The hybrid material was characterized by ft - ir , fluorescence , xps , tg - dta , and dmta . the morphology of the hybrid material was observed by tem . it was showed that sno2 nanoparticles were in the shape of sphere or tube and some tubes even bifurcated ( 2 )表面活性剂dbs能提高纳米sno _ 2在聚合漆酚中的稳定性，对pus sno _ 2杂化材料的形成起了重要作用，使其颗粒大小在纳米范围内。
In the second , we make using of the method of hkw [ 14 ] which based on the center manifold theorem and normal form theory , and list two calculation formulas which reflect the stability with hopf bifurcating periodic solution , and bifurcating direction 其次，利用基于中心流形定理和规范形理论的hkw方法给出了确定hopf分支周期解的稳定性，分支方向的计算公式，为数值模拟计算提供了依据。
Lastly , we apply the formulae about the quality of ilopf bifurcation we have obtained to a concrete example , calculating the stability of periodic solution , the direction of hopf bifurcation and the expression of bifurcated periodic solution 最后，我们将已经得到的判断hopf分支性质的计算公式应用到一个具体的例子上，求出这个方程的hopf分支周期解的稳定性，分支方向及分支周期解的近似表达式。
Firstly , we give the bifurcation diagram in the parameter plane ( r , b ) , according to which we can give the stable and unstable regions of the equation ' s / oro solution and the hopf bifurcated curve of hopf bifurcation in the parameter plane ( r , b ) 我们首先在( r ， b )参数平面内给出一张分支图，根据此图能够给出在( r ， b )参数严面内方程零解的稳定性和不稳定性区域，以及方程产生hopf分支的hopf分支曲线。
Firstly , the first eight singular point quantities are computed and conditions for infinity to be a center are deduced as well , then a system that bifurcates eight limit cycles in the neighborhood of infinity are constructed 首先通过同胚变换将系统无穷远点转化成原点，然后求出该原点的前8奇点量，从而导出无穷远点成为中心和最高阶细焦点的条件，在此基础上给出了五次多项式系统在无穷远点分支出8个极限环的实例。
According to the parameter , the relationship between the individual ratio and the confluent power is established . we can directly design this kind of transmission machine using design parameter a and q according to the requirement of bifurcated power 其次，根据设计参数的意义，分析得到了系统内部的功率流分配情况与系统各单元传动比之间的函数关系，从而可以据此并利用设计参数、 q直接设计满足特定要求的单环路系统。
We exhibit calculating formula about direction of hopf bifurcation and the bifurcation periodic solutions in the first bifurcated to and so on with norm form theory and center mainfold theorem , furthermore , we carry out numerical simulated compution with mathematica . finally , the charting are performed with mat - lab 我们还用中心流形和规范形理论，给出了在第一个分支点_ 0处的hopf分支方向，分支周期解的稳定性的计算公式。
The early stage of bph can bring frequent urination , especially serious frequent urination in night , and will happen gently urinary hesitation , urinate with powerful abdomen force , urination weakness , thin stream of urine or urine bifurcate , dripping wet , urinary incontinence , even retention of urine 早期为尿频尤其是夜尿增多逐渐出现排尿踌躇，增加腹压排尿，排尿无力，尿流变细分叉，以致淋漓不尽，急性尿潴溜或尿失禁。
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
