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On the basis of comparison of several algorithms of the calculation of unstable resonator"s mode. Fast Fourier transform method is chosen in this paper. The model of multi-layer distribution of gain is established. Sampling granularity in real space used in FFT, quotient of guard band and distance between subsections are made certain respectively. The convergence criterion of root-mean-square of plural y which is the quotient of the optical field"s distributions separated by one pass is established. Under the circs of multi-kind of distribution of gain and different measurement of distortion, the output optical field distribution is calculated.

在比较了各种计算腔模方法的基础上，根据角谱传播理论，选择FFT算法，建立谐振腔内多层增益分布模型，分别确定了FFT算法的空间采样间隔、保护带系数和分段计算的距离，选取光场往返一次之比的均方根值收敛准则，计算多种增益分布、不同镜面变形时的谐振腔输出光场分布，同时计算该光场的远场分布和传输有限距离之后的分布。

In the algorithm,the theory of particle system changing from non-equilibrium to equilibrium is used to define the Rank function and Niche function for solving multi-objective problems,all the individuals in the population have chance to participate the evolving operation to solve the Pareto optimal solutions of the multi-objective problems fast and evenly.

由于该算法使用了粒子系统从非平衡达到平衡的理论来定义求解多目标问题的Rank函数和Niche适应值函数，使得种群中的所有个体都有机会参与演化操作，以达到快速、均匀地求出多目标优化问题的Pareto最优解。

In order to embody the fuzzy character in evaluation, the traditional analytic hierarchy process is developed into a fuzzy one. The introduction of triangular fuzzy number can contain more fuzzy information of evaluation. The ranking method for reciprocal judgement matrix with triangular fuzzy numbers is also presented. Based on the mode identification process, the mathematical model of multi-level and multi-object evaluation using fuzzy approach degree is set up primarily.

为了更加有效地反映评估对象的模糊性，本研究将传统的层次分析法拓展到模糊领域，引入三角模糊数的概念，并对模糊评判矩阵的排序方法进行了研究，在此基础上，提出了基于模糊集贴进度的模式识别评估方法，建立起润扬大桥悬索桥多层次多目标综合评估模型。

Furthermore, how to apply the model efficiently in practice is deeply discussed. As the variance produced by the forecasting model as concerned, the real-time revised method of hydrological forecasting is highlighted. Next arranged, the multi-stratum recursive prediction model is put forward to forecast the error series that is a dynamic system. Later, an error selfregressive multi-stratum recursive prediction model is set up as well as a current algorithm offered. Finally, the difference collated model and the gloss control method, which are devoted to updating the mid-long term hydrological forecasting during the meditate period, are put forward.

在综合评述中长期水文预报现有方法和模型的基础上，采用时间序列分析方法，建立中长期水文预报的时间序列组合模型，并对模型如何在实际中有效应用作了较为深入的探讨；针对模型预报所产生的误差，又重点研究了水文预报实时修正方法：提出了采用多层递阶预报方法对误差序列这一动态系统进行预报，建立了误差自回归多层递阶预报模型，并提出了较为通用的解算方法；给出了水文中长期预报中期修正的残差相关模型和总量控制方法。

The input method of multi-scale data and three levels data index are investigated, a new own idea about how to represent multi-scale seamless data is advanced. The viewpoints that seamless GIS is looked on surface of globe reference ellipsoid as spatial information positioning standard and looked on geographic coordinates as reference of spatial data storage are explored, and based on reference ellipsoid surface coordinate, the measurement model of distance, azimuth angle and area are given.(4) The flowchart of data production of seamless GIS is analyzed, on the basis of the program algorithm and the interactive processing of feature adjoining relation, the data production method of seamless GIS is discussed.

