A conformal group approach to the Dirac–Kähler system on the lattice

Starting from the representation of the (n  ? 1) + n  ? dimensional Lorentz pseudo‐sphere on the projective space , we propose a method to derive a class of solutions underlying to a Dirac–Kähler type equation on the lattice. We make use of the Cayley transform to show that the resulting group representation arises from the same mathematical framework as the conformal group representation in terms of the general linear group . That allows us to describe such class of solutions as a commutative n  ? ary product, involving the quasi‐monomials ) with membership in the paravector space . Copyright © 2016 John Wiley & Sons, Ltd.     

Quasi-Whittaker modules over the conformal Galilei algebras

In this paper, we study quasi-Whittaker modules over the conformal Galilei algebras. We determine all quasi-Whittaker vectors and the simplicities of the universal quasi-Whittaker modules. For the reducible ones, we determine the corresponding simple quotient modules. Thus we classify all simple quasi-Whittaker modules for the conformal Galilei algebras.     

非交换傅立叶变换

这是最近子因子和局部紧量子群上的非交换傅立叶变换的一系列工作的综述.简要地介绍子因子和局部紧量子群的定义及其性质,给出了Hausdorff-Young不等式,Young不等式,不确定原理,合集估计以及它们的等号成立条件.     

On the second cohomology of nilpotent orbits in exceptional Lie algebras

In [1], the second de Rham cohomology groups of nilpotent orbits in all the complex simple Lie algebras are described. In this paper we consider non-compact non-complex exceptional Lie algebras, and compute the dimensions of the second cohomology groups for most of the nilpotent orbits. For the rest of cases of nilpotent orbits, which are not covered in the above computations, we obtain upper bounds for the dimensions of the second cohomology groups.     

Super-biderivations of Lie superalgebras

In this paper, we attempt to investigate the super-biderivations of Lie superalgebras. Furthermore, we prove that all super-biderivations on the centerless super-Virasoro algebras are inner super-biderivations. Finally, we study the linear super commuting maps on the centerless super-Virasoro algebras.     

三角代数上的交换零点ξ-Lie可导映射

设u是数域F上的一个三角代数,δ是u上的一个线性映射,ξ∈F且ξ≠1证明了:如果对任意的x,y∈u且xy=yx=0有δ([x,y]_ξ)=[δ(x),y]_ξ+[x,δ(y)]_ξ,则在u上存在一个导子Φ和一个中心元λ使得对任意的x∈u,有δ(x)=Φ(x)+λx.     

Broer-Kaup-Kupershmidt族的非线性双可积耦合及其自相容源

基于新的非半单矩阵李代数,介绍了构造孤子族非线性双可积耦合的方法,由相应的变分恒等式给出了孤子族非线性双可积耦合的Hamilton结构.作为应用,给出了Broer-Kaup-Kupershmidt族的非线性双可积耦合及其Hamilton结构.最后指出了文献中的一些错误,利用源生成理论建立了新的公式,并导出了带自相容源Broer-Kaup-Kupershmidt族的非线性双可积耦合方程.     

基于轮换样本连续性调查的校准组合估计方法研究

校准估计是抽样调查中比较常用的一种利用辅助信息提高估计量精度的方法。回归组合估计量作为轮换样本连续性调查中使用的一种有效的估计量,是可以通过校准程序得到的。基于回归组合估计量和校准程序之间的关系,本文提出了轮换样本连续性抽样调查条件下的不同校准组合估计量及其方差估计。校准组合估计量的主要思想是在校准估计程序中将拼配样本和非拼配样本的辅助信息进行不同的组合利用。本文利用美国现时人口调查的微观数据进行数值模拟,来比较不同校准组合估计量的估计效率,模拟结果表明两步校准组合估计量和两步校准双组合估计量的表现相似,且估计精度都高于H-T估计量及回归组合估计量;而两步校准组合估计量由于其简便性更适合应用于实践中。最后以我国农村住户连续性抽样调查为例,设计一套符合我国实际的轮换样本连续性调查方案,并将提出的校准组合估计量运用于估计阶段,为中国政府统计调查提供一定的借鉴和参考.     

The polynomial representation of the type An−1 rational Cherednik algebra in characteristic p | n

We study the polynomial representation of the rational Cherednik algebra of type A_n?1 with generic parameter in characteristic p for p | n. We give explicit formulas for generators for the maximal proper graded submodule, show that they cut out a complete intersection, and thus compute the Hilbert series of the irreducible quotient. Our methods are motivated by taking characteristic p analogues of existing characteristic 0 results.