| 1. | Oscillation theorems for second order nonlinear differential equation with damping term
带有阻尼项的二阶非线性微分方程的振动性 |
| 2. | Thirdly , we consider the n - dimensional duffing type equation with damping term . by virtue of homeomorphism , extension and fixed point method , we discuss the existence of periodic solution under the nonresonance condition
再次，我们考虑n维的带有阻尼项的duffing型方程，运用同胚延拓及不动点方法，讨论了非共振条件下周期解的存在性问题。 |
| 3. | The global existence of solution to the initial - boundary value problem of a nonlinear fourth - order wave equation with a damping term and a force source term was proved based on the standard semigroup theory and by introducing a modified energy function
摘要根据半群理论，引进修改的能量函数，证明了具有阻尼项和力源项的四阶波动方程的初边值问题解的整体存在性。 |
| 4. | The existing algorithms usually add damping term of the form . xlog . x into their objective function in order to control matching matrix ' s entropy . the shortcoming is that the two - way constraints need to be enforced by using sinkhorn method
这类算法为了控制匹配矩阵元素的熵，通常在目标函数中加入xlogx形式的阻尼项，其缺点是需要用sinkhorn交替归一化方法或其它方法使匹配矩阵满足双向的行列约束。 |
| 5. | In this paper , to counter a flexible beam undergoing large overall motion impacting a fixed slope surface under the effects of grativity , the normal contact model is established based on the hertz theory and non - linear damping term , the tangential contact model is developed by adopting linear tangential contact stiffness to consider the effects of friction force during impact process , and the consistent linear dynamic model including impact is derived by using mode assumption method and lagrangin equation
针对在重力场下作大范围回转运动的柔性梁与一固定斜面发生斜碰撞的情况，根据hertz接触理论和非线性阻尼项建立法向碰撞接触模型。引入线性切线接触刚度建立切向碰撞接触模型，以考虑接触过程中由于切向相对速度的换向作用引起的摩擦力的变化。利用假设模态法和lagrangian方程建立系统含碰撞过程的一致线性化的动力学模型。 |
| 6. | Utilizing backstepping procedure , general expression of control strategy for hvdc converters is acquired . the control strategy can restrain the nonlinear uncertainty through injection of nonlinear damping terms in virtual controllers . the proposed decentralized adaptive control scheme guarantees that all the signals in the closed - loop system are bounded in the presence of high order interconnections and bounded disturbances
设计中引入自适应非线性阻尼项来抑制系统非线性不确定参数和未知有界干扰的影响，同时采用反演设计方法来克服控制器设计的复杂性，最后获得高压直流输电系统换流站的分散鲁棒自适应控制策略的一般表达式，并提供了整个系统的稳定性证明。 |
| 7. | This dissertation mainly investigates the properties of solutions of a class of quasi - linear wave equations with a viscosity , a nonlinear perturbation ( source term ) and a dissipative term ( damping term ) , which arises from the longitudinal motion of a visco - elastic material . it contains the problems of existence and uniqueness of solutions , global existence , asymptotic behaviour and finite time blow up , etc . this thesis consists of four parts
本论文主要研究来自于物体的波动等应用领域中的一类带有粘性项、非线性扰动项(源项)和耗散项(阻尼项)的拟线性波动方程解的定性性质，内容包括解的存在唯一性，解的整体存在性和渐进性态及解在有限时刻爆破等问题 |
| 8. | By citing a series of counterexamples , , e demonstrate in section 5 that famous indian scholar e . thandapani ' s and american scholar k . ravy ' s classification methods are essentially , rong for second order quasi - linear difference equation , ith damped term in " computers and mathematics , ith applications " , state ne , results and solve completely the problem for the classification of this kind of equation
通过列举一系列的反例，我们在第五节指出，著名的印度学者e thandapani和美国学者k ravy在《 computersandmathematicswithapplications 》上关于具有强迫项的二阶拟线性差分方程非振动解的分类方法是根本错误的，给出了新的结论，完整地解决了这类方程的分类问题。 |
| 9. | Based on the reference [ 22 ] , the dynamical modeling converters for hvdc system have been transformed to a nonlinear system represented by input - output model with unmodeled dynamics and bounded disturbances , and a robust adaptive output - feedback nonlinear controller is designed . the controller counteracts the uncertain dynamic nonlinearities and bounded disturbances by nonlinear damping terms , and unmodeled dynamics by a dynamic signal
本文在文献[ 22 ]的基础上，对高压直流输电系统换流站动态模型进行变换处理，将其化为一类具有含未建模动态和有界扰动的输入-输出非线性系统，并设计了一种鲁棒自适应输出反馈控制器，利用非线性阻尼项来抑制系统的动态不确定性和有界扰动，引入一动态信号来抑制系统的未建模动态。 |
| 10. | Our next goal is to separate two suitable domains for the parameters m and p , where the exponent m and p determine the degree of nonlinearity of the damping term and the source term . when m p , the damping term dominates over the source term and the global solution exists for any initial data . in the proof , we use the " modified energy " and the continuation principle
然后分成两种情形： m和p分别决定阻尼项和源项的非线性度，当m p时，阻尼项控制源项，应用修正的能量和连续性原理证得整体存在性；当p m时，源项占主导，应用能量补偿的方法得到解在有限时间内爆破。 |