研究了无缝GIS多格式、多比例尺空间数据入库的模式，创新性地提出了用数据中间件模式解决GIS多源空间数据无缝集成的新方法，研究了多比例尺数据入库的方法和三级索引机制，并对无缝GIS数据的多尺度表示提出了自己的看法；阐述了无缝GIS以地球椭球面为空间信息定位的参考面、以地理坐标进行空间数据存储的观点，并给出了在椭球坐标系下的距离、方位角和面积度量模型。

A multi-layer viscoelastic model is developed, and the boundary-value problem under linear conditions about the multi-layer model is solved. Calculated values of wavelength and damping rate of wave height are compared with measured data. It is showed that the transformation of regular waves over muddy bottoms can be successfully predicted by this model.

建立了多层粘弹性体模型，求解了多层模型在线性化边界条件下的定解问题，得到了规则波在泥床上传播时波要素变化的理论值，并同大量实验数据进行了比较，结果表明，多层模型能够成功地预报规则波在泥床上的传播规律。

On the basis of regular wave transformation equation in a reference[1] incorporating comprehensively environmental current,nonlinear dispersion effect,rapidly varying topography effect,energy loss due to bottom friction,refraction and diffraction, the governing equations are derived for irregular multi-directional wave transformation incorporating multi factors according to the principle of superposition of linear wave and the wave directional spectrum theory.

1引言波浪在由外海向近岸的传播过程中，由于受到复杂地形、障碍物和水流等因素的影响，波浪传播将发生变形。文献[2]对描述波浪在近岸传播变形的各种数学模型方法做了较为全面的、系统的回顾和总结。

High precision format, unstructured dynamic mesh with a large displacement and multi-species gas flows were computationally expensive, the problem of resourceless and inefficient of single computer appeared. Parallel arithmetic based on PC-Cluster system for the oblique detonation wave flow and the muzzle flow include high speed projectile were discussed. The results proved that the rationality of parallel arithmetic provided a new method to simulate the complex chemical reaction flows. The present code represents a validated, efficient and versatile tool developed for the simulation of hypersonic multi-species chemical non-equilibrium flows.

高精度计算格式、化学反应源项的刚性和大位移的运动边界处理都给计算和存储带来了沉重的负担，单机资源不足和计算时间长的问题凸现，利用PC机和局域网资源建立分布存储式并行计算系统，并基于非结构动网格和分区算法开发了复杂化学反应流场数值模拟的并行计算程序，对高速飞行实验弹丸诱导的斜爆轰波流场和含有大位移动边界的膛口燃气射流场进行了并行模拟，有效地缩短了计算时间，扩展了计算规模，为复杂化学反应流数值模拟研究提供了新的手段。

The transepicondylar axis of different position has no effect on volume rendering technique measuring the humeral head retroversion angle with multi slice spiral CT.The top view at which lateral epicondyle of the humerus showing minitriangulum and the anterior surface of the distal humerus articulation with the forearm being shaded is more simple,faster and precise for the volume rendering technique measuring the humeral head retroversion angle with multi slice spiral CT.

结论］肱骨头扭转角变异较大，肩关节假体扭转角设计应个性化；肱骨远端不同位置内外上髁轴线对多层螺旋CT容积再现测量肱骨头扭转角没有影响；俯视位观察肱骨，当外上髁露出呈小三角形、肱骨远端前关节面被肱骨头遮盖重叠的位置是多层螺旋CT三维重建测量肱骨头扭转角的更简单、更快捷而且准确的测量位置。

Ti/TiN/N/ZrN multi-layer film is deposited on head of rotated riveter by using multi-arc ion plating method.

采用多弧离子镀法在旋铆头沉积Ti/TiN/N/ZrN多层膜处理，并对旋铆头的失效形式、膜层的组织形貌、显微硬度、耐磨性能进行了分析和讨论。

They weren't aggressive, but I yelled and threw a rock in their direction to get them off the trail and away from me, just in case.

他们没有侵略性，但我大喊，并在他们的方向扔石头让他们过的线索，远离我，以防万一。

In slot 2 in your bag put wrapping paper, quantity does not matter in this case.

在你的书包里槽2把包装纸、数量无关紧要。