In the second part , we consider a class of reaction - diffusion equations in developmental biology . near the bifurcation points , using the liapunove - schmidt reduction process , we obtain the nontrivial solution branches which are bifurcated from the trival solution when the parameter changes 然后考虑发育生物学中一类反应扩散方程组，在分歧点附近利用liapunov - schmidt约化技巧，得到了从平凡解分歧出来的随参数变化的非平凡解枝以及它们的近似解析表达。
First of all , the method of fredholm alternative is used to obtain the approximate solution of the first order for the bifurcating periodic solutions of a nonlinear system with delayed velocity feedback . the bifurcation direction and the stability of the bifurcating periodic solution are also determined 首先，用fredholm择一方法分析了一具有时滞速度反馈的非线性振动系统的hopf分叉，得到了局部分叉周期解的近似表达式，确定了分叉解的分叉方向及稳定性。
However , according to the bifurcated approach to problems of causation , the scope of damages that defined by the " cause in fact " is provided with the probability of enlargement infinitely and uncertainty , so it is necessary to restrict the scope of damages by some legal means within the meaning of techniques of law . meantime , it is unfair that the risk of transaction is only undertaked by the defaulting party , so it is necessary to make use of some legal means to delimit the reasonable damages for the defaulting party 首先，笔者提出：根据全部赔偿原则，违约方应赔偿因其违约行为给合同债权人造成的所有损害，而借用国外学者关于因果关系二分法的观点，该“事实上的因果关系”所划定的损害赔偿范围具有无限扩大的可能性和不确定性，因此从法技术讲，就有必须要利用一些法律手段对该赔偿范围予以限界；同时，交易活动本身固有的风险单由合同违约方承担也是不公平的，因此也有必要利用一些法律手段为违约方划定一个合理的赔偿责任范围。
In the second section , by means of local bifurcation theories [ 17 ] , we have proved the system generate bifurcation at the semi - trivial solutions ( uo , 0 ) , ( 0 , v0 ) . furthermore , using stability theory [ 16 ] [ 17 ] , we analyze the stability of the positive solutions near the bifurcating points and get ideal results 川、 n吻）处出现正解分支，运用稳定性理论分析‘卜nn并得到了分支点附近的正解的稳定性情况，成功的解决了反应扩散方程研究中的一个基本问题：平衡解的稳定性
It shows many typical characters seen in the type species of the genus of sinornithosaurus , which discovered also from western liaoning . ngmc 00 - 12 - a can further be included in sinornithosaurus by the dentary bifurcated posteriorly , unserrated premaxillary teeth , u - shaped furcula , extremel y short manual phalanx iii - 2 in comparison with the length of phalanx iii - l , very large and developed obturator process of the ischium , partially arctometatarsalian metatarsal iii and so on 它具有许多中国鸟龙属sinornithosaurus所特有的特征，如：齿骨后部分叉、前颌骨齿齿冠前后缘均无小锯齿、叉骨u形、第指第2指节很短、坐骨封闭突极大且具有坐骨后背突、第?骨部分窄足型等，因而无疑应归入该属中。
2 the design and manufacture of focs instrument system the foundation of commercial fiber optical chemical technique is to manufacture a fiber optical chemical instrument system . an instrument is assembled with xenon light as the source , bifurcate quartz fiber as the carrier for light , high precision photomultiplier tube for the conversion of light signal to electron signal and the 16 - digit multi - channels analog - to - digital card for collection of data 生产人作者选择氖灯为光源、设计聚焦系统，以石英分支光纤作为传输光信号介质，高精度光电倍增管检测， 16位多道数据采集卡为a d转换，采用visualbasic编写windows平台操作软件，菜单提示，窗口人机对话，研制成功单通道光纤化学过程传感仪器系统。
It is shown that with the increase of time delay from zero to infinity , the equilibrium of system may experience stability switches at the critical values of time delay , where the hopf bifurcation will necessarily occur with the bifurcating periodic solution having alternative stability on their two - dimensional local center manifolds 结果表明，随着时滞从零不断增大，系统平衡点将有可能发生稳定性切换，并在每一有可能发生稳定性切换的临界时滞处发生hopf分叉，并且分叉解的稳定性在二维局部中心流形上交替变换。
5 . the micro - crack fracture expansive process of adherence of new and old concrete is analyzed by means of chaos theory . the result shows that the stable extension , bifurcate and unstable extension of original micro - crack fracture is coincidence with model of the stationary state zone , bifurcate zone and chaos zone of double periodic bifurcate theory of chaos 用混沌理论分析了新老混凝土粘结界面断裂损伤微裂缝动态扩展过程，界面层原始微裂缝的稳定、稳定扩展和失稳扩展的动态扩展过程与混炖理论中倍周期分叉的定态区、分叉区和混饨区模型相符合。
The trajectories of their , first sequent , then simultaneous , urinations were dissimilar : bloom s longer , less irruent , in the incomplete form of the bifurcated penultimate alphabetical letter who in his ultimate year at high school 1880 had been capable of attaining the point of greatest altitude against the whole concurrent strength of the institution , 210 scholars : stephen s higher , more sibilant , who in the ultimate hours of the previous day had augmented by diuretic consumption an insistent vesical pressure 他们二人那起初有先有后，继而同时撤出去的尿的轨道并不相似。布卢姆的较长，滋得没那么冲，形状有点像那分叉的倒数第二个字母185 ，却又有所不同。敢情，他念高中最后一年一八八0的时候，曾有本事对抗全校二百十名学生拧成的那股力量，尿撒得比谁都高。
The system properties of single - loop system , such as velocity , torque , bifurcated power , transmission efficiency are researched deeply using theoretical analysis and numerical computing , and gives new methods for designing which according to the design parameter a and combine with the system diffluent coefficient q and the ratio of x , p cell transmission . so the theoretical expressions for designing this kind of transmission is established . the design parameter a is put forward as the ratio of confluent power and the input power of single - loop system 通过对单环路系统的运动学和动力学特性、功率流特性、传动效率特性等所进行的理论分析和数值计算，提出了以单环路系统主支路功率大小与输入总功率的比值为关键设计参数的设计新方法，并结合系统的功率分流系数q和各组成单元的传动比，得到了单环路系统的速度、力矩、功率流、传动效率等计算公式，为该种传动类型的设计提供了必要的理论依据。
