Similarity Solutions for Generalized Variable Coefficients Zakharov-Kuznetsov Equation under Some Integrability Conditions

In this paper, the symmetry method has been carried over to the generalized variable coefficients Zakharov- Kuznetsov equation. The infinitesimal symmetries and the optimal system are deduced and from this optimal system seven basic fields are determined, and for every vector field in the optimal system the admissible forms of the coefficients are found and this also leads us to transform the given equation into partial differential equations in two variables. After using some referenced transformations the mentioned partial differential equations eventually reduce to ordinary differential equations. The search for solutions to those equations has yielded many exact solutions in most cases.     

Hawking radiation of Weyl neutrinos in a rectilinearly non—uniformly accelerating Kinnersley black hole

The quantum thermal effect of Weyl neutrinos in a rectilinearly non-uniformly accelerating Kinnersley black hole is investigated using the generalized tortoise coordinate transformation.The equations that determine the location,the Hawking temperature of the event horizon and the thermal radiation spectrum of neutrinos are derived.Our results show that the location and the temperature of the event horizon depend not only on the time but also on the angle.     

Investigation of Heisenberg algebra for a modified anti-de Sitter and modified antiSnyder models

In this paper,we consider a possible modification of the de Sitter and anti-de Sitter space for the extended uncertainty principle.For the modified anti-de Sitter model we discuss the representation and wave functions of the momentum operator for a one-dimensional box problem.Also,we consider modified Snyder and anti-Snyder models for the generalized uncertainty principle.Then,we assume the Hamiltonian with different potential and solve the Heisenberg algebra for the modified(anti)-de Sitter and(anti)-Snyder models in both position and in the momentum space.     

A meshless method for the nonlinear generalized regularized long wave equation

This paper presents a meshless method for the nonlinear generalized regularized long wave(GRLW) equation based on the moving least-squares approximation.The nonlinear discrete scheme of the GRLW equation is obtained and is solved using the iteration method.A theorem on the convergence of the iterative process is presented and proved using theorems of the infinity norm.Compared with numerical methods based on mesh,the meshless method for the GRLW equation only requires the scattered nodes instead of meshing the domain of the problem.Some examples,such as the propagation of single soliton and the interaction of two solitary waves,are given to show the effectiveness of the meshless method.     

On Form Invariance,Lie Symmetry,and Three Kinds of Conserved Quantities of Generalized Lagrange's Equations

In this paper, the form invariance and the Lie symmetry of Lagrange's equations for nonconservative system in generalized classical mechanics under the infinitesimal transformations of group are studied, and the Noether's conserved quantity, the new form conserved quantity, and the Hojman's conserved quantity of system are derived from them. Finally, an example is given to illustrate the application of the result.     

Entanglement of Formation for Quantum States

We investigate the entanglement of formation for a class of high-dimensional quantum mixed states. We present a kind of generalized concurrence for a class of high-dimensional quantum pure states such that the entanglement of formation is a monotonically increasing convex function of the generallzed concurrence, from the monotonicity and convexity the entanglement of formafion for a class of high-dimensional mixed states has been calculated analytically,     

Laurdan and Prodan as Polarity-Sensitive Fluorescent Membrane Probes

The steady-state and dynamic fluorescence spectral properties of 2-dimethylamino-6-lauroylnaphthalene (LAURDAN) and several other naphthalene derivatives are summarized to illustrate their sensitivity to the polarity of the environment. Results obtained both in solvents of different polarity and in phospholipid vesicles in two phase states are presented. The emission red shift observed in polar solvents and in the phospholipid liquid–crystalline phase is explained on the basis of dipolar relaxation of solvent molecules surrounding the fluorescent naphthalene moiety of these probes. In phospholipid environments, experimental evidence is shown that excludes the intramolecular relative reorientation of the dimethylamino and carbonyl groups in the naphthalene and the reorientation of the entire fluorescent moiety. The solvent dipolar relaxation observed for LAURDAN and PRODAN in phospholipid bilayers has been attributed to a small number of water molecules present at the membrane interface. A comparison between LAURDAN emission in phospholipid vesicles prepared in D₂O and in H₂O is also presented. The definition and the derivation of the generalized polarization function are also discussed.     

广义特征坐标系计算膨胀波与激波优越性的数值验证

最近提出的以流体速度和声速的线性组合为速度而运动的广义特征坐标系,是-个更为-般的坐标系统,当参数取不同特殊值的时候,就可以得到其他经典的坐标系统.这种坐标系的最大特点是,它能跟随膨胀波(当然也可以跟随激波和接触间断)运动,从而在使用同-计算格式的前提下,使得膨胀波的计算精度更高.对膨胀波和激波进行数值试验,结果显示广义特征坐标系在计算膨胀波和激波时明显优于传统的坐标系.     

Thermodynamical Aspects of Modified Holographic Dark Energy Model

We investigate the unified first law and the generalized second law in a modified holographic dark energy model. The thermodynamical analysis on the apparent horizon can work and the corresponding entropy formula is extracted from the systematic algorithm. The entropy correction term depends on the extra-dimension number of the brane as expected, but the interplay between the correction term and the extra dimensions is more complicated. With the unified first law of thermodynamics well-founded, the generalized second law of thermodynamics is discussed and it is found that the second law can be violated in certain circumstances. Particularly, if the number of the extra dimensions is larger than one, the generalized law of thermodynamics is always satisfied; otherwise, the validity of the second law can only be guaranteed with the Hubble radius greatly smaller than the crossover scale r_c of the 5-dimensional DGP model.     

Statistics of strange attractors by generalized cell mapping

It is proposed in this paper to use the generalized cell mapping to locate strange attractors of dynamical systems and to determine their statistical properties. The cell-to-cell mapping method is based upon the idea of replacing the state space continuum by a large collection of state space cells and of expressing the evolution of the dynamical system in terms of a cell-to-cell mapping. This leads to a Markov chain which in turn allows us to compute all the statistical properties as well as the invariant distribution. After a general discussion, the method is applied in this paper to strange attractors of a variety of systems governed either by point mappings or by differential equations. The results indicate that it is a viable, effective and attractive method. Some comments on this method in comparison with the method of direct iteration will also be made.