The particle is not the continuous but fractal medium.It has a diverse scale from several to angstroms.Through different density function of the particle system,mutual influences among factors can be get;especially in...The particle is not the continuous but fractal medium.It has a diverse scale from several to angstroms.Through different density function of the particle system,mutual influences among factors can be get;especially in the micro aspect,fractal dimension of particle radius distribution influences the system and has a significance to denote the fluidity of the particle.The influences among the particle size,spatial coordinates,density(or concentration)and time are analyzed theoretically and numerically.According to first-grade reaction diffusion model of fractal medium DLK model,the movement of the Brown particle and thermodynamics theory of mechanics can be popularized to the storm current field and getsΓ(t)-D model.展开更多
We investigate rigidity problems for odd-dimensional compact submanifolds.We show that if Mn（n 5） is an odd-dimensional compact submanifold with parallel mean curvature in Sn＋p,and if RicM ＆gt;（n- 2-1n）（1 ＋ H2...We investigate rigidity problems for odd-dimensional compact submanifolds.We show that if Mn（n 5） is an odd-dimensional compact submanifold with parallel mean curvature in Sn＋p,and if RicM ＆gt;（n- 2-1n）（1 ＋ H2） and H ＆lt; δn,where δn is an explicit positive constant depending only on n,then M is a totally umbilical sphere.Here H is the mean curvature of M.Moreover,we prove that if Mn（n 5） is an odd-dimensional compact submanifold in the space form Fn＋p（c） with c 0,and if RicM ＆gt;（n-2-εn）（c＋H2）,where εn is an explicit positive constant depending only on n,then M is homeomorphic to a sphere.展开更多
文摘The particle is not the continuous but fractal medium.It has a diverse scale from several to angstroms.Through different density function of the particle system,mutual influences among factors can be get;especially in the micro aspect,fractal dimension of particle radius distribution influences the system and has a significance to denote the fluidity of the particle.The influences among the particle size,spatial coordinates,density(or concentration)and time are analyzed theoretically and numerically.According to first-grade reaction diffusion model of fractal medium DLK model,the movement of the Brown particle and thermodynamics theory of mechanics can be popularized to the storm current field and getsΓ(t)-D model.
基金supported by National Natural Science Foundation of China (Grant Nos.11071211,11371315 and 11301476)the Trans-Century Training Programme Foundation for Talents by the Ministry of Education of Chinathe China Postdoctoral Science Foundation (Grant No.2012M521156)
文摘We investigate rigidity problems for odd-dimensional compact submanifolds.We show that if Mn（n 5） is an odd-dimensional compact submanifold with parallel mean curvature in Sn＋p,and if RicM ＆gt;（n- 2-1n）（1 ＋ H2） and H ＆lt; δn,where δn is an explicit positive constant depending only on n,then M is a totally umbilical sphere.Here H is the mean curvature of M.Moreover,we prove that if Mn（n 5） is an odd-dimensional compact submanifold in the space form Fn＋p（c） with c 0,and if RicM ＆gt;（n-2-εn）（c＋H2）,where εn is an explicit positive constant depending only on n,then M is homeomorphic to a sphere.
