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脉冲系统中闭集稳定性与集值映射连续性的关系
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作者 李克华 刘粒 《厦门理工学院学报》 2021年第1期91-96,共6页
为进一步探讨脉冲动力系统中闭集的局部稳定性和集值映射的连续性的关系,在脉冲动力系统中引入闭集在某一点处稳定的定义及其等价条件,参照一般连续动力系统中的情形,以度量空间中的HAUSDORFF度量为工具,讨论脉冲动力系统中两类特殊的闭... 为进一步探讨脉冲动力系统中闭集的局部稳定性和集值映射的连续性的关系,在脉冲动力系统中引入闭集在某一点处稳定的定义及其等价条件,参照一般连续动力系统中的情形,以度量空间中的HAUSDORFF度量为工具,讨论脉冲动力系统中两类特殊的闭集,即正延伸集和正延伸极限集的稳定性与相应的集值映射的连续性之间的关系。研究表明:集值映射D^(+)(或K^(+))在x点上半连续当且仅当集合D^(+)(x)(或K^(+)(x))在x点稳定,映射L^(+)在x点上半连续当且仅当闭集L^(+)(x)在x点最终稳定,映射J^(+)在x点上半连续,蕴含着闭集J^(+)(x)在x点最终稳定,反之,若J^(+)(x)在x点一致最终稳定,那么映射J^(+)在x点上半连续。 展开更多
关键词 脉冲动力系统 延伸 延伸极限 稳定性 极限映射 半连续性
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连续函数空间Cr上的无穷延滞NFDE中的T.Yoshizawa定理
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作者 刘恒峰 《工业工程》 1991年第2期42-52,共11页
本文讨论了无穷时滞中立型泛函微分方程解的正极限集和半不变集,以及解的渐近性态。文章是在Cr空间中把T.Yoshizawa的理论推广到无穷时滞的NFDE之中,证明其结果成立,使这方面的理论在泛函微分方程中得到补充与完善.
关键词 函数空间 算子/李亚普诺夫泛函 一致稳定 正极限集 半不变
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Bearing characteristics of coal pillars based on modified limit equilibrium theory 被引量:6
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作者 Wang Xiangyu Bai Jianbiao +1 位作者 Wang Ruofan Sheng Wenlong 《International Journal of Mining Science and Technology》 SCIE EI CSCD 2015年第6期943-947,共5页
There are two states for the coal-mass on the goal-side which is in stress equilibrium: the state of limit equilibrium (the bearing stress in the coal-mass equals its ultimate bearing stress) and the state of non- ... There are two states for the coal-mass on the goal-side which is in stress equilibrium: the state of limit equilibrium (the bearing stress in the coal-mass equals its ultimate bearing stress) and the state of non- ultimate equilibrium (the bearing stress in the coal-mass is less than its ultimate bearing stress). To ana- lyze the bearing characteristics of a coal pillar in the state of limit equilibrium and guide the design of pillar width, we established a mechanical analytical model of the non-ultimate equilibrium zone in the coal-mass on the goal-side combined with the limit equilibrium theory as well as adopting the methods of theory analysis and mechanical analysis based on the assumption of a state of non-ultimate equilibrium. The width correction coeffident of the limit equilibrium zone has been given. The influence of mining depth, stress concentration coefficient of the surrounding rock, the non-limit strength of the coal-mass and stability of the coal rock interface has been studied. On this basis, we have confirmed that when the width ofa longwall mining face roadway protection coal pillar is between 11.6 m and 13.16 m in No. 4 coal seam of Xinrui coal mine in Lvliang in Shanxi province the elastic core region in the coal pillar can be assured and the roadway will be located in the area of lower stress which is outside the peak stress. So the revised width of the limit eauilibrium zone is more oractical. 展开更多
关键词 Coal bearingZone of non-ultimate equilibriumWidth correction coefficient of plastic zoneWidth of roadway protection pillar
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