阶矩

Random parameters ; multi degree of freedom nonlinear vibration systems ; reliability ; statistical fourth moment method ; Edgeworth series

随机参数；多自由度非线性振动系统；可靠度；四阶矩技术； Edgeworth级数

Based on the equivalent transformation from fuzzy possibility distribution to random probability density distribution, the fuzzy random failure probability calculation can be formulated easily, and a First Order and Second Moment method for fuzzy - random analysis is established.

提出了模糊随机可靠性分析的近似解析和数字模拟综合方法，基于模糊变量的等价随机化变换，可以方便地得到模糊随机失效概率的计算公式，并建立了模糊随机可靠性分析的一次二阶矩法。

A linear feasible direction algorithm is proposed to calculate reliability index of structure.

为克服当极限状态曲面方程非线性程度较高时应用一次二阶矩法求解可靠指标可能不收敛的问题，提出一种求解结构可靠指标的线性可行方向算法。

Based on the improved first order second moment theory and aimed at the problems of mechanical reliability analysis and mechanical reliability design of single designing variable, this paper put forward a kind of explicit iteration algorithm for computing the structural reliability and determining the designing parameters of structural reliability.

引言改进的一次二阶矩理论是结构可靠性分析和设计的一种实用方法[1]，具有建立结构可靠性分析和设计计算模型简单等优点，在这种方法中，Hasofer和Lind推荐的可靠度指标是定量评估机械可靠性的一种基本参数。

In order to compute the failure probability of structural systems for stability of gravity retaining walls, firstly, two performance functions against overturning and sliding of gravity retaining walls were established. Then, the first order second moment theory in structural reliability analysis, i.e., the checking point method was introduced to compute the two failure modes respectively, and two corresponding reliability indexes could be obtained.

为了计算重力式挡土墙稳定性的结构体系失效概率，首先分别建立重力式挡土墙结构抗倾覆稳定性和抗滑移稳定性的功能函数，然后引入结构可靠度分析一次二阶矩法中的验算点法分别对两种失效模式进行计算，得出两个相应的可靠度指标。

The diffraction distributions of Gaussian beam limited by the circular apertures with different sizes in scanning objectives focal plane were studied, and then the effective spot radius in focal plane was calculated using second moment and compared with the ideal one. The influence of apertures with different sizes on resolution was analyzed.

在不同孔径圆孔的限制下，对扫描物镜焦面上的衍射光场分布进行数值计算，并利用二阶矩统计的方法对焦面上的等效光斑半径进行数值计算，将其与不受限时的理想情况进行对比，分析孔径尺度对激光束扫描系统分辨率的影响。

Based on the second-order moment of the power density, the far-field divergence angle of nonparaxial rotationally symmetric Laguerre-Gaussian beams is derived and expressed in a sum of the series of the Gamma function.

基于功率密度的二阶矩方法，推导出了非傍轴旋转对称拉盖尔－高斯光束远场发散角的解析公式，并表示为伽玛函数的幂级数求和形式。

It usually takes a long time to fill the impedance matrix when using higher-order MoM. To solve this problem, the properties of the impedance matrix elements and the involved integral are investigated. Then it is proposed to take advantage of the symmetry of impedance matrix and the integral table to expedite the impedance matrix filling.

针对高阶矩量法阻抗矩阵填充时间很长的问题，从阻抗矩阵元素本身的性质和积分计算过程入手，提出了应用阻抗矩阵对称性和积分表方法两种加快阻抗矩阵填充的手段。

The objective of this study is to investigate systematic risk in asset pricing with higher moments, especially for skewness and kurtosis.

本研究的目的，在于探讨偏态与峰态等高阶矩系统风险对资产定价的影响。

A portfolio selection model with transaction costs under the constraint of higher moments such as skewness and kurtosis was discussed.

讨论了有交易费用的、包括偏度和峰度在内的高阶矩约束的多目标最优投资组合选择模型。

According to the clear water experiment, aeration performance of the new equipment is good with high total oxygen transfer coefficient and oxygen utilization ratio.

曝气设备的动力效率在叶轮转速为120rpm～150rpm时取得最大值，此时氧利用率和充氧能力也具有较高值。

The environmental stability of that world - including its crushing pressures and icy darkness - means that some of its most famous inhabitants have survived for eons as evolutionary throwbacks, their bodies undergoing little change.

稳定的海底环境─包括能把人压扁的压力和冰冷的黑暗─意谓海底某些最知名的栖居生物已以演化返祖的样态活了万世，形体几无变化。