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1·In the new algorithm, a bank of Gauss-Hermite filter (GHF) is used for generating the importance density function.

在滤波算法中，我们用一簇高斯厄米特滤波器(GHF)来产生重要性概率密度函数。

2·Adopting the Hermite polynomial instead of the Taylor polynomial can greatly decrease the order of high-order cross sensitivity.

采用埃尔米特插值多项式代替泰勒展开式逼近目标函数，极大地降低了高阶交叉灵敏度的阶数。

3·The transformation of Hermite Gaussian laser beam through random phase plate is discussed in detail by partial coherence theory in this paper.

本文利用部分相干理论研究了高阶厄米-高斯光束通过随机位相片的变换。

4·In this paper, we discuss properties of positive definite complex matrix, and the relation between it and the Hermite positive definite matrix.

本文给出了全正定矩阵的概念，讨论了全对称实矩阵是全正定矩阵的几个充分必要条件。

5·The axial intensity distribution of Hermite-cosh-Gaussian (HChG) beams passing through a system with the aperture and lens separated is studied numerically.

对双曲余弦高斯光束通过光阑透镜分离系统的轴上光强分布做了详细的数值分析。

6·The twisted Laguerre-Gaussian beam was generated by transforming of Hermite-Gaussian beams through an optical system consisting of three rotated cylindrical lenses.

研究了采用扭转三柱面镜光学系统将厄米-高斯光束变换成为具有轨道角动量的拉盖尔-高斯扭转对称光束。

7·When the initial power is equal to the critical power and light beam is incident at the beam waist, the elliptical Hermite-Gaussian spatial optical soliton is obtained.

当初始功率等于这一临界功率，光束从光腰处入射时，可得到椭圆厄米高斯空间光孤子。

8·In order to decrease the influence of non-observability of distance, based on Gauss-Hermite filter, multihypothesis of distance is adopted to operate collateral filter.

该算法为了减小距离的不可观测性对于非线性滤波的影响，在假设的多段距离间隔中采用并行的高斯-厄密特滤波并加权获得目标的状态估计。

9·Based on this, the evolution equations, evolution laws of elliptical Hermite-Gaussian light beam's every variable and two critical powers are also derived using variational method.

在此基础上，运用变分法得到了椭圆厄米高斯光束各参量的演化方程、演化规律和两个临界功率。

10·All ordinary polynomials have series expansion of orthogonal polynomials, while Legendre polynomials, Hermite polynomials and Laguerre polynomials are special orthogonal polynomials.

一般多项式都可以展开为正交多项式的级数形式，而勒让德多项式、厄米特多项式和拉盖尔多项式都是典型的正交多项式。