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首次证明了拟五次多项式系统在无穷远点能分支出7个极限环。It is the first time that 7 limit cycles can bifurcated from the infinity for a class of quasi quintic system.

本文研究一类五次平面多项式系统赤道极限环分支问题。In this paper, the problem of limit cycles bifurcated from the equator for a quintic polynomial system is investigated.

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运用奇点量方法，首次证明了五次多项式系统可在赤道分支出十个极限环。In this paper, the problem of limit cycles bifurcated from the equator for a quintic polynomial system is investigated.

虽然样条曲线具有广泛的应用，但对五次样条插值算法的研究却很少。Although spline curves are applied widely, but the research on the algorithms of quintic spline interpolation is little.

研究一类五次多项式系统无穷远点的中心条件与赤道极限环分支。Center conditions and bifurcation of limit cycles at the infinity for a class of quintic polynomial system were studied.

此外，负五阶非线性的存在使预啁啾对脉冲频谱的影响发生了较大的变化。In addition, the negative quintic nonlinearity can also make the effects of initial chirps on spectra of pulses change considerably.

同时还研究了一类五次系统原点的中心条件及在同步扰动下原点与无穷远点的极限环分支问题。At the same time, the center conditions and bifurcation of limit cycles at the origin of the quintic polynomial system are also investigated.

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为提高裁刀拐角过渡速度及获得良好的运动平稳性，提出五次样条曲线拐角重构算法。A algorithm to reconstruct the corner with quintic spline curves was proposed for improving cutter's motion stability and transition velocity.

本文给出了构成五次PH曲线的充要条件，分析了其控制多边形的几何意义。This paper present a sufficient and necessary condition of constructing quintic PH curves and analyze the geometric meaning of the control polygon.

其中有些问题，诸如求解五次方程的根，后来被证实是不可能完成的。Some of the tasks turned out to be impossible. For example, people tried for centuries to solve quintic equations. We now know that this is impossible.

作为应用，我们在复域中详细地求出了一类五次多项式系统的原点成为中心、拟等时中心的条件。As an application of our method, we solve the problems of center conditions and bifurcation of limit cycles at infinity for a quintic polynomial system.

采用常微分方程定性理论的经典方法，对一类平面五次多项式系统进行定性分析。By using qualitative classical theory of ordinary differential equation, a class of planar quintic polynomial differential system is qualitatively analyzed.

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相应地，给出了一个拟五次系统在原点分支出7个极限环的实例。In chapter 5, using an indirect method to study center conditions and bifurcation of limit cycle for a class of quasi quintic system, We obtain 7 limit cycles.

在第四章和第五章，分别对一类五次系统和七次系统的无穷远点的中心条件和中心积分进行了完整研究。In Chapter 4 and Chapter 5, complete researches have been done respectively on the center conditions and center integral of a quintic system and a septic system.

五次样条插值算法及其配套算法的系统深入研究，为五次样条曲线在数控加工技术领域中的应用奠定了坚实的算法基础。The systemic research on the algorithms and the correlative algorithms establish massive foundation for the application of quintic spline curves in NC machining.

文章考虑了一类具有等变性质的五次哈密顿向量场的全局性质，得到了其全局相图并对参数空间进行了划分。In this paper, we consider some planar quintic Hamiltonian vector field with Z3-equivariant property, get its global phase portraits, and classify its parameter space.

本章讨论了一类具有Z3-等变性质的五次哈密顿向量场的全局性质，得到了其全局相图，并对参数空间进行了划分。In this paper, we discuss some planar quintic Hamiltionian vector field with Z3-equivariant property, get its global phase portraits, and classify its parameter space.

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从带五次非线性项的扩展非线性薛定谔方程出发，重点考虑了五次非线性对常用的自聚焦光纤中反常色散区调制不稳定性的影响。In this paper, the effect of quintic nonlinearity on modulational instability in the anomalous dispersion regime of self focusing fiber from extended nonlinear Schrodinger equation is considered.

所提出的插补方法采用五次样条和四次曲线多项式微分法近似求取导数，能够更好的满足精确加工的需要。The applied interpolation method adopts quintic spline and derivatives generation approach for discrete points by using quartic polynomial, which can better meet the needs of high-accuracy machining.