To deal with the case of 2 dimension spatial self - focusing , it predicts the catastrophic collapse of a self - focusing beam in a kerr medium . this un - physical collapse is due to the invalidity of the paraxial wave equation in the neighborhood of a self - focus 在该理论应用于空间二维的自聚焦时，出现了光束将无限聚焦的结果，这在物理上是不可想像的，原因是在自聚焦点附近傍轴方程已经失效了。
Based on the structure of the subarray , we construct the signal model at subarray level . by generalizing it to 2 - d , we construct 2 - d signal model at subarray level , this model has no limitation to the array configuration and can be applied to any plane array 基于阵列的子阵结构,我们构造了子阵级adbf信号模型,并将其推广到二维,建立二维的子阵级信号模型,该模型对阵列形状没有限制,适用于任意的平面阵。
To facilitate rules detection , the rules are loaded dynamically into a two - dimensional rules list , and patterns in multiple rules with common attributes are organized as an intrusion pattern tree which can satisfy the demand for multiple - pattern matching 为便于系统对规则的检测，在系统进行初始化时，动态地把规则加载到一个二维的规则链表中，并把多个具有共同属性的规则中的入侵模式组织成一棵入侵模式树以适应多模式匹配的需要。
Hence , analytical expressions are developed to allow for characterization of the vehicle ’ s dynamics early in the design cycle . the method involves a two - dimensional hypersonic aerodynamic analysis utilizing newtonian theory , coupled with a one - dimensional aero / thermo analysis of the flow in the engine of the vehicle 方法中包括一个应用牛顿力学理论的二维的高超声速空气动力学分析以及一个一维的气动/热分析,后者用于模型发动机中的流体分析。
For 2d case , we design high order global and local artificial boundary conditions . for 3d case , the computational cost increases and the design of artificial boundary conditions becomes more difficult , we successfully design high order global artificial boundary condition 对于二维的情形我们设计出了高精度的整体型和局部型人工边界条件，对三维情形计算量大大增加，人工边界条件的设计也相对复杂，我们也成功地设计出高精度的整体型人工边界条件。
In virtue of self - organizing map , the network output layer characteristic flat of which reflects roughly the distribution of sample data with different kinds of sample data of t he faults are d imensionally r educed , c lustered and are s hown on a two - dimensional plane where different kind of sample data of the fault takes different area 借助自组织特征映射的特点：即网络输出层特征平面能基本反映样本数据的分布情况，将高维的，不同种类的故障样本数据进行降维和聚类，显示在一个二维的平面上。使每种类别的样本占据平面上不同的区域。
Compared with the old ones , some improvements are obtained by using this method , such as pattern recognition scope , speed of pattern searching and matching , etc . furthermore , the new algorithm has stronger flexibility and stability . the information acquisition technique of intersected primitive based on combined relationship is provided . with the help of obtained engineering semantics , the correlative projections implying combined relationship among primitives are defined as combined factor 根据已经获取的工程语义，将隐含基元体之间组合关系的相关投影定义为组合因子，由此建立组合关系表，最后借助组合关系表，采用回溯的方法，即从二维的组合因子出发，找出它所隐含的两两基元体在三维空间中的组合关系，进而对该组合关系的主体?基元体的信息进行识别和获取。
The old two dimensional gis has been used widely in the power systems and become more functional . but its traditional means of using symbols to express buildings and geographic environment does n ' t simulate the true terrain near the power lines and electric facilities , and does n ' t give the maintenance men the true information of their working surroundings 传统的二维的电力企业地理信息系统已由技术研究阶段进入大规模使用阶段，功能日益完善，但是其简单的几何图形加注记的形式不能真实的反映电力线路、设备设施周遭的地形地貌，不能为线路、设备的巡视、检修人员提供真实的工作环境信息。
After analyzing and comparing nonlinear evolution of r - t instability in two dimension with that in three dimension , it is the conclusions given that three - dimensional ( 3d ) disturbance grows rapider than two - dimensional ( 2d ) one , its timely evolution factor being 1 . 41 to 1 . 26 time as large as 2d ' s , in r - t instability linearly developing regime , and with time increasing , three - dimensional wave shape gradually deviates from 2d ' s 通过比较二维和三维r - t不稳定性的非线性发展，得出结论： r - t不稳定的线性发展阶段，三维扰动比对应的二维扰动增长要快，它的时间增长因子大致为二维的1 . 41到1 . 26倍。
