设L=S(m;n)是定义在特征p>3的代数闭合域F上的阶化特殊型李代数,利用已研究L的不可约表示的方法,通过定义L的如下阶化:限制情形定义L=(?)L_([q],I),非限制情形定义L=(?)L_([q],I),这里L是L的本原p-包络,有表达式L=L (?) sum from i=1...设L=S(m;n)是定义在特征p>3的代数闭合域F上的阶化特殊型李代数,利用已研究L的不可约表示的方法,通过定义L的如下阶化:限制情形定义L=(?)L_([q],I),非限制情形定义L=(?)L_([q],I),这里L是L的本原p-包络,有表达式L=L (?) sum from i=1 to m sum from (d_i=1)to (n_i-1) FD_i^(P^(d_i)),而I是{1、2,…,m}的子集,得到当p-特征标χ是正则半单时,在限制李代数情形所有不可约L_χ(L)-模都是从不可约U_χ(L_([0],I))-模诱导的;在非限制的情形,所有不可约U_(?)(U_(p^s)(L,χ))-模都是从不可约U_(?)(L_([0],I))-模诱导的,这里(?)是χ到L~*上的平凡扩张.展开更多
In this study,on the basis of absolute first-arrival times of 84756 P-and S-waves from 6085 earthquakes recorded at 56 fixed stations in Yibin and surrounding areas in China from January 2009 to January 2019,focal par...In this study,on the basis of absolute first-arrival times of 84756 P-and S-waves from 6085 earthquakes recorded at 56 fixed stations in Yibin and surrounding areas in China from January 2009 to January 2019,focal parameters and three-dimensional(3 D)body-wave high-resolution velocity structures at depths of 0–30 km were retrieved by double-difference tomography.Results show that there is a good correspondence between the spatial distribution of the relocated earthquakes and velocity structures,which were concentrated mainly in the high-velocity-anomaly region or edge of high-velocity region.Velocity structure of P-and S-waves in the Yibin area clearly shows lateral inhomogeneity.The distribution characteristics of the P-and S-waves near the surface are closely related to the geomorphology and geologic structure.The low-velocity anomaly appears at the depth of 15–25 km,which is affected by the lower crust current.The Junlian–Gongxian and Gongxian–Changning earthquake areas,which are the two most earthquake-prone areas in the Yibin region,clearly differ in earthquake distribution and tectonic characteristics.We analyzed the structural characteristics of the Junlian–Gongxian and Gongxian–Changning earthquake areas on the basis of the 3 D bodywave velocity structures in the Yibin region.We found that although most seismicity in the Yibin area is caused by fluid injection,the spatial position of seismicity is controlled by the velocity structures of the middle and upper crust and local geologic structure.Fine-scale 3 D velocity structures in the Yibin area provide important local reference information for further understanding the crustal medium,seismogenic structure,and seismicity.展开更多
We first use the Schwarz rearrangement to solve a minimization problem on eigenvalues of the one-dimensional p-Laplacian with integrable potentials. Then we construct an optimal class of non-degenerate potentials for ...We first use the Schwarz rearrangement to solve a minimization problem on eigenvalues of the one-dimensional p-Laplacian with integrable potentials. Then we construct an optimal class of non-degenerate potentials for the one-dimensional p-Laplacian with the Dirichlet boundary condition. Such a class of nondegenerate potentials is a generalization of many known classes of non-degenerate potentials and will be useful in many problems of nonlinear differential equations.展开更多
This paper proves that the first eigenfunctions of the Finsler p-Lapalcian are C^(1,α). Using a gradient comparison theorem and one-dimensional model, we obtain the sharp lower bound of the first Neumann and closed e...This paper proves that the first eigenfunctions of the Finsler p-Lapalcian are C^(1,α). Using a gradient comparison theorem and one-dimensional model, we obtain the sharp lower bound of the first Neumann and closed eigenvalue of the p-Laplacian on a compact Finsler manifold with nonnegative weighted Ricci curvature,on which a lower bound of the first Dirichlet eigenvalue of the p-Laplacian is also obtained.展开更多
文摘设L=S(m;n)是定义在特征p>3的代数闭合域F上的阶化特殊型李代数,利用已研究L的不可约表示的方法,通过定义L的如下阶化:限制情形定义L=(?)L_([q],I),非限制情形定义L=(?)L_([q],I),这里L是L的本原p-包络,有表达式L=L (?) sum from i=1 to m sum from (d_i=1)to (n_i-1) FD_i^(P^(d_i)),而I是{1、2,…,m}的子集,得到当p-特征标χ是正则半单时,在限制李代数情形所有不可约L_χ(L)-模都是从不可约U_χ(L_([0],I))-模诱导的;在非限制的情形,所有不可约U_(?)(U_(p^s)(L,χ))-模都是从不可约U_(?)(L_([0],I))-模诱导的,这里(?)是χ到L~*上的平凡扩张.
