查询词典 probability distribution function

During a measurement, the probability that a system collapses from a given initial state to a particular eigenstate is given by the square of the absolute value of the probability amplitudes between the initial and final states.

在测量期间，从一给出起始态到特定特征值的一系统坍塌的概率被初值与终值间的概率振幅的绝对值平方来赋值。

And then Laplace published in 1812,"probability theory", first made clear to the classical definition of probability.

而接着拉普拉斯在1812年出版的《概率的分析理论》中，第一明确地对概率作了古典的定义。

Consider the dependencies between the coefficients and their parents, a non-Gaussian bivariate distribution is given, and corresponding nonlinear threshold function is derived from the model using Bayesian estimation theory. According to non-subsampled Contourlet transform and bivariate threshold function, a novel Non-Subsampled Contourlet Transform based on Bivariate threshold function for image denoising is proposed. This scheme achieves enhanced estimation results for images that are corrupted with additive Gaussian noise over a wide range of noise variance.

该文依据非下采样Contourlet分解系数与其父系数之间的相关性，给出非高斯双变量分布，对该模型应用Bayes估值理论推导得到相应的非线性双变量阈值函数，综合非下采样Contourlet分解和双变量阈值函数，提出一种基于双变量阈值的非下采样Contourlet变换图像去噪方法。

Firstly, the equation for stress intensity factors under static uniform pressure is used as the reference case, and then the weight function for a thick-walled cylinder containing a radial edge crack can be worked out. Secondly, the dynamic stresses in uncracked thick-walled cylinders are solved under internal impulsive pressure by using mode shape function method. The solution consists of a quasi-static solution satisfying inhomogeneous boundary conditions and a dynamic solution satisfying homogeneous boundary conditions, and the history and distribution of dynamic stresses in thick-walled cylinders are derived in terms of Fourier–Bessel series. Finally, the dynamic stress intensity factor equations for thick-walled cylinder containing a radial edge crack subjected to internal impulsive pressure are given by dynamic weight function method.

首先采用静态内压下的应力强度因子作为参考解，得到了带径向边裂纹厚壁圆筒的权函数；然后用振型函数方法推导无裂纹厚壁圆筒在冲击内压下的动应力响应，分析中将相应的弹性动力学方程解分为满足非齐次边界条件的准静态解和满足齐次边界条件的动态解的叠加，利用傅立叶-贝塞尔级数展开，推导出了厚壁圆筒内动应力的响应历程和分布规律；最后由动应力权函数方法导出带径向边裂纹厚壁筒在冲击内压下的动态应力强度因子计算公式。

As the connection of marginal distribution function, the Copula function may not only reflect the relativity of random variable, but also may describe the random variable's related pattern well. Therefore we may use the different Copula function to describe the different related pattern.

作为连接随机变量边缘分布到联合分布的函数，Copula函数不仅可以反映出随机变量间的相关程度，而且可以较好地描述随机变量间的相关模式，因此可以用不同的Copula函数来表示不同的相关模式。

Reduced SQP based on orthonormal bases, orthogonal bases and coordinate bases are studied and compared. With the correction item introduced, the null-space move is adjusted and the reduced SQP based on coordinate bases decomposition is improved.●The key problem of steady-state data processing for RTOPT is studied. A new algorithm of simultaneous strategies for data reconciliation and gross error detection is proposed. Here the objective function that is constructed using maximum likelihood principle and joint distribution function is minimized. Efficient algorithm is developed which exploited the nonlinear lease-square structure of this objective function.

