一类Schrdinger-Virasoro型李代数的量子化

李双代数的量子化是获取新的量子群的重要方法.本文通过Drinfel'd扭元,对一类Schr(o|¨)dinger-Virasoro型李代数进行了量子化,得到了一类既非交换又非余交换的Hopf代数.     

一个导子李代数的二阶上同调群

Gelfand和Fuks曾计算过圆上向量场李代数的上同调。作者计算了微分算子代数上的2-上循环。本文的目的是计算多元Laurent多项式环上的导子李代数上的二阶上同调群,把[1]的讨论推广到多元的情形。 设C[t_1,t_2,t_1~(-1),t_2~(-1)]是复数域C上的二元Laurent多项式环[t_1,t_2,t_1~(-1),t_2~(-1)]是C[t_1,t_2,t_1~(-1),t_2~(-1)]上的导子作成的李代数,其中,·有基{t_1~ml+~1t_2~m2D_1,t_1~mlt_心~m2~(+1) D_2|m_1,m_2∈Z)。     

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.     

Schrdinger-Virasoro变形代数的二上循环

Henkel,Roger和Unterberger在一系列文章中对Sschrdinger-Virasoro代数及其变形代数做过介绍和研究.本文主要研究了(原)Schrdinger—Virasoro变形代数的二上循环.     

广义扩张的Schr?dinger-Virasoro代数的二上同调群

假设F是特征为0的域,Γ是F上的一个加法子群,域F上的元s满足s?Γ但2s∈Γ.我们定义了一类无限维李代数W[Γ,s],称之为广义扩张的Schr?dinger-Virasoro代数.本文确定了W[Γ,s]上的所有二上同调群.     

Hom-李代数的广义导子

给出Hom-李代数L的广义导子代数、拟导子代数和中心导子代数的一些基本性质.进一步地,有GDer(L)=QDer(L)+QC(L).同时,得到QDer(L)可以嵌入并成为一个更大的Hom-李代数的导子.     

非线性Schr\"{o}dinger 方程解的整体存在和爆破的门槛结果

研究了非线性 Schr\"{o}dinger 方程的柯西问题. 通过引进位势井及其外部集合, 得到了解的整体存在性和爆破的门槛结果.     

filiform李代数R_n的triple导子

对filiform李代数R_n的triple导子进行了研究.利用triple导子的定义,通过计算线性变换在一组特殊的基上的作用结果,得到了filiform李代数R_n的triple导子的矩阵形式,并发现其triple导子代数是一个维数为2n-1的可解李代数.     

扭Schr?dinger-Virasoro代数的Poisson结构

扭Schr?dinger-Virasoro代数的结构理论和表示理论密切相关.通过确定扭Schr?dinger-Virasoro代数的Poisson结构,使得扭Schr?dinger-Virasoro代数不仅具有李代数结构且兼有代数乘法结构,为继续研究其性质提供更多思路.     

有限维单李代数的2-局部导子

设F是特征为零的代数封闭域,g为F上有限维单李代数.g上的一个映射φ称为2-局部导子,如果对任意的x,y∈g,存在导子D_(x,y):g→g,使φ(x)=D_(x,y)(x),φ(y)=D_(x,y)(y).本文证明g上的所有2-局部导子一定是内导子.     

n-Derivations of the Extended Schr(o)dinger-Virasoro Lie Algebra

Let (sb～) be the extended Schr(o)dinger-Virasoro Lie algebra and n ≥ 1 an integer.A map f: (sb～)n =(sb～) × (sb～) × … × (sb～) → (sb～) is called an n-derivation if it is a derivation inone variable while other variables fixed.We investigate n-derivations of the extendedSchr(o)dinger-Virasoro Lie algebra (sb～).The main result when n =2 is then applied tocharacterize the linear commuting maps and the commutative post-Lie algebra structureson (sb～).     

幂零李群上的薛定谔算子的加权估计

In this paper we consider the SchrSdinger operator -△G ＋ W on the nilpotent Lie group G where the nonnegative potential W belongs to the reverse H51der class Bq1 for some q1 ≥ D and D is the dimension at infinity of G. The weighted L^p -L6q estimates for the operators W^a（-△G ＋ W）^-β and W^a△G（-△G ＋ W）^-β are obtained.     

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.     

The new exact solutions of variant types of time fractional coupled Schr\"{o}dinger equations in plasma physics

In the present article, the new exact solutions of fractional coupled Schr\"{o}dinger type equations have been studied by using a new reliable analytical method. We applied a relatively new method for finding some new exact solutions of time fractional coupled equations viz. time fractional coupled Schr\"{o}dinger--KdV and coupled Schr\"{o}dinger--Boussinesq equations. The fractional complex transform have been used here along with the property of local fractional calculus for reduction of fractional partial differential equations (FPDE) to ordinary differential equations (ODE). The obtained results have been plotted here for demonstrating the nature of the solutions.     

Local exact controllability of Schr\"{o}dinger equation with Sturm- Liouville boundary value problems

In this paper, we investigate the controllability of 1D bilinear Schr\"{o}dinger equation with Sturm-Liouville boundary value condition. The system represents a quantumn particle controlled by an electric field. K. Beauchard and C. Laurent have proved local controllability of 1D bilinear Schr\"{o}dinger equation with Dirichlet boundary value condition in some suitable Sobolev space based on the classical inverse mapping theorem. Using a similar method, we extend this result to Sturm-Liouville boundary value proplems.     

$C_3$型的退化Ringel-Hall代数的Gr\"{o}bner-Shirshov基

The Gr?bner-Shirshov basis of the degenerate Ringel-Hall Algebras of type C₃ is obtained by studying the generic extension monoid algebra.     

On the Growth Properties of Solutions for a Generalized Bi-Axially Symmetric Schr\"{o}dinger Equation

In this paper, we have considered the generalized bi-axially symmetric Schr\"{o}dinger equation $$\frac{\partial^2\varphi}{\partial x^2}+\frac{\partial^2\varphi}{\partial y^2} + \frac{2\nu} {x}\frac{\partial \varphi} {\partial x} + \frac{2\mu} {y}\frac{\partial \varphi} {\partial y} + \{K^2-V(r)\} \varphi=0,$$ where $\mu,\nu\ge 0$, and $rV(r)$ is an entire function of $r=+(x^2+y^2)^{1/2}$ corresponding to a scattering potential $V(r)$. Growth parameters of entire function solutions in terms of their expansion coefficients, which are analogous to the formulas for order and type occurring in classical function theory, have been obtained. Our results are applicable for the scattering of particles in quantum mechanics.     

First Cohomology Group from the Virasoro-Like Algebra to its Larsson Functor Module

Let 𝒲 be the Virasoro-like algebra, and d ₁, d ₂ be the degree derivations of 𝒲. Set ? = W⊕C d ₁⊕C d ₂. Let F ^α(V) be the ?-module defined by Larsson's functor applied to a finite dimensional sl ₂-module V. In this article, the derivations from ? to ?-modules F ^α(V) and the first cohomology group H ¹(?, F ^α(V)) are given.     

广义映射Schr?dinger-Virasoro代数的二上同调群

该文给出了广义映射Schr?dinger-Virasoro代数的所有二上同调群,并且给出了这类李代数的所有泛中心扩张.