一些稀疏图的强边染色（英文）

图G的强边染色是指对图G进行正常边染色使得任意长度为3的路的三条边染不同的颜色.图G的强边色数,记为χ’_s(G),是使得图G是强k边着色的最小正整数kk.2015年,Zang [arXiv:1510.00785]证明了:最大度△(G)=5的图G,χ’_s(G)≤37.本文证明了:最大度△(G)=5且最大平均度小于8/3(或者14/5)的图G,χ’_s(G)≤13 (或者14).另外,本文证明了:最大度△(G)≥3的不含K_2,3-图子式的图G,χ’_s(G)≤4△(G)-6,这个界是紧的.     

Observational constraints on the accelerating universe in the framework of a 5D bounce cosmological model

In the framework of a five-dimensional (5D) bounce cosmological model, a useful function f(z) is obtained by giving a concrete expression of deceleration parameter q(z)=q₁+{q₂}/{1+ln (1+ z)}. Then using the obtained Hubble parameter H(z) according to the function f(z), we constrain the accelerating universe from recent cosmic observations: the 192 ESSENCE SNe Ia and the 9 observational H(z) data. The best fitting values of transition redshift z_T and current deceleration parameter q₀ are given as z_T= 0.65_-0.12^0.25 and q₀ = - 0.76_-0.15^+0.15 (1σ). Furthermore, in the 5D bounce model it can be seen that the evolution of equation of state (EOS) for dark energy w_de can cross over -1 at about z=0.23 and the current value w_0de= - 1.15<- 1. On the other hand, by giving a concrete expression of model-independent EOS of dark energy w_de, in the 5D bounce model we obtain the best fitting values z_T= 0.66_0.08^+0.11 and q₀ = - 0.69_0.10^+0.10 (1σ) from the recently observed data: the 192 ESSENCE SNe Ia, the observational H(z) data, the 3-year Wilkinson Microwave Anisotropy Probe (WMAP), the Sloan Digital Sky Survey (SDSS) baryon acoustic peak and the x-ray gas mass fraction in clusters.     

Reconstruction of New Holographic Chaplygin Gas Model with Viscosity

We investigate the interacting new holographic dark energy （HDE） with viscosity. Specifically, we not only study the dynamical evolutions of the new HDE with viscosity and the influences of viscosity as well as the coupling constant on the equation of state for the new HDE, but also establish the correspondence between the new HDE with viscosity and variable generalized Chaplygin gas （VGCG） models in the fiat Friedmann-Robertson-Walker universe. Furthermore, we also reconstruct the potential and the dynamics of VGCG as the scalar field. By analysis we show that for the new holographic Chaplygin gas model, if the related parameters to the potential satisfy some constraints, the accelerated expansion can be achieved. These research results can reduce to the ones without viscosity.     

Reconstructing dark energy potentials from parameterized deceleration parameters

In this paper, the properties of dark energy are investigated according to the parameterized deceleration parameter q(z), which is used to describe the extent of the accelerating expansion of the universe. The potential of dark energy V(φ) and the cosmological parameters, such as the dimensionless energy density \varOmega_φ, \varOmega_m, and the state parameter w_φ, are connected to it. Concretely, by giving two kinds of parameterized deceleration parameters q(z)=a+bz/(1+z) and q(z)=1/2+(az+b)/(1+z)^2, the evolution of these parameters and the reconstructed potentials V(φ) are plotted and analysed. It is found that the potentials run away with the evolution of universe.     

Clifford代数中的双曲相位变换群及其在四维相对论时空中的应用

将Clifford代数所定义的双曲复空间R_H和作用在双曲复空间R_H上的双曲相位变换群U₄(H)赋予了明确的物理意义. 双曲复空间R_H同构于四维Minkowski时空，而其上的双曲相位变换群U₄(H)就是四维相对论时空中的洛仑兹(Lorentz)变换群. 进一步，利用U₄(H)群的复合变换性质，自然导出了四维Minkowski时空中Lorentz变换和速度变换的一般表达式. 由此，将狭义相对论中的特殊Lorentz变换作为特例包含其中. 关键词： 双曲复数 双曲相位变换 Minkowski时空 Clifford代数     

五维大反弹宇宙学模型的重建及其相关宇宙学量的演化

在五维大反弹宇宙学模型框架下,通过给定三种不同的暗能量有效态方程,确定了在该模型中起重要作用的函数f(z),从而描述了五维大反弹模型中相关的宇宙学量随红移量z的演化.研究表明,与情形Ⅰ中有效态方程相对应的宇宙学量的演化规律和当前天文观测数据符合最好. 关键词： 大反弹宇宙学模型 暗能量 态方程     

The double Lagrangian its applications with U（1, J） symmetry and to the cosmology

By introducing the double complex scalar field, this paper constructs the double Lagrangian with the potential V（Ф（J）,Ф（J）） = V（│Ф（J）│）, which not only can describe the evolution of quintom Universe, but also can naturally give the spintessence and hessence Universe. Furthermore, the U（1, J） symmetry of the double complex Lagrangian is verified, and the total conserved charge within the physical volume is derived by means of the Norther theorem. Moreover, it can point out that the ＇imaginary motion＇ of the angular parameter in Ref.[14], in fact, is only a real phase displacement in our model.     

Evolution of Variable Generalized Chaplygin Gas

We consider the variable Generalized Chaplygin gas （VGCG） proposal for unification of dark matter and dark energy with p = pdc and ρ= pdm ＋ ρdc. The equation of state of the VGCG is given by p = -A0a^-n/ρ^α, where a is the scale factor. Some cosmological quantities such as the fractional contributions of different components of the universe Ωi （i respectively denotes baryons, dark matter and dark energy） to the critical density, the deceleration parameter q are all obtained. The transition from deceleration to acceleration is described in this model. In addition, we find the behaviour of variable Generalized Chaplgin gas is similar to dust-like matter at early times and will be quiessence or phantom at late stage.     

Constraints on the unified model of dark matter and dark energy

Using recently observed data:the Constitution dataset of type supernovae Ia (SNIa),the observational Hubble data (OHD),the measurement results of baryon acoustic oscillation (BAO) from the Sloan Digital Sky Survey (SDSS) and the Two Degree Field Galaxy Redshift Survey (2dFGRS),and the current cosmic microwave background (CMB) data from the five-year Wilkinson Microwave Anisotropy Probe (WMAP),we apply the Markov Chain Monte Carlo method to investigate the observational constraints on the generalized Chaplygin gas (GCG) model as the unification of dark matter and dark energy.For this unified model,the constraints on GCG mixture are discussed by considering the different expressions of current matter density or considering constraints as being independent of the matter quantity Ωm.     

The properties and geodesics related to the NUT--Taub-like spacetime

Some properties related to the NUT--Taub-like spacetime, such as the surface of infinite red-shift, horizon, singularity and the area of the NUT--Taub-like black hole are discussed. Furthermore, the geodesics in the NUT--Taub-like spacetime are obtained in some special cases. Specifically, the circular orbits for a massive particle are derived, which can reduce to the cases of the Schwarzschild spacetime and the NUT--Taub spacetime when m^*=0 and m^*\ll M, respectively.