both the magnetic field
in the hollow of an armature and the conducting current density in the stator, is
developed by means of a diffusion equation. A relationship between frequency of the
conducting current, root of the characteristic function of Bessel equation and decay
time in the armature is given. The skin depth in the helical stator is calculated
and is compared with the approximate one which is widely used in the calculation of
magnetic diffusion. Our analytical results are helpful to understanding the
mechanism of the loss of magnetic flux in both the armature and stator and to
suggesting an optimal design for improving performance of the helical flux
compression generator.

This paper reports that a new plasma generator at atmospheric pressure, which is composed of two homocentric cylindrical all-metal tubes, successfully generates a cold plasma jet. The inside tube electrode is connected to ground, the outside tube electrode is connected to a high-voltage power supply, and a dielectric layer is covered on the outside tube electrode. When the reactor is operated by low-frequency (6 kHz--20 kHz) AC supply in atmospheric pressure and argon is
steadily fed as a discharge gas through inside tube electrode, a cold plasma jet is
blown out into air and the plasma gas temperature is only 25--30℃. The electric character of the discharge is studied by using digital real-time oscilloscope (TDS 200-Series), and the discharge is capacitive. Preliminary results are presented on the decontamination of E.colis bacteria and Bacillus subtilis bacteria by this plasma jet, and an optical emission analysis of the plasma jet is
presented in this paper. The ozone concentration generated by the plasma jet is 1.0×10^{16}cm^{-3} which is acquired by using the ultraviolet absorption spectroscopy.

CONDENSED MATTER: STRUCTURAL, MECHANICAL, AND THERMAL PROPERTIES

Pr-based bulk metallic amorphous (BMA) rods (Pr_{60}Ni_{30}Al_{10}) and
Al-based amorphous ribbons (Al_{87}Ni_{10}Pr_{3}) have been prepared by using
copper mould casting and single roller melt-spun techniques, respectively. Thermal parameters deduced from differential scanning calorimeter (DSC) indicate that the glass-forming ability (GFA) of Pr\xj{60}Ni\xj{30}Al\xj{10} BMA rod is far higher than that of Al_{87}Ni_{10}Pr_{3} ribbon. A comparative study about the
differences in structure between the two kinds of glass-forming alloys, superheated
viscosity and crystallization are also made. Compared with the amorphous alloy
Al_{87}Ni_{10}Pr_{3}, the BMA alloy Pr_{60}Ni_{30}Al_{10} shows high thermal stability and large viscosity, small diffusivity at the same superheated temperatures. The results of x-Ray diffraction (XRD) and transmission electron microscope (TEM) show the pronounced difference in structure between the two
amorphous alloys. Together with crystallization results, the main structure compositions of the amorphous samples are confirmed. It seems that the higher the GFA, the more topological type clusters in the Pr--Ni--Al amorphous alloys, the GFAs of the present glass-forming alloys are closely related to their structures.

The low-energy electron point source (LEEPS) microscope, which creates enlarged projection images with low-energy field emission electron beams, can be used to observe the projection image of
nano-scale samples and to characterize the coherence of the field emission beam. In this paper we report the design and test operation performance of a home-made LEEPS microscope. Multi-walled carbon
nanotubes (MWCNTs) synthesized by the CVD method were observed by LEEPS microscope using a conventional tungsten tip, and projection images with the magnification of up to 10_{4} was obtained. The resolution of the acquired images is \sim10 nm. A higher resolution and a larger magnification can be expected when the AC magnetic field inside the equipment is shielded and the vibration of the instrument reduced.

In this paper, we investigate the length dependence of linear and nonlinear
optical properties of finite-length BN nanotubes. The recently predicted
smallest BN(5,0) nanotube with configuration stabilization is selected as an
example. The energy gap and optical gap show the obvious length dependence
with the increase of nanotube length. When the length reaches about 24
{\AA}, the energy gap will saturate at about 3.2 eV, which agrees well with
the corrected quasi-particle energy gap. The third-order polarizabilities
increase with the increase of tube length. Two-photon allowed excited states
have significant contributions to the third-order polarizabilities of
BN(5,0) nanotube.

We introduce a velocity-difference-separation model that modifies the previous
models in the literature. The improvement of this new model over the previous ones
lies in that it not only theoretically retains many strong points of the previous
ones, but also performs more realistically than others in the dynamical evolution of
congestion. Furthermore, the proposed model is investigated with analytic and
numerical methods, with the finding that it can demonstrate some complex physical
features observed in real traffic such as the existence of three phases: free flow,
synchronized flow, and wide moving jam; sudden flow drop in flow-density plane; and
traffic hysteresis in transition between the free and the synchronized flow.

Based on Bogoliubov's truncated Hamiltonian H_{B} for a weakly interacting Bose system, and adding a U(1) symmetry breaking term $\sqrt{V}(\lambda a_{0}+\lambda^{*}a_{0}^{+}) to H_{B}, we show by
using the coherent state theory and the mean-field approximation rather than the c-number approximations, that the Bose--Einstein condensation(BEC) occurs if and only if the U(1) symmetry of the system is spontaneously broken. The real ground state energy and the justification of the Bogoliubov c-number substitution are given by solving the Schr\"{o}dinger eigenvalue equation and using the self-consistent condition.

In this paper, the structure of cubic CaTiO_{3} (001) surfaces with CaO and
TiO_{2} terminations has been studied from density functional calculations. It has
been found that the Ca atom has the largest relaxation for both kinds of
terminations, and the rumpling of the CaO-terminated surface is much larger than
that of TiO_{2}-terminated surface. Also we have found that the metal atom
relaxes much more prominently than the O atom does in each layer. The
CaO-terminated surface is slightly more energetically favourable than the
TiO_{2}-terminated surface from the analysis of the calculated surface energy.

