密度函数

Probability density function, cumulative distribution function, survival function, hazard function, PP plot, and others.

概率密度函数，累积分布函数，生存函数，危险函数，聚丙烯阴谋，等等。

The identity and difference in the expressional patterns between distribution functions of discrete random variables and distribution functions of continuous random variables are elaborated,and the main expressional patterns of distribution functions of continuous random variables are summarized,and the derivability of distribution functions of continuous random variables is discussed.

0引言在概率论中，连续型随机变量分布函数的表达形式及其可导性是一难点。其一，离散型随机变量的分布函数有较明显的性质和统一的表达形式，而连续型随机变量，由于其概率密度函数一般为分段函数，根据其分段区间的差异，表达形式差异较大，不容易总结其规律，本文主要比较连续型随机

Properties are discussed for a class of exponential sum function on recurrence relationship,integral formula,it has been proved that its curve configuration is single peak and it is a probability density,the application of this function is showed in proving equalities and a differential equation model of substance transform reaction.

对一类指数和函数的递推关系、积分公式、曲线的单峰形态等性质进行了讨论，证明了该函数为概率密度函数，并给出了该函数在等式证明、物质转化反应的微分方程模型等方面的应用。

In the proposed frame of theory, probability density function or distribution function are also involved, but their standing are secondary. Probability density function is treated only as a probabilistic features of the failure rate function.

在本文倡导的理论体系中，也要涉及概率密度函数或分布函数，但他们仅被视为失效率函数的概率特征，讨论的路线是失效率函数的模式如何决定寿命分布的概率性质。

In study of the truss structural dynamic characteristics analysis, randomness of the structural physical parameters and geomtric ones are all considered. The finite element model of the stochastic truss is built and the random functions of its natural frequencies are obtained by use of the Rayleigh quotient. Employing probabilistic distribution function expression for the random functions, through a series of mathematical processing including determination of limits of integrals, variable substitution etc., the probaabilistic density function for the truss natural frequencies are gained to realige accurate calculation for the reliability of the truss natural frequencies.

考虑结构物理参数和几何参数的随机性，通过构建随机参数桁架结构的有限元模型，利用瑞利商公式获得了结构固有频率随机函数的计算表达式，应用随机函数的概率分布函数表达式，通过确定积分区间、变量替换、积分顺序变换等一系列数学上的处理，获得结构固有频率的概率密度函数，进而实现对结构固有频率可靠度的精确计算。

The tensor quality of energy density function, which contains coordinate vector, is mathematically proofed.

考虑到模型中能量密度函数含有坐标轴方向向量一项，该文对能量密度函数的张量性进行了严格的数学证明，并将VMIB模型初步应用到脆性材料的单轴受压破坏。

This thesis investigates the profile extraction and shape optimization on the result of topology optimization of planar compliant mechanisms. The main context includes the following work:(1) summarizing and analyzing the recent research status, some harvest and unsolved problems;(2) analyzing the conceptual design of planar path-generating compliant mechanisms and its mathematical model and tools;(3) Modifying the method of density contour as the method of profile extraction, and developing a method to optimize the density function in the profile extraction according to the requirement of the design of compliant mechanism;(4) developing a method to abstract the compliant mechanism into a form of links and joints by using the principle of connectivity on topology;(5) developing a method of shape optimization of planar path-generating compliant mechanisms, by representing the profile of the abstracted compliant mechanism as simple curves such as straight lines and arcs, establishing the models of the size optimization of the parameters of these curves, so that the compliant mechanism has a machinable shape;(6) At last, proving the feasibleness and effectiveness of the design method by making simulation design and validating it in FEA software.

主要工作包括：(1)分析了柔顺机构拓扑优化和形状优化的研究现状，分析了目前柔顺机构的研究重点、主要成果和尚未解决的问题；(2)分析了基于SIMP的柔顺机构概念设计方法及其相关工具和模型；(3)针对柔顺机构轮廓提取的特殊要求，提出了密度等值线法的改进方案，对密度函数插值点密度值进行优化，提出优化模型和选择优化算法；(4)根据轨迹输出平面全柔顺机构自身的形状特点，提出了轨迹输出平面全柔顺机构的抽象方法，即应用拓扑学上的连通性原理将柔顺机构抽象成杆件和结点形式，并对相应的数学原理进行了证明；(5)提出了平面全柔顺机构的形状还原和尺寸优化方法，对抽象的柔顺机构进行还原，将其轮廓还原成简单曲线的连接，从而建立尺寸优化模型，对机构进行尺寸优化设计，在得到可加工的机构轮廓的同时又能对关键部位进行特别处理；(6)进行了柔顺机构的数值仿真设计，并将所得设计结果导入商用有限元软件中进行仿真实验，证明了设计方法的可行性和有效性。

The method based on the geometric moment invariants is the typical method in these applications.

其实质是对原有几何矩定义中的密度函数经过变换得到新的密度函数。

When gas superficial velocity was about equal to liquid superficial velocity,the probability density function of liquid holdup had a twin-peaked,when liquid superficial velocity was constant,one of the peaks would fade out and disa...

在段塞流动中，当气相折算速度和液相折算速度相差不大时，持液率概率密度函数呈双峰分布；当液相折算速度不变时，随着气相折算速度的增大，持液率概率密度函数第2峰值逐渐减小，直至消失而变为单峰分布；利用这一特征可初步确定段塞流动中气、液相流量相对大小。

When gas superficial velocity was about equal to liquid superficial velocity, the probability density function of liquid holdup had a twin-peaked, when liquid superficial velocity was constant, one of the peaks would fade out and disappear with the in crease of gas superficial velocity. Through using the characteristics, the relative size of gas and liquid superficial velocity can be set initially.

在段塞流动中，当气相折算速度和液相折算速度相差不大时，持液率概率密度函数呈双峰分布；当液相折算速度不变时，随着气相折算速度的增大，持液率概率密度函数第2峰值逐渐减小，直至消失而变为单峰分布；利用这一特征可初步确定段塞流动中气、液相流量相对大小。

I think he's learned how to approach hitters....

Johhny Damon说，『他已是最好的了，再没有人能够比他做的更好，我想他的球技已经完全成熟了，而且他也已经学会了如何去对付和压迫各种打击者。。。。。。

In effect, an 18 foot King Cobra could actually look down onto the average human being.

际上，一个18尺眼镜蛇王其实可以俯视到的平均人。