全连续算子的歧点

本文得到全连续算子和锥映象的新的歧点和渐近歧点定理,并指出它们的固有值的某种全局特征．     

伪单调映射的拓扑度及应用

利用S+型映射的拓扑度,导出了伪单调映射紧扰动的拓扑度,并讨论了该拓扑度对算子值域的应用．     

Quantum Weak Invariants: Dynamical Evolution of Fluctuations and Correlations

Weak invariants are time-dependent observables with conserved expectation values. Their fluctuations, however, do not remain constant in time. On the assumption that time evolution of the state of an open quantum system is given in terms of a completely positive map, the fluctuations monotonically grow even if the map is not unital, in contrast to the fact that monotonic increases of both the von Neumann entropy and Rényi entropy require the map to be unital. In this way, the weak invariants describe temporal asymmetry in a manner different from the entropies. A formula is presented for time evolution of the covariance matrix associated with the weak invariants in cases where the system density matrix obeys the Gorini–Kossakowski–Lindblad–Sudarshan equation.     

Identification of nonlinear dynamical system equations using dynamic mode decomposition under invariant quantity constraints

In this paper, an algorithm for identifying equations representing a continuous nonlinear dynamical system from a noise-free state and time-derivative state measurements is proposed. It is based on a variant of the extended dynamic mode decomposition. A particular attention is paid to guarantee that the physical invariant quantities stay constant along the integral curves. The numerical methodology is validated on a two-dimensional Lotka–Volterra system. For this case, the differential equations are perfectly retrieved from data measurements. Perspectives of extension to more complex systems are discussed.     

基于物理统一存储大规模数字导航地图道路网拓扑自动生成算法

道路网络的拓扑信息是GIS进行空间分析,如最优路径、地图匹配等算法的数据基础。目前,获取和建立道路网络的拓扑信息非常繁琐,不仅费时、费力,并且容易出错。采用逻辑分幅物理统一的存储策略,在探讨了拓扑生成的一般算法的前提下,提出了大规模超大规模数字地图自动生成道路网络拓扑关系的步骤和算法。该算法采用网格索引检索每个子图的元素,用hash索引映射实体ID和实体对象信息,并将整图的拓扑信息生成转化为对每个子图的拓扑求取,并对跨子图道路拓扑求解特别讨论。然后,对算法复杂度进行了分析,并且通过建立不同道路数的多个虚拟道路网络子图对算法性能进行了测试和比较。最后用本算法跟踪处理了南京市道路网络（部分）,并给出了结果。本算法在保留地理数据完整性的前提下,解决了常规方法的内存限制,并且具有准线性的运算代价,并能够自动恢复数据处理。     

关于向量集值优化的Benson真有效性

对广义锥次数凸向量集值优化问题Benson真有效性解的标量化问题进行了研究,借助于一种新的择一性定理建立了广义锥次类凸向是集值优化问题Benson真有效解的Lagrange乘子型定理并讨论了乘子型对偶问题。     

集值映射向量优化问题的ε-真有效解

本文讨论集值映射向量优化问题的ε-真有效解。在集值映射为广义锥-次类凸的假设下,建立了这种解的标量化定理,ε-Lagrange乘子定理,ε-真鞍点定理和ε-真对偶性定理。     

An obstruction to quantizing compact symplectic manifolds

We prove that there are no nontrivial finite-dimensional Lie representations of certain Poisson algebras of polynomials on a compact symplectic manifold. This result is used to establish the existence of a universal obstruction to quantizing a compact symplectic manifold, regardless of the dimensionality of the representation.

     

Modeling Relationships among Multiple Graphical Structures

Many researchers have investigated the social and cognitive processes underlying organizational behavior, with particular interest in understanding the interaction between the social and cognitive dimensions. Because of the widespread use of graphs as models of social and cognitive structures, these studies frequently encounter the problem of analyzing collections of graphical structures. Such analyses have used a variety of approaches to address specific aspects of such structures. However, no single unified approach has emerged that supports the several different types of analyses required. The purpose of this paper is to define such an approach, based on a mathematical model for capturing the relationships among multiple graphs, and to demonstrate its application to the investigation of social and cognitive structures in organizations.     

Normal Forms of Symplectic Matrices

Abstract In this paper, we prove that for every symplectic matrix M possessing eigenvalues on the unit circle, there exists a symplectic matrix P such that P ⁻¹ MP is a symplectic matrix of the normal forms defined in this paper. Partially supported by the NSF, MCSEC of China, and the Qiu Shi Sci. Tech. Foundation * Associate Member of the ICTP