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

The electronic and optical properties of zincblende ZnX(X=S, Se, Te) and
ZnX:Co are studied from density functional theory (DFT) based first principles
calculations. The local crystal structure changes around the Co atoms in the lattice
are studied after Co atoms are doped. It is shown that the Co-doped materials have
smaller lattice constant (about 0.6%--0.9%). This is mainly due to the shortened
Co--X bond length. The (partial) density of states (DOS) is calculated and
differences between the pure and doped materials are studied. Results show that for
the Co-doped materials, the valence bands are moving upward due to the existence of
Co 3d electron states while the conductance bands are moving downward due to the
reduced lattice constants. This results in the narrowed band gap of the doped
materials. The complex dielectric indices and the absorption coefficients are
calculated to examine the influences of the Co atoms on the optical properties.
Results show that for the Co-doped materials, the absorption peaks in the high
wavelength region are not as sharp and distinct as the undoped materials, and the
absorption ranges are extended to even higher wavelength region.

The extraordinary light transmission through a 200-nm thick gold
film when passing through different subwavelength hole arrays is
observed experimentally. The sample is fabricated by electron beam
lithography and reactive ion etching system. A comparison between
light transmissions shows that the hole shape changing from
rectangular to diamond strongly affects the transmission intensity
although both structures possess the same lattice constant of
600,nm. Moreover, the position of the transmission maximum
undergoes a spectral red-shift of about 63,nm. Numerical
simulations by using a transfer matrix method reproduce the observed
transmission spectrum quite well.

The rotational anisotropies in the exchange bias structures of
ferromagnetism/antiferromagnetism 1/antiferromagnetism 2 are studied in this
paper. Based on the model, in which the antiferromagnetism is treated with
an Ising mean field theory and the rotational anisotropy is assumed to be
related to the field created by the moment induced on the antiferromagnetic
layer next to the ferromagnetic layer, we can explain why in experiments for
ferromagnetism (FM)/antiferromagntism 1 (AFM1)/antiferromagnetism 2 (AFM2)
systems the thickness-dependent rotational anisotropy value is
non-monotonic, i.e. it reaches a minimum for this system at a specific
thickness of the first antiferromagnetic layer and exhibits oscillatory
behaviour. In addition, we find that the temperature-dependent rotational
anisotropy value is in good agreement with the experimental result.

Based on Monte Carlo method, the oscillatory behaviour of the
average magnetic moment as a function of the cluster sizes and the
temperature dependences of magnetic moment with different sizes have
been studied. It is found that the oscillations superimposed on the
decreasing moment are associated with not only the geometrical
structure effects but also the thermal fluctuation. The hystereses
and thermal coercivities for free clusters with zero and finite
uniaxial anisotropies have been calculated. The simulated thermal
dependence of the coercivity is consistent with the experimental
result, but does not fit the T^{α} law in the whole temperature
range. It is evident that an easy magnetization direction and an
anisotropy resulting from the spin configurations exist in the free
clusters with the pure exchange interaction, which is also proved by
the natural angle and energy distribution of clusters. A systematic
theoretical analysis is also made to establish the relationship
between natural angle and coercivity.

This paper investigates the dielectric properties of
(Na_{0.5}K_{0.5}Bi)_{0.5}TiO_{3} crystal at intermediate frequencies (1kHz
\le f \le 1MHz) in the temperature range of 30--560℃. A pronounced
high-temperature diffuse dielectric anomaly has been observed. This dielectric
anomaly is shown to arise from a Debye-like dielectric dispersion that slows down
following an Arrhenius law. The activation energy E_{r} obtained in the fitting
process is about 0.69eV. It proposes that the dielectric peak measured at low
frequency above 400℃ is not related to the phase transition but to a
space-charge relaxation.

A modified U-tube conical bubble sonoluminescence device is used to
study the conical bubble photoluminescence. The spectra of conical
bubble sonoluminescence at different concentrations of rhodamine 6G
(Rh6G) solution in 1,2-propanediol have been measured. Results show
that the sonoluminescence from the conical bubbles can directly
excite Rh6G, which in turn can fluoresce. The light emission of this
kind is referred to as conical bubble photoluminescence. The maximum
of fluorescence spectral line intensity in the conical bubble
photoluminescence has a red shift in relative to that of the
standard photo-excited fluorescence, which is due to the higher
self-absorption of Rh6G, and the spectral line of conical bubble
photoluminescence is broadened in width compared with that of
photo-excited fluorescence.

Qin Yi-Ping, Zhang Bin-Bin, Dong Yun-Ming, Zhang Fu-Wen, Li Huai-Zhen, Jia Lan-Wei, Mao Li-Sheng, Lu Rui-Jing, Yi Ting-Feng, Cui Xiao-Hong, Zhang Zhi-Bin

In this paper, the effect of the intrinsic distribution of cosmological candles is
investigated. We find that in the case of a narrow distribution the deviation of the
observed modulus of sources from the expected central value can be estimated within
a ceratin range. We thus introduce lower and upper limits of X^{2}, X
_{min}^{2} and X_{max}^{2} to estimate cosmological parameters by
applying the conventional minimizing X^{2} method. We apply this method to a
gamma-ray burst (GRB) sample as well as to a combined sample including this GRB
sample and an SN Ia sample. Our analysis shows that: a) in the case of assuming an
intrinsic distribution of candles of the GRB sample, the effect of the distribution
is obvious and should not be neglected; b) taking into account this effect would
lead to a poorer constraint of the cosmological parameter ranges. The analysis
suggests that in the attempt of constraining the cosmological model with current GRB
samples, the results tend to be worse than was previously anticipated if the
mentioned intrinsic distribution does exist.