经典空间正则、李代数和二次变形的Newton方程

Twisted acceleration-enlarged Newton-Hooke Hopf algebras

Ten Abelian twist deformations of acceleration-enlarged Newton-Hooke Hopf algebra are considered. The corresponding quantum space-times are derived as well. It is demonstrate that their contraction limit $τ\to \infty$ leads to the new twisted acceleration-enlarged Galilei spaces.

Poisson quasi-Nijenhuis deformations of the canonical PN structure

We present a result which allows us to deform a Poisson-Nijenhuis manifold into a Poisson quasi-Nijenhuis manifold by means of a closed 2-form. Under an additional assumption, the deformed structure is also Poisson-Nijenhuis. We apply this result to show that the canonical Poisson-Nijenhuis structure on R^2n gives rise to both the Poisson-Nijenhuis structure of the open (or non periodic) n-particle Toda lattice, introduced by Das and Okubo [6], and the Poisson quasi-Nijenhuis structure of the closed (or periodic) n-particle Toda lattice, described in our recent work [7].

Almost Kahler模型的形变量子化与Lagrange-Finsler空间

Deformation Quantization of Almost Kahler Models and Lagrange-Finsler Spaces

Finsler和Lagrange空间可以等价地表示为几乎Kahler流形，该流形具有度量相容的典型区别联络结构，推广了Levi Civita联络。本文的目标是执行一个自然的Fedosov型变形量子化的几何形状。所有构造都是针对切丛上的正则拉格朗日函数和/或基本芬斯勒函数规范推导的。

Newton's Second Law in Field Theory

In this article we present a natural generalization of Newton's Second Law valid in field theory, i.e., when the parameterized curves are replaced by parameterized submanifolds of higher dimension. For it we introduce what we have called the geodesic $k$-vector field, analogous to the ordinary geodesic field and which describes the inertial motions (i.e., evolution in the absence of forces). From this generalized Newton's law, the corresponding Hamilton's canonical equations of field theory (Hamilton-De Donder-Weyl equations) are obtained by a simple procedure. It is shown that solutions of ge…

关于形变理论与图的同调

On deformation theory and graph homology

综述了结合代数特别是Poisson代数的形变理论。几乎收缩导致相应的Maurer-Cartan方程的正则解的作用被注意到。这个角色是让人想起同伦扰动引理，与无穷小变形上循环作为发起人。适用于星产品，我们展示了如何Moyal的公式可以得到使用这样一个几乎收缩和猜想，合并操作提供了一个规范的解决方案，至少在线性泊松结构的情况下。

Twisted acceleration-enlarged Newton-Hooke space-times and conservative force terms

There are analyzed two classical systems defined on twist-deformed acceleration-enlarged Newton-Hooke space-times - nonrelativistic particle moving in constant field force $\vec{F}$ and harmonic oscillator model. It is demonstrated that only in the case of canonical twist deformation the force terms generated by space-time noncommutativity remain conservative for both models.

New Periodic Solutions for Newtonian $n$-Body Problems with Dihedral Group Symmetry and Topological Constraints

In this paper, we prove the existence of a family of new non-collision periodic solutions for the classical Newtonian $n$-body problems. In our assumption, the $n=2l\geq4$ particles are invariant under the dihedral rotation group $D_l$ in $\mathbb{R}^3$ such that, at each instant, the $n$ particles form two twisted $l$-regular polygons. Our approach is variational minimizing method and we show that the minimizers are collision-free by level estimates and local deformations.

Some a priori estimates for a critical Schrodinger-Newton equation

Under natural energy and decay assumptions, we derive a priori estimates for solutions of a Schrodinger-Newton type of equation with critical exponent. On one hand, such an equation generalizes the traditional Schrodinger-Newton and Choquard equations, while, on the other hand, it is naturally related to problems involving scalar curvature and conformal deformation of metrics.