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Estimate shows the resonant gaps between KAM tori can be as large as of order 〓, while the transversality which can be obtained by Poincaré-Melnikov method in the stable manifold and the unstable manifold, as best as we can hope, is only order 〓.

但在通有的摄动下，部分双曲环面会破裂，仅用Poincaré-Melnikov方法无法构造出足够长的"传递链"。

By using integral periodogram to estimate the spectral functions of a stationary time series, the invariance principle for the error process has been demonstrated either for Gaussian or non-Gaussian series.

用积分周期图估计平稳时间序列的谱函数，不论是高斯序列还是非高斯序列，其误差过程的不变原理都已被证明￣（［1］，［3］），许重光￣［5］采用自迥归谱估计的积分估计谱函数也证明了误差过程的不变原理成立。

Kalman filter in mathematics is a statistical estimation methods, By a series of errors with the actual measurement data and the physical parameters of the best estimate.

卡尔曼滤波在数学上是一种统计估算方法，通过处理一系列带有误差的实际量测数据而得到的物理参数的最佳估算。

Meanwhile, the maneuverability, time and angle of mining motion for avoiding collision, is simulated for inland waterway ship. Knowledge of these is essential for ship colliding avoidance maneuvering, which often choosed with estimate by the steerer.

在此基础上对内河船舶回转运动、Z型运动的情况进行了数值模拟，重点考虑受环境干扰因素影响下的内河船舶操纵运动，以及内河船舶避碰操纵的运动特点。

In the first part, we will first deal with the strong Bonnesen-style inequality (2.1.3) for closed convex curves in the plane (the numbers of formulae and references are those of them in the context below). Bonnesen had first proved the weaker inequality (2.1.2) in [12] and several years later, he outlined in his monograph [13] various Bonnesen-style inequalities including (2.1.3), he considered, however,(2.1.3) as a direct consequence of Kritikos theorem for convex bodies in higher dimensional Euclidean spaces,. Here, we will give an independent proof of the existence for inequality (2.1.3), and by the way, give an estimate on the width of the bi-enclosing annulus of closed convex curves in the plane.

具体地讲，在第一部分中，首先讨论平面上闭凸曲线的强Bonnesen型不等式(2.1.3)(公式的编号和参考文献的编号引自后面的正文)，Bonnesen在文[12]中先证明了较弱的不等式(2.1.2)，几年以后，在他的著作[13]中，讨论了多种Bonnesen型不等式，其中包括不等式(2.1.3)，不过，他把(2.1.3)作为高维欧氏空间中凸体的Kritikos定理的直接推论，我们这里对不等式(2.1.3)给出独立的存在性证明，并且还对平面闭凸曲线的bi-enclosing环的宽度给出了一个估计。

We use the information of the first DL subframe to estimate the more accurate timing and fractional CFO by cyclic prefix correlation.

我们使用循环字首的相关性及在第一个下行次讯框里的资讯来估计出较准确的符码时间偏移和小数部分载波偏移。

A new method to estimate the distribution of a set of subsurface fractures by core data is suggested in this paper.

本文提出一种利用岩心资料估测地下一组裂缝分布的新方法。

To implement this guidance law, the thesis purposed one new target state model and adaptive algorithm for radar homing missile attacking maneuvering target, which is based on the slowly changing of the tangential acceleration and the normal acceleration of the spiral maneuvering and snaking maneuvering in target trace frame coordinate system, and on that the most of them equipped with Strapdown Inertial Navigation System, to meet the demand of the advanced homing missile to target state, It can estimate target position, velocity and acceleration accurately by real-time processing.

为了实现该制导律，重点针对先进自寻的制导律对目标机动运动状态的需求和导弹系统大都具有捷联惯导系统的条件，基于目标螺旋机动和蛇形机动的切向加速度和法向加速度在目标轨迹活动标架上缓变的特点，本文提出了一种建立在目标轨迹活动标架上的运动状态方程和扩展观测方程的自适应估计算法。

By using the coefficient estimation of Taylor expansion, we obtain an estimate of the n-th derivatives for bounded analytic functions.

利用有界解析函数泰勒展开式的系数估计，得到了n阶导数估计的一般式，改进了己有的相关结果。

Taylor formula for the basic idea is to use polynomials to approximate a known function, and the coefficients of the polynomial by the given function to determine the derivative , and this approach gives an effective estimate.

泰勒公式的基本思想是用多项式来逼近一个已知函数，而这个多项式的系数由给定函数的各阶导数确定，并对这种逼近给出有效地估计。

The X-ray diffract was used to analyze the crystal structure of the composite. Results show that after the talc was treated with blend coupling agent, the crystal structure of talc changed, and effect Intercalation phenomenon.

通过X射线衍射分析可知，用混合偶联剂对滑石粉进行预处理后，滑石粉晶体结构发生改变，产生了插层现象，使PP／滑石粉复合材料为纳米复合材料。

An authentic Maui wedding might require the services of a 'kahu', which is a Hawaiian minister.

毛伊可能需要一个真实婚礼服务'kahu'，这是夏威夷部长。