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...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.展开更多
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.
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...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.展开更多
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 ...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.展开更多
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 chaxacterize...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.展开更多
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-...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.展开更多
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 Dur...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.展开更多
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 ...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.展开更多
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 ...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] .展开更多
基金Foundation item: Supported by the National Natural Science Foundation of China(10647112)
文摘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.
基金Supported by the Natural Science Foundation of Zhumadian, Henan, China(11704)Supported by the National Natural Science Foundation of Shandong Province(60973042)Supported by the Natural Science Foundation of Shandong Province(Y2008F61, Y2008G20)
文摘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.
基金Project of Young Teachers’Research Fund of Xinyang College of Agriculture and Forestry(Project number:QN2021014)。
文摘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.
基金supported by the Collaborative Innovation Center on Beijing Society-building and Social GovernanceNSFC(11371042)+2 种基金BNSF(1132006)the key fund of the Beijing education committee of ChinaChina Postdoctoral Science Foundation funded project
文摘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.
基金Supported by the Natural Science Foundation of Ningxia Province(NZ0691)
文摘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.
基金Supported by the Foundation Project of Doctor Graduate Student Innovation of Beijing University of Technology(ykj-2012-6724)Supported by the NSFC(10771009)Supported by the BSF(1082001)
文摘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.
基金This work was supported by funds from the National Key R&D Program of China(2019YFA0110300,2017YFA0104100)Shanghai Easter Scholar(8101219003)to Z.L.G.+2 种基金the National Natural Science Foundation of China(31600819 to C.H.C.,81773302 to Y.T.F.,31571058 and 32070862 to Z.L.G.,31701282 to M.J.,and 81901031 to X.X.H.)Shanghai Municipal Planning Commission of science and Research Fund(20174Y0216)to C.C.H.the Natural Science Foundation of Shanghai(19ZR1445400)to X.X.H.
文摘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.
基金Project supported by the National Natural Science Foundation of China(Nos.61475132,11475143,61501392,11304141)the National Training Programs of Innovation and Entrepreneurship for Undergraduates(No.201510477001)
文摘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.
基金supported by the National Natural Science Foundation of China(Nos.11201119,11471099)the International Cultivation of Henan Advanced Talents and the Research Foundation of Henan University(No.yqpy20140043)
文摘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] .