A KAM-type Theorem for Generalized Hamiltonian Systems

In this paper we mainly concern the persistence of invariant tori in generalized Hamiltonian systems. Here the generalized Hamiltonian systems refer to the systems which may admit a distinct number of action and angle variables. In particular, system under consideration can be odd dimensional. Under the Riissmann type non-degenerate condition, we proved that the majority of the lower-dimension invariant tori of the integrable systems in generalized Hamiltonian system are persistent under small perturbation. The surviving lower-dimensional tori might be elliptic, hyperbolic, or of mixed type.     

离散发热器件基于(火积)耗散率最小和最高温度最小的构形优化比较

建立了导热基座上圆柱体离散发热器件的三维湍流散热模型,基于构形理论,考虑空气变物性及可压缩性和黏性耗散,研究了器件材料的热导率、热源强度和流体流速对器件最高温度、基于(火积)耗散定义的当量热阻和平均Nu数的影响.结果表明:在总发热功率一定的条件下,以器件最高温度和当量热阻为性能指标进行热设计,均存在最优热源强度分布使得散热性能最优.当各热源强度相同且热源热导率小于基座热导率时,提高热源热导率可明显改善散热性能;将热源热导率沿流动方向从低到高布置可降低器件最高温度,而将热源热导率均匀布置可使当量热阻最小.所得结果可为实际热设计中不同材质和不同发热率的电子器件最优布置提供理论支撑.     

两电子体系自旋态本征值及本征函数的另类解法

运用矩阵直积算法求解两电子体系自旋态本征值及本征函数并对所得结果进行了讨论,与一般教材中已有结果取得了很好的一致性.     

An Integrable Symplectic Map Related to Discrete Nonlinear SchrSdinger Equation

The method of nonlinearization of spectral problem is developed and applied to the discrete nonlinear Schr6dinger （DNLS） equation which is a reduction of the Ablowitz-Ladik equation with a reality condition. A new integable symplectic map is obtained and its integrable properties such as the Lax representation, r-matrix, and invariants are established.     

A New Lie Algebra and Its Related Liouville Integrable Hierarchies

A new Lie algebra G and its two types of loop algebras G1 and G2 are constructed. Basing on G1 and G2, two different isospectral problems are designed, furthermore, two Liouville integrable soliton hierarchies are obtained respectively under the framework of zero curvature equation, which is derived from the compatibility of the isospectral problems expressed by Hirota operators. At the same time, we obtain the Hamiltonian structure of the first hierarchy and the bi-Hamiltonian structure of the second one with the help of the quadratic-form identity.     

Two Types of Expanding Lie Algebra and New Expanding Integrable Systems

From a new Lie algebra proposed by Zhang, two expanding Lie algebras and its corresponding loop algebras are obtained. Two expanding integrable systems are produced with the help of the generalized zero curvature equation. One of them has complex Hamiltion structure with the help of generalized Tu formula （GTM）.     

New Integrable Decomposition of Super AKNS Equation

In this paper, a new 7 ×7 matrix spectral problem, which is associated with the super AKNS equation is constructed. With the use of the binary nonlinearization method, a new integrable decomposition of the super AKNS equation is presented.     

Two Integrable Couplings of Modified Tu Hierarchy

Two different integrable couplings of the modified Tu hierarchy are obtained under the zero curvature equation by using two higher dimension Lie algebras. Furthermore, a complex Hamiltonian structures of the second integrable couplings is presented by taking use of the variational identity.     

基于改进的时空图卷积网络的交通流预测模型研究

智能交通系统(ITS)作为协调城市交通的核心正快速发展,而交通流量预测是智能交通系统的重要组成部分,被视为成功部署ITS的关键因素.由于交通网络的复杂空间拓扑结构,使交通流量表现出高阶非线性及动态时空复杂性.为更好地对交通网格数据进行预测,文章提出了一种新的时空网络模型DCSTGCN,具备以下特点:1)将切比雪夫多项式(Ch)应用于图卷积神经网络,结合自扩散卷积将传统的固定式交通拓扑结构进行转换,使其更具有随机性、动态性;2)加入空间Transformer模型,在考虑数据异质性问题的同时,利用多头自注意力机制考虑节点、本地邻居节点以及非本地节点的多属性问题,从高维的子空间进行考虑节点之间的隐藏特征信息;3)将时间Transformer与1×1的二维卷积神经网络(Conv2d)相结合,对交通流时间序列信息进行多重权重分配获取重要的时间特征,利用Conv2d网络进行预测输出.通过试验验证,表明该方法模型优于多种对比基线模型.