It is a main task of general topology to compare different spaces . mappings which connect different spaces are important tools to complete it . which mapping preserves some special generalized metric space is a basic probleme in investigating generalized metric spaces by mappings . g - first countable spaces and g - metri / able spaces have many important topological properities so to investigate which mapping preserves them is very necessary . in [ 7 ] , clnian liu and mu - ming dai prove that open - closed mappings preserve g - metri / able spaces ; whether open mappings preserve g - first countable spaces is an open probleme asked by tanaka in [ 6 ] . in [ 4 ] , sheng - xiang xia introduces weak opewn mappings and investigates the relations between them and 1 - sequence - covering mappings . in the second section of this article , we investigate weak open mappings have the relations with other mappings and prove that the finite - to - one weak open mappings preserve g - first countable , spaces and weak open closed mapping preserve g - metrizable spaces . in the third section , we investigate an example to show that perfect mappings do not preserve g - first countable spaces , g - metrizable spaces , sn - first countable spaces and sn - metrizable spaces 在文献[ 4 ]中，夏省祥引进了弱开映射，并研究了它和1 -序列覆盖映射的关系。本文在第二节研究了弱开映射与序列商映射，几乎开映射的关系，证明了有限到一的弱开映射保持g -第一可数空间；弱开闭映射保持g -度量空间。第三节研究了文献[ 5 ]中的一个例子，证明了完备映射不保持g -第一可数空间， g -度量空间， sn -第一可数空间， sn -度量空间。
A open - close mathematic model is introduced into calculation of torsional vibration . results show : kurtosisness and high harmonic will increase when crankshaft have crack . 5 . cylinder score is also diagnosed by torsional vibration in this paper , when cylinder score occurring , the friction of piston will decrease the action of air pressure 本文借鉴了裂纹转子刚度的开闭模型，首次对含有变刚度单元的柴油机动力装置进行了扭振计算，结果表明柴油机曲轴有裂纹后，扭振的角位移和附加振动力矩的高谐次分量会增加，峭度值增加。
Abstract : iterative learning control is an effective approach to the control of processes that are repetitive in nature . in this paper , an open - closed - loop pi - type iterative learning control scheme for the precise tracking control of a class of discrete nonlinear time - varying systems over a finite time interval is presented . the scheme updates control input with tracking errors of both current and last iterations simultaneously . sufficient and necessary conditions which guarantee the convergence of the scheme are given and then proved with inductive method . finally , the conditions are verified with simulation results 文摘:对于具有重复运动性质的对象，迭代学习控制是一种有效的控制方法.针对一类离散非线性时变系统在有限时域上的精确轨迹跟踪问题，提出了一种开闭环pi型迭代学习控制律.这种迭代律同时利用系统当前的跟踪误差和前次迭代控制的跟踪误差修正控制作用.给出了所提出的学习控制律收敛的充分必要条件，并采用归纳法进行了证明.最后用仿真结果对收敛条件进行了验证
Since vehicles are being used more often , the frequency of lifting glass up and down is getting higher . and lifter glass is used to lift the glass up and down , therefore it becomes more crucial whether window regulator functions well or not . glass lifter functions mainly as to ensure window glass in rising and descending smoothly , which helps people with their normal activities in the vehicle 既然人们在车辆上的活动增加，则开闭车门玻璃的次数就会相应增多，而车门玻璃升降器的主要作用就是保证车门玻璃能够比较顺畅地升降，以实现车门玻璃的开闭，为此，车门玻璃能否平顺升降，安全可靠地工作就显得尤为重要车门玻璃升降器的主要作用就是保证车门玻璃能够顺畅升降，以方便驾乘人员在车辆上进行正常活动。
The main contributions of this dissertation are summarized as follow : ( 1 ) an ilc approach combining feedforward with current feedback is developed based on optimal feedback control and the gradient method . a sufficient condition that guarantees the convergences is given for linear system . the procedures of designing the algorithm can employ lqr , h2 or h approaches to improve the convergence rate of learning in iterations 本文的主要成果有： 1 、在开闭环综合迭代学习控制结构的基础上，分析了利用梯度下降法设计前馈迭代学习控制器时，为保证算法的收敛性，闭环控制系统应该满足的充分条件，并依据提高算法收敛速率的优化条件，给出了基于lqr 、 h _ 2和h等优化控制技术的迭代学习控制算法的设计方法。