基金supported by the Research Project of Tianjin Earthquake Agency(No.yb201901)Seismic Regime Tracking Project of CEA(No.2019010127)Combination Project with Monitoring,Prediction and Scientific Research of Earthquake Technology,CEA(No.3JH-201901006)
文摘In this study,on the basis of absolute first-arrival times of 84756 P-and S-waves from 6085 earthquakes recorded at 56 fixed stations in Yibin and surrounding areas in China from January 2009 to January 2019,focal parameters and three-dimensional(3 D)body-wave high-resolution velocity structures at depths of 0–30 km were retrieved by double-difference tomography.Results show that there is a good correspondence between the spatial distribution of the relocated earthquakes and velocity structures,which were concentrated mainly in the high-velocity-anomaly region or edge of high-velocity region.Velocity structure of P-and S-waves in the Yibin area clearly shows lateral inhomogeneity.The distribution characteristics of the P-and S-waves near the surface are closely related to the geomorphology and geologic structure.The low-velocity anomaly appears at the depth of 15–25 km,which is affected by the lower crust current.The Junlian–Gongxian and Gongxian–Changning earthquake areas,which are the two most earthquake-prone areas in the Yibin region,clearly differ in earthquake distribution and tectonic characteristics.We analyzed the structural characteristics of the Junlian–Gongxian and Gongxian–Changning earthquake areas on the basis of the 3 D bodywave velocity structures in the Yibin region.We found that although most seismicity in the Yibin area is caused by fluid injection,the spatial position of seismicity is controlled by the velocity structures of the middle and upper crust and local geologic structure.Fine-scale 3 D velocity structures in the Yibin area provide important local reference information for further understanding the crustal medium,seismogenic structure,and seismicity.
基金supported by National Natural Science Foundation of China(Grant Nos.11231001 and 11371213)the Programme of Introducing Talents of Discipline to Universities of China(Grant No.111-2-01)
文摘We first use the Schwarz rearrangement to solve a minimization problem on eigenvalues of the one-dimensional p-Laplacian with integrable potentials. Then we construct an optimal class of non-degenerate potentials for the one-dimensional p-Laplacian with the Dirichlet boundary condition. Such a class of nondegenerate potentials is a generalization of many known classes of non-degenerate potentials and will be useful in many problems of nonlinear differential equations.
基金supported by National Natural Science Foundation of China (Grant No. 11471246)Natural Science Foundation of Higher Education in Anhui Province (Grant No. KJ2014A257)
文摘This paper proves that the first eigenfunctions of the Finsler p-Lapalcian are C^(1,α). Using a gradient comparison theorem and one-dimensional model, we obtain the sharp lower bound of the first Neumann and closed eigenvalue of the p-Laplacian on a compact Finsler manifold with nonnegative weighted Ricci curvature,on which a lower bound of the first Dirichlet eigenvalue of the p-Laplacian is also obtained.
