The stability perturbation bounds of a single - input - single - output system with both parametric and dynamic uncertainties is studied . the parametric uncertainties of the systems are described by interval perturbation mode , and the dynamic uncertainties are characterized by an integral quadratic constraint . based on the concepts of the minkowski functional , the problem of stability perturbation bounds is discussed , and for different uncertainty structures of the systems , the infinite stability checking problem of the mixed uncertain system can be converted to finite vertex - checking results and the edge - checking results 系统的正向通道为带有参数不确定性的线性系统，其不确定性为区间摄动模式，反馈通道为由积分二次约束给出的输入输出不确定性加以描述。用minkowski泛函给出区间摄动模式下的摄动界的定义，并给出参数空间中混合摄动模式下系统摄动界的估计式。
Secondly , in this part , we will introduce the notation of average geodesic curvature for curves in the hyperbolic plane , and investigate the relationship between the embeddedness of the curve and its average geodesic curvature . finally , we will employ the minkowski ' s support function to construct a new kind of non - circular smooth constant breadth curves in order to attack some open problems on the constant width curves ( for example , whether there is a non - circular polynomial curve of constant width , etc . ) in the second part , we will first follow the ideas of gage - hamilton [ 28 ] , gage [ 26 ] and the author ' s dissertation [ 47 ] to present a perimeter - preserving closed convex curve flow in the plane , which is from physical phenomena 其次，对双曲平面上的曲线引入平均测地曲率的概念，并讨论双曲平面上凸曲线的嵌入性与它的平均测地曲率之间的关系，其目的是为了将双曲平面上曲线的性质与欧氏平面中曲线的性质作一些对比；最后，我们利用minkowski支撑函数构造了一类新的非圆的光滑常宽曲线，其目的是想回答有关常宽曲线的一些未解决问题(如是否存在非圆的多项式常宽曲线
Under the assuption of generalized subconvexlikeness , the optimality conditions of set - valued optimization problems in linear space are established by using obtained gordan - farkas type alternative theorem . under the assuption of near subconvexlikeness and - generalized convexity , the optimality conditions of set - valued optimization problems in linear topological space are established by using alternative theorem of near subconvexlikeness and obtained farkas - minkowski type alternative theorem . the concepts of super efficient solution and - super efficient solution are defined in normed space , and the optimality conditions of set - valued optimization problems are established under the assuption of semi - preinvexity 在广义次似凸性假设下，利用已获得的gordan - farkas型的择一性定理，建立了线性空间中集值优化问题的最优性条件。在近次似凸和-广义锥凸性假设下，利用近次似凸集值映射的择一性定理和已获得的farkas - minkowski型的择一性定理，建立了线性拓扑空间中集值优化问题的最优性条件。
