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本文首次定义了方阵与多维数组的一种乘法，进而将定义于规则区域内的多维离散Poisson方程转变成一种包含一系列小矩阵的矩阵―数组方程的形式。由数学归纳法证明，该矩阵―数组方程可以利用Kronecker和转变成常见的线性代数方程组的形式，即AX=b。提出并证明一个定理：矩阵A的特征值及相应的特征向量可以直接通过包含于矩阵―数组方程中的那些小矩阵的特征值及相应的特征向量计算得到。根据这一定理，给出了矩...
Poisson-Furstenberg boundary and growth of groups
Poisson-Furstenberg boundary Group Theory
2011/9/22
Abstract: We study the Poisson-Furstenberg boundary of random walks on permutational wreath products. We give a sufficient condition for a group to admit a symmetric measure of finite first moment wit...
Calabi-Yau algebras viewed as deformations of Poisson algebras
Koszul algebras Calabi-Yau algebras Poisson algebras deformations of algebras Poisson homology Hochschild homology
2011/9/19
Abstract: We define a family of 3-Calabi-Yau algebras by potentials. For some of these algebras, we explicitly compute the Hochschild homology with the help of Poisson homology. The point is that the ...
Poisson Ideals in Cluster Algebras and the Spectra of Quantized Coordinate Rings
Poisson Ideals Cluster Algebras the Spectra of Quantized Coordinate Rings Quantum Algebra
2011/9/6
Abstract: We describe the Poisson ideals and attached symplectic geometry of a cluster algebra with compatible Poisson structure. We apply these results to determine the spectrum of a quantum cluster ...
Quantized Nambu-Poisson Manifolds in a 3-Lie Algebra Reduced Model
Quantized Nambu-Poisson Manifolds 3-Lie Algebra Reduced Model
2011/3/2
We consider dimensional reduction of the Bagger-Lambert-Gustavsson theory to a zero-dimensional 3-Lie algebra model and construct various stable solutions corresponding to quantized Nambu-Poisson mani...
Homogenization of the Vlasov Equation and of the Vlasov - Poisson System with a Strong External Magnetic Field
the Vlasov Equation the Vlasov - Poisson System
2010/11/23
Motivated by the difficulty arising in the numerical simulation of the movement of charged particles in presence of a large external magnetic field, which adds an additional time scale and thus impos...
Quantization of Poisson algebras associated to Lie algebroids
Quantization Poisson algebras Lie algebroids
2010/11/1
We prove the existence of a strict deformation quantization for the canonical Poisson structure on the dual of an integrable Lie algebroid. It follows that any Lie groupoid C*-algebra may be regarded...
Adaptive Finite Element Modeling Techniques for the Poisson-Boltzmann Equation
Poisson-Boltzmann equation semi-linear partial differential equations
2010/12/14
We consider the design of an effective and reliable adaptive finite element method (AFEM) for the nonlinear Poisson-Boltzmann equation (PBE).We first examine the two-term regularization technique for ...
This paper investigates the Poisson geometry associate to a cluster algebra over the complex numbers, and its relationship to compatible torus actions.
Poisson 方程的一个降维算法
2007/8/7
Lions 建立在变分形式中的渐近展开方法,用于解决 Stiff 问题是很有力的工具.Ciarlet 利用[1]的方法,研究弹性薄板问题,对薄板不做任何假设,仅用严格的数学推理,证明了简化的二维模型是三维薄板模型的一阶近似.利用算子和边界条件,同时进行ε幂级数的渐近展开,研究在定义域 D={(x,y)|(x,y)∈R~2,x∈(0,1),y∈(0,ε)}(即细杆)上的抛物型问题.本文第一部分,利用...