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Chapter 2、When treat propagate problem of high power laser beams, ordinary assume beam to be ideal plane wave or Gaussian. Actually, beams is not ideal Gaussian or plane wave. The reason is that is phase aberraed and intensity nonuniform. In this chapter, we have developed a method on frequency conversion of aberrated beam. Based on statistical optics method and within the limits of thin crystal, we have studies on second harmonic generation of the phase aberrted beam. And the phase aberration is assumed to be a Gaussian random variable.

第二部分：在处理高功率光束传输问题中，通常假设光束为理想平面波或高斯型，而实际光束都不可能是理想的高斯光束或平面波，均会有一定的位相畸变及光强不均匀，本部分从统计光学的观点出发，在薄晶体近似下，建立了具有高斯型随机相位畸变光束倍频转换的一种统计描述方法，并对倍频转换光束的横向空间特性进行了分析。

Provided that the initial prior intensity of the states is Gaussian or can be identified as a Gaus- sian sum, the analytical results of the algorithm show that the posterior intensity at any subsequent time step remains a Gaussian sum under the assumption that the state noise, the measurement noise, target spawn intensity, new target birth intensity, target survival prob- ability, and detection probability are all Gaussian sums.

分析的结果表明，当初始的先验强度满足高斯或者可以表示成高斯和的形式时，通过将状态噪声、观测噪声、目标的繁衍、新目标的产生、目标的存活概率和检测概率表示成高斯和的形式，之后每个时刻的后验强度均能表示成高斯和形式。

Using the relations between Hermite and Laguerre-Gaussian modes and expanding the window function of two-dimensional rectangular hard-edged apertures into a finite sum of complex Gaussian functions, the propagation of complex- argument Laguerre-Gaussian beams through a paraxial optical ABCD system with a rectangular hard-edged aperture is studied. An analytical propagation equation is derived and used to study the diffraction at the rectangular hard-edged aperture and the focusing properties of complex-argument LG beams.

利用拉盖尔－高斯模和厄米－高斯模的变换公式，并使用将二维矩孔光阑窗口函数展开为有限个复高斯函数之和的方法，得到了复宗量拉盖尔－高斯光束通过含矩形硬边光阑近轴ABCD光学系统的变换的解析传输公式，并对复宗量LG光束通过矩形硬边光阑的衍射和聚焦特性进行了研究。

A generalized Gaussian Laplacian eigenmap algorithm based on geodesic distance is proposed,which incorporates geodesic distance and generalized Gaussian function into the original Laplacian eigenmap algorithm.GGLE algorithm can adjust the similarities between nodes of neighborhood graph,and can preserve the different degrees of local properties by using super-Gaussian function,Gaussian function or sub-Gaussian function.Moreover,GGLE can avoid the deficiency of Euclidean distance by using geodesic distance when neighborhoods of data points are enlarged for preserving more neighborhood relations.Experimental results show that the global low-dimensional coordinates obtained by GGLE have different clustering properties and different degrees of preserving local neighborhood structures when different generalized Gaussian functions are used to measuring the similarities between high-dimensional data points.(3) An ensemble-based discriminant algorithm based on GGLE is proposed.

该算法将测地线距离和广义高斯函数融合到传统的拉普拉斯特征映射算法中，可以调整近邻图结点间的相似度，通过选择超高斯、高斯或者次高斯函数来实现不同程度的近邻局部特性的保持；而且当需要保持更多的近邻关系使得数据点邻域增大时，采用测地线距离可以避免欧氏距离度量不合理的缺陷；实验结果表明在用不同的广义高斯函数度量高维数据点间的相似度时，局部近邻结构保持的程度是不同的，GGLE获得的全局低维坐标也呈现出不同的聚类特性。

①postoperative pain after hemorrhoidectomy can be safely and effectively controlled by Acuepoint inject of lappaconitine hydrobromide ②Using the Ashi-points-injection of lappaconitine hydrobromide after hemorrhoidectomy can reduce the pain for a longtime ③Combined with Yaoshu-point-injection can enhance the anaesthetic effect at the day of surgery④The edema at anal margin can be reduced by using of Ashi-points-injection of lappaconitine hydrobromide

①穴位注射氢溴酸高乌甲素对痔术后镇痛是安全而有效的；②术毕时使用氢溴酸高乌甲素阿是穴注射具有术后长效镇痛作用；③联合使用氢溴酸高乌甲素腰俞穴注射可增强手术当天的镇痛效果；④氢溴酸高乌甲素穴位注射具有防止痔术后肛缘水肿的作用。

Men's 110-meter hurdles for the column 106 centimeters high, 400-meter high hurdles for the column 91.4 centimeters; women's 100-meter hurdles for the column 84 centimeters high, 400-meter hurdles for the column 76.2 centimeters high.

男子110米跨栏跑的栏高为106厘米，400米跨栏跑的栏高为91.4厘米；女子100米跨栏跑的栏高为84厘米，400米跨栏跑的栏高为76.2厘米。

Soft saturated soil has a practical characteristics of high-compression, high sensitivity, high flow variability and low-intensity, low-permeability coefficient.

中文摘要：饱和软土具有高压缩性、高灵敏度、高流变性和低强度、低渗透系数的工程特性，因此在软基上施工面临着孔压高、变形大、承载力低的难题。

On the service concept, we are pure, are really products concept, it is necessary and pure, is really a combination of the service concept and wholeheartedly for owners of service, so service is live products, is a high-concept, high-quality services, high-concept, an extension of high-quality products.

的服务理念，我们是纯粹的，真正的产品概念，它是必要的，纯粹的，确实是一个结合的服务理念和全心全意为业主服务，因此服务是生活的产品，是高概念，高品质的服务，高的概念，延长高品质的产品。

Compared with D buffalo, the withers height, hip croop height, hucklebone width of ND buffalo respectively increase 5.5%, 7.4%, 9%, the withers height, hip croop height, hucklebone width of MD buffalo respectively increase

结果显示，杂交水牛尼本的鬐甲高、十字部高、坐骨节宽比德宏水牛分别提高5.5%、7.4%、9%，差异显著。杂交水牛摩本的鬐甲高、十字部高、坐骨节宽比德宏水牛提高5.9%、8.0%、11.9%，差异显著。

The drawing testing、cutting testing and fracture analysis of high chromium casting iron－carbon steel's compounding interface showed: the compounding interface has higher strength and the impact toughness of composite plate is about 5 times of high chromium casting iron, which make it possible to make full use of high chromium casting iron's excellent wear resistance in practice under the high impactive condition.

需要特别指出的是：复合板的冲击韧性高铬铸铁5倍以上，这为高铬铸铁在高冲击工况发挥其优异耐磨性能提供了可能。采用试验方法生产的双金属复合板件正在矿山冲击较大的工况下使用，实际使用时间已经超过以前使用的高锰钢的使用寿命，目前仍在继续使用中。

On the other hand, the more important thing is because the urban housing is a kind of heterogeneity products.

另一方面，更重要的是由于城市住房是一种异质性产品。

Climate histogram is the fall that collects place measure calm value, cent serves as cross axle for a few equal interval, the area that the frequency that the value appears according to place is accumulated and becomes will be determined inside each interval, discharge the graph that rise with post, also be called histogram.

气候直方图是将所收集的降水量测定值，分为几个相等的区间作为横轴，并将各区间内所测定值依所出现的次数累积而成的面积，用柱子排起来的图形，也叫做柱状图。