Auxiliary Equation Method and New Exact Solutions of BKP Equation

In this paper, auxiliary equation method is proposed for constructing more general exact solutions of nonlinear partial differential equation with the aid of symbolic computation. We study the （2＋1）-dimensional BKP equation and get a series of new types of traveling wave solutions. The method used here can be also extended to other nonlinear partial differential equations.

P-sets and Its Dependence Characteristic

P-sets is a set pair, it is composed of internal P-set and outer P-set, it has dynamic characteristic. By using structure of P-sets, dependence theorem and identification theorem are proposed in this paper.

Research on Civics Teaching in Surveying Program

The integration of the civics course and surveying professional course is an important part of the teaching reform of surveying,which is an important way to implement the principle of cultivating educated talents with moral characters for the country.Based on the surveying course,this paper deeply analyses the spirit of hard work and endurance,craftsmanship,innovation,and national sentiment contained in surveying,carries the civics education with professional knowledge,and makes the civics element subliminally enter the brain and heart,so as to improve the patriotic sentiment and professional quality of students.

ASYMPTOTIC BEHAVIOR OF GLOBAL SMOOTH SOLUTIONS FOR BIPOLAR COMPRESSIBLE NAVIER-STOKES-MAXWELL SYSTEM FROM PLASMAS

This paper is concerned with the bipolar compressible Navier-Stokes-Maxwell system for plasmas. We investigated, by means of the techniques of symmetrizer and elaborate energy method, the Cauchy problem in R^3. Under the assumption that the initial values are close to a equilibrium solutions, we prove that the smooth solutions of this problem converge to a steady state as the time goes to the infinity. It is shown that the difference of densities of two carriers converge to the equilibrium states with the norm ｜｜·｜｜H^s-1, while the velocities and the electromagnetic fields converge to the equilibrium states with weaker norms than ｜｜·｜｜H^s-1. This phenomenon on the charge transport shows the essential difference between the unipolar Navier-Stokes-Maxwell and the bipolar Navier-Stokes-Maxwell system.

The Study on Scaling Function of L^2(R^s)

In this paper, using the orthonormal multiresolution analysis（MRA） of L^2（R^s）, we get two important properties of the scaling function with dilation matrix A = MI of L^2 （R^s）. These properties axe chaxacterized by some inequalities and equalities.

Global Existence of Smooth Solutions of Compressible Bipolar Euler-Maxwell Equations

The bipolar compressible Euler-Maxwell equations as a fluid dynamic model arising from plasma physics to describe the dynamics of the compressible electrons and ions is investigated. This work is concerned with three-dimensional Euler-Maxwell equations with smooth periodic solutions. With the help of the symmetry operator techniques and energy method, the global smooth solution with small amplitude is constructed around a constant equilibrium solution with asymptotic stability property.

c-Myc regulates neural stem cell quiescence and activation by coordinating the cell cycle and mitochondrial remodeling

Dear Editor,In the adult brain,the transition from neural stem cell(NSC)quiescence to activation is a focal regulatory point for neural regeneration and dysregulations in the transition lead to brain disorders.1,2 During this transition,both cell cycle states and metabolism including mitochondria undergo extensive reprogramming.A deep understanding of such comprehensive changes is a prerequisite for a holistic picture of physiology and may aid disease combats.

First-principles study on the electronic,elastic and thermodynamic properties of three novel germanium nitrides

The ultrasoft pseudo-potential plane wave method combined with the quasi-harmonic approach have been used to study the electronic, elastic and thermodynamic properties of the tetragonal, monoclinic and or- thorhombic Ge3N4. The negative formation enthalpies, the satisfactory of Born＇s criteria and the linear variations of elastic constants with pressure indicate that the three polymorphs can retain their stabilities in the pressure range of 0-25 GPa. The three GeaN4 are brittle solids at 0 GPa, while they behave in ductile manners in the pressure range of 5-25 GPa. t- and o-GeaN4 are hard materials but anisotropic, m-Ge3N4 has the largest ductility among the three phases. The results reveal that m-Ge3N4 belongs to an indirect band gap semiconductor, while t- and o-Ge3N4 have direct band gaps. For the thermal properties, several interesting features can be observed above 300 K. o-GeaN4 exhibits the largest heat capacity, while m-Ge3N4 shows the highest Debye temperature. The results predicted in this work can provide reference data for future experiments.

Singularity of the Extremal Solution for Supercritical Biharmonic Equations with Power-Type Nonlinearity

Let B R^n be the unit ball centered at the origin. The authors consider the following biharmonic equation:{?~2u = λ(1 + u)~p in B,u =?u/?ν= 0 on ?B, where p >n+4/ n-4and ν is the outward unit normal vector. It is well-known that there exists a λ*> 0 such that the biharmonic equation has a solution for λ∈ (0, λ*) and has a unique weak solution u*with parameter λ = λ*, called the extremal solution. It is proved that u* is singular when n ≥ 13 for p large enough and satisfies u*≤ r^(-4/ (p-1)) - 1 on the unit ball, which actually solve a part of the open problem left in [D`avila, J., Flores, I., Guerra, I., Multiplicity of solutions for a fourth order equation with power-type nonlinearity, Math. Ann., 348(1), 2009, 143–193] .