邻域

The integrability conditions and coefficient conditions for the appearance of 5 and 6 limit cycles from the neighborhood of the equator are obtained. An example of cubic system with 6 limit cycles bifurcating from the equator is given for the first time.

同时计算出系统的前6个赤道环量，得到了系统在赤道邻域的可积性条件及在赤道附近分支出5个和6个极限环的系数条件，从而首次给出了一个平面三次系统在赤道附近分支出6个极限环的计算实例。

First,image structure vector field is derived from source luminance orthonormal vector sets. Andusing neighbor vectors to improve the weak gradient fields produces the structure vectorfield that is needed by LIC rendering. Then, LIC convolution step-length is adjustedaccording to local curvature in the structure vector field. LIC convolution length iscalculated according to the local statistical characteristics of the texture image. Finally, thealgorithm transfers the reference image\'s color characteristics to the rendering result tomake it full of rich color like oil paintings.

该算法通过计算源图像亮度分量的切矢量产生图像的结构矢量场，并对弱矢量区域进行邻域填充处理，获得LIC绘制所需的结构矢量场；然后，根据结构矢量场的局部曲率特征调整LIC的积分步长，并根据纹理参考图像的局部统计特征，自适应地改变LIC的积分长度；最后，将颜色传输算法引入LIC绘制结果，对绘制效果颜色进行渲染。

In this part, the characteristics of transient responses of flexible rotor systems with arbitrarily distributed mass on isotropic or anisotropic supports passing through several critical speeds seguencially are examined. Here, the current knowledge of rotor dynamics on the eigenproblem of damped free whirling vibration, the generaliged damped mode theary, the transient forced vibration and so on combined with KBM asymptotic method in the nonlinear vibration theory is employed and extended.

作者综合运用并引伸推广转子动力学关于阻尼自由回旋振动的特征问题、广义阻尼模态理论、瞬态强廹振动等現代理论和方法，结合非线性振动理论中的KBM渐近法，提出自己独創見解和覌点，成功地建立起正回旋和逆回旋两种情况下转子通过临界点的瞬态振动一阶微分方程组，可以在临界点的邻域内从事方程的数值积分计算。

Moreover, it can be proven that if its proximal relation is dense in a neighbourhood of some point in the diagonal then it is chaotic in the sense of Li-Yorke.

进而，我们证明了如果proximal关系在对角线上某个点的一个邻域中稠密，则它为Li-Yorke混沌的。

This function is infinite-order differentiable with respect to wavelet coefficient, and can adaptively shrink wavelet coefficient in the neighborhood of the threshold.

其为收缩因子函数与小波系数的乘积，对小波系数无穷可导、可在阈值邻域内对小波系数自适应收缩。

Theorem 3.2. Assume that is compact and that is continuously differentiable on a neighborhood of .

定理 3.2。假设紧密的并且f在的邻域中是连续可微的。

Let be defined on the open interval for some. If is differentiable at, and for any in

设函数在点的某邻域内有定义，并且在处可导，如果对任意的，有，那么。

By Code extraction method is to investigate the edge of each image pixel in a neighborhood Gray-scale changes in the region, using the edge of the neighboring first-order or second-order directional derivative Changes of a few simple ways to detect the edge.

经 典的边缘提取方法是考察图像的每个像素在某个邻域内灰度的变化，利用边缘邻近一阶或二阶方向导数变化规律，用简单的方法检测边缘。

The set of points surrounding a specified point,each of which is within a certain ,usually small distance from the specified point.

邻域定点周围的点的集合，其中每个点离定点在一定的，通常是很小的距离内

We compared this two model and found that the two model is coincident when dual relation was symmetric.

接着我们又用前继邻域代替等价类建立了另一个准一般关系下模糊粗糙集模型，并把两种模型进行比较，指出当二元关系满足对称性时两种模型是一致的。

According to the clear water experiment, aeration performance of the new equipment is good with high total oxygen transfer coefficient and oxygen utilization ratio.

曝气设备的动力效率在叶轮转速为120rpm～150rpm时取得最大值，此时氧利用率和充氧能力也具有较高值。

The environmental stability of that world - including its crushing pressures and icy darkness - means that some of its most famous inhabitants have survived for eons as evolutionary throwbacks, their bodies undergoing little change.

稳定的海底环境─包括能把人压扁的压力和冰冷的黑暗─意谓海底某些最知名的栖居生物已以演化返祖的样态活了万世，形体几无变化。