Necessary extremum conditions for differential inclusion with aftereffect

Necessary extremum conditions for optimization problem on the minimum of a functional specified at the right-hand end of the trajectory of differential inclusion with aftereffect are obtained. The constraints, specified at the left-hand end of the trajectory, imply that the initial function belongs to some rnultivalued mapping. The problem is considered at the fixed interval of time     

基于映射理论下的决策评判模型

按照映射理论,通过建立评价指标标准值与评价指标标准值顺序数之间的函数,将非等长度区间映射成长度为1的等长区间,提出了一种求解决策评判的新模型,解决了不同标度下的评价因子、评价类别的决策评判问题,纠正了可拓理论关联函数基本公式的错误,简化了可变模糊集模型中的M矩阵和B矩阵,进而统一了可拓评价和可变模糊集理论在决策评判中的一致性,并实例验证了模型的优越性和正确性,对决策评判问题具有重要的应用拓广参考价值.     

Uniqueness Theorems for Some Free Boundary Problems in Univalent Functions

Let Φ be a bounded positive continuous function in the complex plane C. We will consider the following problem. We can find a simply connected region Ω containing the origin such that the Riemann mapping function f _Ω mapping the unit disk D onto Ω will satisfy <artwork name="GCOV31013eu1"> We show that there is a unique solution which is starlike with respect to the origin when Φ satisfies <artwork name="GCOV31013eu2"> We also show that if in addtion, ?Φ/?|w|>0 and ?log Φ is subharmonic, then Ω will be a convex region.     

Growth and Distortion Results for Convex Mappings in Infinite Dimensional Spaces

In this paper, we obtain the growth result for normalized convex mappings on the unit ball of a complex Banach space. Also we give some bounds of coefficients and a distortion result for convex mappings on the unit ball of a complex Hilbert space.