辛代数的极大幂零子代数的保李括积零的线性映射

Let F be a field with char F = 2, l a maximal nilpotent subalgebra of the symplectic algebra sp（2m,F）. In this paper, we characterize linear maps of l which preserve zero Lie brackets in both directions. It is shown that for m ≥ 4, a map φ of l preserves zero Lie brackets in both directions if and only if φ = ψcσT0λαφdηf, where ψc,σT0,λα,φd,ηf are the standard maps preserving zero Lie brackets in both directions.     

以幂零李代数R_n为幂零根基的可解李代数(英文)

In this paper we explicitly determine automorphism group of filiform Lie algebra Rn to find the indecomposable solvable Lie algebras with filiform Lie algebra Rn nilradicals.We also prove that the indecomposable solvable Lie algebras with filiform Rn nilradicals is complete.     

海森堡群上薛定谔算子的黎斯位势的某些性质

设L=-△_(H~n)+V是Heisenberg群H~n上的Schr(o|¨)dinger算子,其中△_(H~n)为H~n上的次Laplacian,V≠0为满足逆H(o|¨)lder不等式的非负函数.本文研究H~n上Riesz位势I_α~L=L~(-α/2)在Campanato型空间A_L~β和Hardy型空间H_L~p上的某些性质.     

多元盘Bergman空间上可逆的Toeplitz算子乘积

We prove a reverse Hlder inequality by using the cartesian product of dyadic rectangles and the dyadic cartesian product maximal function on Bergman space of polydisk.Next,we further describe when for which square integrable analytic functions f and g on the polydisk the densely defined products Tf Tg are bounded invertible Toeplitz operators.     

由Schr?dinger算子定义的Riesz变换的Lp估计

本文主要讨论了当非负位势 V(x)属于某逆Holder类时,由一致椭圆算子L=-div(A(x))+V(x)所定义的 Riesz变换在 L^p空间的有界性。     

幂零李群上半空间内的加权Poincaré不等式

该文在幂零李群上半空间内建立了一类加权的Poincaré不等式.并且证明了所得的常数是最佳的.     

高阶Schrdinger方程的加权估计

本文主要研究的是相函数为齐次椭圆多项式的自由高阶 Schrdinger 方程．通过相函数等值面的几何性质,得到了解算子的 Strichartz 加权估计和极大算子加权估计．     

二步幂零李群上一类左不变微分算子亚椭圆的充要条件

本文我们用幂零李群表示的方法给出了二步幂零李群上一类左不变微分算子是亚椭圆的充要条件。     

二步幂零李群上—类左不变微分算子亚椭圆的充要条件

本文我们用幂零李群表示的方法,给出了二步幂零李群上一类左不变微分算子是亚椭圆的充要条件．     

广义扭Schr\"{o}dinger-Virasoro李代数的导子和2-上同调

通过计算,得到了广义扭Schr\"{o}dinger-Virasoro李代数的导子代数和2-上同调群.     

强耗散KDV型方程的指数吸引子

In this paper,we consider the strong dissipative KDV type equation on an unbounded domain R1.By applying the theory of decomposing operator and the method of constructing some compact operator in weighted space,the existence of exponential attractor in phase space H2（R1） is obtained.     

稳态Schr\"{o}dinger方程解的Liouville型定理

给出了锥中稳态Schr\"{o}dinger方程解的Liouville型定理, 推广了邓冠铁在半空间中关于拉普拉斯方程解的相关结论.     

关于薛定谔算子的极点散射: 基于狄利克雷级数的视角

本文讨论了在实轴上具有紧支集的势的薛定谔算子的极点散射问题. 本文旨在将狄利克雷级数理论与散射理论相结合, 文中运用了Littlewood的经典方法得到关于极点个数的新的估计. 本文首次将狄利克雷级数方法用于极点估计, 由此得到了极点个数的上界与下界, 这些结果改进和推广了该论题的一些相关结论.     

Strichartz Estimates for Schr(o)dinger Equations with Non-degenerate Coefficients

In the present paper, the full range Strichartz estimates for homogeneous Schr(o)dinger equations with non-degenerate and non-smooth coefficients are proved. For inhomogeneous equation, the non-endpoint Strichartz estimates are also obtained.     

一类带调和势的耗散非线性Schr\"{o}dinger方程的全局和爆破性质

针对一类带调和势的耗散非线性Schr\"{o}dinger方程,本文运用一些不等式和先验估计方法研究了其解的行为特征.     

抛物型薛定谔方程的最优正则性估计(英文)

本文通过特征化抛物型薛定谔算子t-Δ+V的域,探讨了抛物型薛定谔方程u/t-Δu+Vu=f在Orlicz空间中的最优正则性估计,并且对空间的维数没有限制.     

Divergent Solution to the Nonlinear Schr\"{o}dinger Equation with the Combined Power-Type Nonlinearities

In this paper, we consider the Cauchy problem for the nonlinear Schr\"{o}dinger equation with combined power-type nonlinearities, which is mass-critical/supercr-itical, and energy-subcritical. Combing Du, Wu and Zhang'' argument with the variational method, we prove that if the energy of the initial data is negative (or under some more general condition), then the $H^1$-norm of the solution to the Cauchy problem will go to infinity in some finite time or infinite time.