Martingale representation theorem for set-valued martingales

The present paper contains a martingale representation theorem for set-valued martingales defined on a filtered probability space with a filtration generated by a Brownian motion. It is proved that such type martingales can be defined by some generalized set-valued stochastic integrals with respect to a given Brownian motion. The main result of the paper is preceded by short part devoted to the definition and some properties of generalized set-valued stochastic integrals.     

凸度量空间非自混合映射的共同点定理

该文得到了凸度量空间上混合映射的共同点的一些结果.推广了Ciric在文献[3]中的结论.     

Banach空间一类Lipschitz映射不动点的迭代逼近

文章利用正规对偶映射的定义,给出了任意Banach空间Lipschitz强伪压缩映射不动点的Ishikawa迭代收敛定理．该定理不仅推广了已知结果,而且还简化了目前相应结果的证明．     

Mizoguchi–Takahashi’s type common fixed point theorem

Recently Kamran extended the result of Mizoguchi and Takahashi for closed multi-valued mappings and proved a fixed point theorem. In this paper we further extend the result concluded by Kamran and prove a common fixed point theorem by using the concept of lower semi-continuity.     

一类集值映射向量优化问题的ε-有效解

集值映射向量优化问题是最优化理论中的一个重要方向.在集值映射为生成锥内部-锥一类凸(简记为ic-锥类凸)的假设条件下,利用择一定理,给出了集值映射向量优化问题ε-弱有效解和ε-有效解的最优性条件和ε-Lagrange乘子定理,是弱有效解和有效解相应结果的推广.     

Bubbling and bistability in two parameter discrete systems

We present a graphical analysis of the mechanisms underlying the occurrences of bubbling sequences and bistability regions in the bifurcation scenario of a special class of one dimensional two parameter maps. The main result of the analysis is that whether it is bubbling or bistability is decided by the sign of the third derivative at the inflection point of the map function.     

Symmetry Reduction in Symplectic and Poisson Geometry

We present a quick review of several reduction techniques for symplectic and Poisson manifolds using local and global symmetries compatible with these structures. Reduction based on the standard momentum map (symplectic or Marsden–Weinstein reduction) and on generalized distributions (the optimal momentum map and optimal reduction) is emphasized. Reduction of Poisson brackets is also discussed and it is shown how it defines induced Poisson structures on cosymplectic and coisotropic submanifolds.