仿真结果表明了算法的有效性；●深入研究了在线优化中的一个关键问题——稳态数据处理问题，用基于组合概率分布的目标函数联立求解粗劣误差检测和数据调和问题；以精馏塔在线优化的数据处理和模型修正为例，提出一种根据模型方程对参数的依赖性进行过程模型分解的分层策略，可以将数据调和和参数估计统一在数据处理的大框架中，为进一步的过程性能分析、操作状况评价以及在线优化提供可靠的基准，具有非常重要的工程应用价值；●将优化命题的形式扩展到更通用的形式。

In Chapter 2,I consider a queuing system in which there are two exponential servers, each having his own queue, and arriving customers will join the two queues separately, and analyze the two-dimensional Markov process representing the numbers of jobs in the two stations. A functional equation for the generating function of the stationary distribution of this two-dimensional process is derived and solved through the theory of Riemann-Hilbert boundary value problems. In Chapter 3, I consider the system with two parallel queues, in which arrivals join the shorter queue.I describe the problem of coupling and show that the generating function Fcan be continued as a meromorphic function to the whole complex plane.

全文包括三大部分：第一章介绍了基本的背景、研究进展和文章主要采用的方法；第二章研究的是有两个服务员共享的简单的排队方式的模型，即每个服务员有各自的队列，两队队长互不相关，分析了代表两个队长的二维马尔柯夫过程，推导出了二维过程的平稳分布的母函数的方程，并运用Riemann—Hilbert边值问题理论解出了母函数的表达式；第三章研究的是JSQ-PS模型(the joining the shortest queue model with processor sharing)，模型是组合了加入最短队模型和处理器共享模型而成的有用排队模型。

Therefore, to subsample"s observation of continuous random sample parent population, if we can"t get its material function easily, or we dont know its density function, we can use this way to approximate its distribution function. And these methods can achieve good approximation effect.

对连续型随机样本母体中的简单随机子样的观察值，在不易得到其具体分布或不知道其密度函数的情况下，可用此方法来近似求出其分布函数并可达到很好的逼近效果。

This paper first discusses the nature of the kernel function,and then based on Riemannian geometry dependent on the data structure and method,an improved modifying kernel function is proposed,the kernel function is a simple and less calculation method,which conformal factor and support vector irrelevant,compared with previous studies overcomes the impact of support vector's number and distribution.

首先讨论核函数的本质，并且基于黎曼几何结构和数据依赖的方法，提出了一种改进的修正核函数，改进后的核函数形式简单，计算量较低，其中保形因子与支持向量无关，较之于以前的研究克服了支持向量的数目和分布的影响。

During the first part, investigate the numbers and location of the different nature reserve, and review about its development, discuss the cause about the rapid developmeng about the protection areas of nature around Beijing. During the second part, this paper use the Geographical Information System to analyze the different sight function, plot our distinct function about the protection area of nature around Beijing. In the third part of this paper, the ecology function was special analyzed. This paper picked up several factor about the ecology and establish mathematics model to detect the most rational ecology distribution, bring forward the new constructive, wilder constructive and combination project. In the last parts of the paper, this paper use the Geographical Information System to analyze the different brim about the protection area of nature around Beijing, calculating the p/a and figure coefficient, and bring forward the brim theory for the nature reserve and city system.

在数量布局方面，包括北京周边各个不同级别的保护区的数目、位置分配布局和发展趋势研究，探讨北京市周边自然保护区数目和面积在99年和2000年突然增长的主要原因，以及今后北京自然保护区的发展方向；在景观布局方面，主要根据不同自然保护区的空间和功能的不同，计算延庆县各个自然保护区的景观多样性指数和景观优势度指数，并结合地理信息系统和航片，划分出不同的景观功能区间，以及各个功能区间之间的相互关系；在生态布局方面，综合考察北京周边自然状况，提取多项因子，建立评价模型，计算出各项因子权重，从而对其自然保护区的生态功能布局的合理性进行评价和趋势分析，为本文提出北京市周边自然保护区新建、扩建与合并的方案提供依据；在边缘布局方面，利用边缘效应理论和研究方法，创新提出&边缘类型样块分析法&，提取多个样方并结合地理信息系统，计算p/a比和自然保护区边缘的形状系数，划出自然保护区边缘效应趋势变化图，考察北京周边自然保护区的边缘效应，以及对城市的生态边缘功能。

Chimborazo and Cotopaxi, took me by the hand.

越过琴博腊索山和科托帕克西山。

This car is in a good condition.

这辆车的状况很好。